Time series forecasting plays a critical role in various fields such as finance, economics, weather forecasting, and more. One powerful tool in the time series forecasting toolbox is SARIMAX, which stands for Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors. In this article, we will guide you through the process of applying SARIMAX to forecast time series data.
Before diving into modeling, it's crucial to familiarize yourself with the time series data you're working with. This involves understanding any existing patterns, trends, and potential seasonality in the data.
Ensure you have the required Python libraries installed. These typically include pandas for data manipulation, statsmodels for time series analysis, and matplotlib for plotting.
# Import necessary libraries for data manipulation and analysis
import numpy as np # Numerical operations
import pandas as pd # Data manipulation
from datetime import datetime, timedelta # Date operations
# Import libraries for plotting and visualization
import matplotlib.pyplot as plt # Matplotlib for basic plotting
import seaborn as sns # Seaborn for enhanced visualization
import plotly.express as px # Plotly for interactive plots
# Import libraries for time series analysis and modeling
import yfinance as yf # Yahoo Finance for retrieving financial data
from statsmodels.tsa.stattools import adfuller # Augmented Dickey-Fuller Test for stationarity check
from statsmodels.tsa.statespace.sarimax import SARIMAX # SARIMAX model for time series forecasting
from statsmodels.tsa.seasonal import seasonal_decompose # Seasonal decomposition for trend, seasonal, and residual componentsLoad the time series data into a suitable data structure, such as a pandas DataFrame or a numpy array. Check for missing values and outliers, and handle them appropriately, either by imputing missing values or removing outliers.
# Define the stock ticker symbol
ticker = 'AMD'
# Download the data
df = yf.download(ticker, start='2022-06-24', end='2023-06-24') # Download data from Yahoo Finance
# Print the first few rows of the data
print(df.head()) # Display the first few rows of the downloaded data[*********************100%%**********************] 1 of 1 completed
Open High Low Close Adj Close Volume
Date
2022-06-24 83.559998 87.529999 83.080002 87.080002 87.080002 88553900
2022-06-27 87.360001 88.220001 85.250000 86.160004 86.160004 74663500
2022-06-28 85.709999 86.730003 80.430000 80.779999 80.779999 95618600
2022-06-29 79.550003 79.750000 76.510002 77.989998 77.989998 104140900
2022-06-30 77.730003 78.910004 75.480003 76.470001 76.470001 105368600
Data Preprocessing and Column Selection
# Add a 'Date' column based on the index
df["Date"] = df.index
# Reset the index and drop the old index column
df.reset_index(drop=True, inplace=True)
# Keep only the 'Date' and 'Close' columns
df = df[['Date', 'Close']]Plotting the time series data provides a visual understanding of its characteristics. This can help in identifying trends, seasonality, and any unusual patterns.
# Create the line plot
fig1 = px.line(df, x='Date', y='Close')
# Set the title using the ticker value
fig1.update_layout(title=f"Stock Price for {ticker}")
# Display the plot
fig1.show()
Stationarity is a crucial concept in time series forecasting. It refers to a property of a time series where the statistical properties (such as mean, variance, and autocovariance) remain constant over time. In other words, a stationary time series does not exhibit trends or seasonality in its behavior. Here are several reasons why stationarity is important in time series forecasting:
- Statistical Validity:  - Many time series models, including ARIMA and SARIMAX, assume stationarity. If the data is not stationary, the results from these models may not be reliable or interpretable.
- Model Assumptions:  - Stationarity is a key assumption for various time series models. When the data is non-stationary, it may violate these assumptions and lead to inaccurate forecasts.
- Mean and Variance Stability:  - In a stationary time series, the mean and variance are constant over time. This makes it easier to understand and interpret the data, as there are no major shifts or fluctuations in these properties.
- Forecasting Accuracy:  - Stationary data often leads to more accurate and reliable forecasts. Models trained on stationary data can better capture the underlying patterns and relationships, leading to more accurate predictions.
- Removal of Trends and Seasonality:  - Non-stationary data often contains trends or seasonal patterns. By making the data stationary through techniques like differencing or detrending, we can isolate the underlying patterns from the trend or seasonality.
- Easier Interpretation:  - Stationary time series are easier to interpret and analyze. Patterns, relationships, and anomalies are more apparent when the data exhibits stationarity.
- Time-Invariance:  - Stationarity implies that the time series is time-invariant. This means that the behavior of the series is consistent regardless of when the observations were made.
- Model Stability:  - Stationary time series are typically more stable over time. This means that the behavior of the time series is less likely to change dramatically in the future.
- Mean Reversion:  - In finance and economics, stationarity is often associated with mean reversion, where a series tends to revert back to its mean over time. This can have important implications for investment strategies. In summary, ensuring stationarity in a time series is a critical step in preparing the data for accurate forecasting. It helps to meet the assumptions of many forecasting models, leads to more reliable predictions, and facilitates a better understanding of the underlying patterns in the data.
Decomposing time series data
Decomposing time series data into its constituent components (trend, seasonality, and residuals) is a crucial step in understanding and modeling time-dependent patterns. This decomposition helps identify underlying patterns and enables more accurate forecasting. Here's a detailed explanation of each component: Trend Component
The trend component represents the long-term progression or direction of the data. It captures the overall pattern that is not attributable to seasonal or cyclical fluctuations. Trends can be increasing (upward), decreasing (downward), or stable (horizontal).
Methods for Identifying Trends:
- Moving Averages: Calculating the average of a fixed-size window of data points to smooth out short-term fluctuations and highlight the overall trend.
- Exponential Smoothing: Assigning exponentially decreasing weights to past observations, giving more importance to recent data.
- Regression Analysis: Fitting a regression model to the time series data to estimate the trend component. Seasonality Component The seasonality component captures patterns that repeat at regular intervals, typically within a year. For example, retail sales often exhibit higher numbers during holiday seasons. Seasonality can be additive (constant amplitude) or multiplicative (varying amplitude). Methods for Identifying Seasonality:
- Seasonal Decomposition of Time Series (STL): This method decomposes time series data into trend, seasonal, and residual components using a seasonal-trend decomposition procedure based on loess.
- Periodogram Analysis: Examining the frequency domain of the data to identify dominant seasonal frequencies. Residual Component The residual component, also known as the error or noise, represents the random, unexplained variation in the data after accounting for the trend and seasonality. It contains any irregularities, noise, or unexpected events that cannot be attributed to the trend or seasonal patterns. Methods for Identifying Residuals:
- Residuals are typically obtained by subtracting the estimated trend and seasonality components from the original time series data. Decomposition Process The process of decomposing a time series involves separating the observed data (Xt) into its constituent components: The resulting trend, seasonality, and residuals are then used to model and forecast future values. Â Importance of Decomposition
- Improved Understanding: Decomposition provides insight into the underlying patterns and dynamics of the time series data.
- Enhanced Forecasting: Analyzing and modeling individual components allows for more accurate and interpretable forecasts.
- Anomaly Detection: Residuals can help identify unusual or unexpected events in the data. By decomposing time series data, analysts can gain a deeper understanding of the patterns within the data, allowing for more informed decision-making and better forecasting capabilities. This process is a fundamental step in time series analysis.
Additive and multiplicative seasonality are two different ways in which seasonal patterns can be expressed in a time series. Understanding the nature of seasonality (whether additive or multiplicative) is crucial for accurate modeling and forecasting.
Additive Seasonality
In an additive seasonal pattern, the seasonal component is added to the trend and error terms. Mathematically, it can be represented as: Characteristics:  - The seasonal fluctuations have a constant amplitude (the same amount of fluctuation occurs regardless of the level of the time series).  - The impact of seasonality is consistent over time.
 - For example, if you're looking at monthly ice cream sales, an additive seasonal pattern would imply a consistent increase in sales during summer months, regardless of the overall level of sales.
In a multiplicative seasonal pattern, the seasonal component is multiplied with the trend and error terms. Mathematically, it can be represented as:
- Characteristics:  - The seasonal fluctuations are proportional to the level of the time series. As the level of the time series increases, so does the seasonal effect.  - The impact of seasonality grows with the level of the time series.
 - Using the ice cream sales example, if there's multiplicative seasonality, it would mean that during high sales months, the increase in sales is proportionally larger compared to lower sales months.
Example
Determining Seasonality Type Deciding whether seasonality is additive or multiplicative depends on analyzing the data and visual inspection. It can also be determined through statistical methods and model diagnostics.
It's worth noting that incorrectly identifying the type of seasonality can lead to inaccurate forecasts. Therefore, a careful examination of the data and consideration of the underlying mechanisms driving the seasonality are crucial steps in the time series analysis process.
Understanding whether seasonality is additive or multiplicative helps in selecting appropriate models, as different models are better suited for handling different types of seasonality.
Transformation from Multiplicative to Additive
Multiplicative time series data can often be transformed into additive time series through methods like taking logarithms. This transformation can be advantageous in specific situations. When a seasonal time series exhibits multiplicative seasonality, it can be advantageous to convert it into an additive series by applying a logarithmic transformation. This transformation changes the multiplicative elements into additive components, resulting in stabilized variance. This logarithmic transformation is particularly valuable when the seasonal component's amplitude is proportionate to the level of the series, resulting in a varying seasonal amplitude. The transformation effectively stabilizes the fluctuation in seasonal amplitude, facilitating more straightforward forecasting.
The Augmented Dickey-Fuller (ADF) test is a statistical hypothesis test used to determine whether a unit root is present in a univariate time series dataset. In simpler terms, it helps us assess whether a time series is stationary or non-stationary.
Purpose of the ADF Test
The presence of a unit root in a time series indicates non-stationarity. Non-stationary data can exhibit trends, which can lead to inaccurate forecasts when using models that assume stationarity. The ADF test is employed to assess whether differencing the data (to achieve stationarity) is necessary before applying certain time series models.
How the ADF Test Works
- Null Hypothesis : The null hypothesis of the ADF test is that the time series has a unit root, indicating it is non-stationary.
- Alternative Hypothesis: The alternative hypothesis is that the time series is stationary (i.e., it does not have a unit root).
- Test Statistic: The ADF test statistic is computed. This statistic is used to compare against critical values to determine the likelihood of rejecting the null hypothesis.
- Critical Values: The ADF test provides critical values at various confidence levels. These critical values depend on the sample size and the chosen significance level.
- Decision: Based on the test statistic and critical values, you can decide whether to reject or fail to reject the null hypothesis.
Interpretation
Rejecting the Null Hypothesis: If the test statistic is less than the critical value, you reject the null hypothesis. This suggests that the time series is stationary, and differencing may not be necessary.
Failing to Reject the Null Hypothesis: If the test statistic is greater than the critical value, you fail to reject the null hypothesis. This implies that the time series may be non-stationary and differencing could be beneficial.
def perform_adf_test(data):
# Perform ADF test
result = adfuller(data)
# Print the results
print('ADF Statistic:', result[0])
print('p-value:', result[1])
print('Critical Values:', result[4])
# Check if the data is stationary based on the p-value
if result[1] <= 0.05:
print("The data is stationary")
else:
print("The data is not stationary, Data can be processed further")
# Example Usage
perform_adf_test(df['Close'])ADF Statistic: -2.013213174219679
p-value: 0.28080980278926104
Critical Values: {'1%': -3.4577787098622674, '5%': -2.873608704758507, '10%': -2.573201765981991}
The data is not stationary
If the data is not stationary, apply differencing to make it stationary. This process involves subtracting the previous value from the current value.
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
def plot_differencing_acf_pacf(data):
fig, axes = plt.subplots(3, 2, sharex=True)
# Original Series
axes[0, 0].plot(data)
axes[0, 0].set_title('Original Series')
plot_acf(data, ax=axes[0, 1])
# 1st Differencing
diff_1 = data.diff().dropna()
axes[1, 0].plot(diff_1)
axes[1, 0].set_title('1st Order Differencing')
plot_acf(diff_1, ax=axes[1, 1])
# 2nd Differencing
diff_2 = data.diff().diff().dropna()
axes[2, 0].plot(diff_2)
axes[2, 0].set_title('2nd Order Differencing')
plot_acf(diff_2, ax=axes[2, 1])
plt.tight_layout()
plt.show()
# Example Usage
plot_differencing_acf_pacf(df['Close'])
Utilize autocorrelation and partial autocorrelation plots to identify the order of autoregressive (AR) and moving average (MA) components, as well as the seasonal order.
# Import necessary libraries
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf # For autocorrelation and partial autocorrelation plots
from statsmodels.tsa.stattools import acf, pacf # For computing autocorrelation and partial autocorrelation
# Visualize autocorrelation using pandas
pd.plotting.autocorrelation_plot(df['Close']) # Plot autocorrelation using pandas
# Visualize autocorrelation using plot_acf
plot_acf(df['Close'], alpha=0.05) # Plot autocorrelation using plot_acf with confidence interval
# Compute autocorrelation function (ACF) values
x_acf = pd.DataFrame(acf(df['Close'])) # Calculate autocorrelation function (ACF) values
# Print ACF values
print(x_acf) # Print the ACF values
# Generate a partial autocorrelation plot
plot_pacf(df['Close'], lags=20, alpha=0.05) 0
0 1.000000
1 0.980285
2 0.957557
3 0.935598
4 0.914009
5 0.893179
6 0.868831
7 0.839151
8 0.808492
9 0.774980
10 0.740682
11 0.707750
12 0.676324
13 0.641283
14 0.607955
15 0.574249
16 0.539390
17 0.506053
18 0.474119
19 0.440244
20 0.409584
21 0.383322
22 0.358802
23 0.337378
Based on the insights from step 7, select the appropriate orders for the AR, I (differencing), MA, seasonal AR, seasonal I, and seasonal MA components. for example our values are q = 2 d = 2 p = 1
q = 2
d = 2
p = 1pip install pmdarimafrom pmdarima.arima import auto_arimamodel_sarimax =auto_arima(df['Close'],start_p=0,d=1,start_q=0,
max_p=1,max_d=2,max_q=2, start_P=0,
D=1, start_Q=2, max_P=2,max_D=1,
max_Q=5, m=12, seasonal=True,
error_action='warn',trace=True,
supress_warnings=True,stepwise=True,
random_state=20,n_fits=50)Performing stepwise search to minimize aic
ARIMA(0,1,0)(0,1,2)[12] : AIC=inf, Time=0.89 sec
ARIMA(0,1,0)(0,1,0)[12] : AIC=1328.314, Time=0.04 sec
ARIMA(1,1,0)(1,1,0)[12] : AIC=1280.778, Time=0.18 sec
ARIMA(0,1,1)(0,1,1)[12] : AIC=inf, Time=0.45 sec
ARIMA(1,1,0)(0,1,0)[12] : AIC=1327.712, Time=0.05 sec
ARIMA(1,1,0)(2,1,0)[12] : AIC=1240.871, Time=0.58 sec
ARIMA(1,1,0)(2,1,1)[12] : AIC=1215.670, Time=2.83 sec
ARIMA(1,1,0)(1,1,1)[12] : AIC=inf, Time=0.55 sec
ARIMA(1,1,0)(2,1,2)[12] : AIC=1214.822, Time=2.38 sec
ARIMA(1,1,0)(1,1,2)[12] : AIC=inf, Time=2.44 sec
ARIMA(1,1,0)(2,1,3)[12] : AIC=inf, Time=12.11 sec
ARIMA(1,1,0)(1,1,3)[12] : AIC=1214.779, Time=3.38 sec
ARIMA(1,1,0)(0,1,3)[12] : AIC=1214.716, Time=2.04 sec
ARIMA(1,1,0)(0,1,2)[12] : AIC=inf, Time=2.02 sec
ARIMA(1,1,0)(0,1,4)[12] : AIC=1216.231, Time=4.88 sec
ARIMA(1,1,0)(1,1,4)[12] : AIC=1216.752, Time=14.12 sec
ARIMA(0,1,0)(0,1,3)[12] : AIC=1214.650, Time=1.57 sec
ARIMA(0,1,0)(1,1,3)[12] : AIC=1215.229, Time=2.66 sec
ARIMA(0,1,0)(0,1,4)[12] : AIC=1216.323, Time=4.97 sec
ARIMA(0,1,0)(1,1,2)[12] : AIC=inf, Time=1.82 sec
ARIMA(0,1,0)(1,1,4)[12] : AIC=1217.110, Time=13.65 sec
ARIMA(0,1,1)(0,1,3)[12] : AIC=1214.490, Time=2.40 sec
ARIMA(0,1,1)(0,1,2)[12] : AIC=inf, Time=1.35 sec
ARIMA(0,1,1)(1,1,3)[12] : AIC=1214.453, Time=4.89 sec
ARIMA(0,1,1)(1,1,2)[12] : AIC=inf, Time=3.98 sec
ARIMA(0,1,1)(2,1,3)[12] : AIC=1216.073, Time=13.09 sec
ARIMA(0,1,1)(1,1,4)[12] : AIC=1216.430, Time=15.94 sec
ARIMA(0,1,1)(0,1,4)[12] : AIC=1215.970, Time=4.96 sec
ARIMA(0,1,1)(2,1,2)[12] : AIC=1214.496, Time=4.23 sec
ARIMA(0,1,1)(2,1,4)[12] : AIC=inf, Time=21.78 sec
ARIMA(1,1,1)(1,1,3)[12] : AIC=1216.257, Time=8.60 sec
ARIMA(0,1,2)(1,1,3)[12] : AIC=1215.926, Time=4.79 sec
ARIMA(1,1,2)(1,1,3)[12] : AIC=1217.335, Time=8.03 sec
ARIMA(0,1,1)(1,1,3)[12] intercept : AIC=1215.707, Time=5.05 sec
Best model: ARIMA(0,1,1)(1,1,3)[12]
Total fit time: 172.810 seconds
print(model_sarimax.summary())
# predict next 30 days
forecast = model_sarimax.predict(len(df["Close"]), len(df['Close'])+30)
print(forecast)
#plot forecast
plt.figure(figsize=(10, 5))
plt.plot(df['Close'], label='Actual')
plt.plot(forecast, label='Forecast') SARIMAX Results
==================================================================================================
Dep. Variable: y No. Observations: 251
Model: SARIMAX(0, 1, 1)x(1, 1, [1, 2, 3], 12) Log Likelihood -601.227
Date: Tue, 07 Nov 2023 AIC 1214.453
Time: 13:41:31 BIC 1235.287
Sample: 0 HQIC 1222.850
- 251
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
ma.L1 0.1142 0.061 1.878 0.060 -0.005 0.233
ar.S.L12 -0.6155 0.249 -2.474 0.013 -1.103 -0.128
ma.S.L12 -0.2396 0.252 -0.951 0.342 -0.734 0.254
ma.S.L24 -0.6872 0.205 -3.350 0.001 -1.089 -0.285
ma.S.L36 0.1214 0.108 1.126 0.260 -0.090 0.333
sigma2 8.4233 0.631 13.359 0.000 7.187 9.659
===================================================================================
Ljung-Box (L1) (Q): 0.01 Jarque-Bera (JB): 31.07
Prob(Q): 0.92 Prob(JB): 0.00
Heteroskedasticity (H): 1.37 Skew: 0.21
Prob(H) (two-sided): 0.16 Kurtosis: 4.72
===================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
251 107.574462
252 109.041287
253 110.842939
254 112.268545
255 110.882080
...
497 166.860710
498 165.528492
499 165.689534
500 165.560889
501 165.569422
Length: 251, dtype: float64
[<matplotlib.lines.Line2D at 0x7b157c5803d0>]
SARIMAX using Statsmodel
import statsmodels.api as sm
import warnings
p, d, q = 2, 1, 2
model = sm.tsa.statespace.SARIMAX(df['Close'],
order=(p, d, q),
seasonal_order=(p, d, q, 12))
model = model.fit()
print(model.summary())/usr/local/lib/python3.10/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:
Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
SARIMAX Results
==========================================================================================
Dep. Variable: Close No. Observations: 251
Model: SARIMAX(2, 1, 2)x(2, 1, 2, 12) Log Likelihood -600.589
Date: Tue, 07 Nov 2023 AIC 1219.177
Time: 13:47:52 BIC 1250.428
Sample: 0 HQIC 1231.772
- 251
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
ar.L1 1.4826 0.103 14.451 0.000 1.282 1.684
ar.L2 -0.9195 0.089 -10.315 0.000 -1.094 -0.745
ma.L1 -1.5071 0.114 -13.235 0.000 -1.730 -1.284
ma.L2 0.9043 0.108 8.398 0.000 0.693 1.115
ar.S.L12 -0.6702 0.206 -3.251 0.001 -1.074 -0.266
ar.S.L24 -0.0905 0.121 -0.751 0.453 -0.327 0.146
ma.S.L12 -0.1486 0.201 -0.740 0.460 -0.543 0.245
ma.S.L24 -0.6625 0.221 -2.994 0.003 -1.096 -0.229
sigma2 8.3340 0.642 12.983 0.000 7.076 9.592
===================================================================================
Ljung-Box (L1) (Q): 2.80 Jarque-Bera (JB): 29.13
Prob(Q): 0.09 Prob(JB): 0.00
Heteroskedasticity (H): 1.45 Skew: 0.25
Prob(H) (two-sided): 0.10 Kurtosis: 4.64
===================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
# predict next 30 days BN
forecast = model.predict(len(df["Close"]), len(df['Close'])+30)
print(forecast)
#plot forecast
plt.figure(figsize=(10, 5))
plt.plot(df['Close'], label='Actual')
plt.plot(forecast, label='Forecast')251 106.342095
252 108.990280
253 111.292078
254 113.456288
255 114.363421
256 115.542002
257 114.213088
258 112.174290
259 113.304572
260 112.585059
261 112.572702
262 113.051447
263 109.365605
264 112.261605
265 114.586721
266 116.807268
267 118.165806
268 119.315343
269 117.912382
270 115.851244
271 117.207688
272 116.693073
273 116.711063
274 117.323382
275 113.276801
276 116.474547
277 118.917424
278 121.324298
279 122.814593
280 124.029864
281 122.435882
Name: predicted_mean, dtype: float64
[<matplotlib.lines.Line2D at 0x7b156b7e0310>]
SARIMA (Seasonal AutoRegressive Integrated Moving Average) hyperparameter tuning involves the process of selecting the optimal values for the parameters of the SARIMA model in order to improve its forecasting accuracy. The hyperparameters in a SARIMA model include:
p (AR Order): The number of lag observations included in the model (AutoRegressive term).
d (Differencing Order): The number of times the data needs to be differenced to achieve stationarity.
q (MA Order): The size of the moving average window (Moving Average term).
P (Seasonal AR Order): The seasonal autoregressive order.
D (Seasonal Differencing Order): The number of seasonal differences.
Q (Seasonal MA Order): The seasonal moving average order.
s (Seasonal Period): The number of time units in a seasonal cycle.
Hyperparameter tuning involves finding the combination of these parameters that minimizes a chosen evaluation metric (such as Mean Absolute Error, Mean Squared Error, etc.) on a validation dataset. This process is crucial for improving the accuracy of the SARIMA model.
from statsmodels.tsa.statespace.sarimax import SARIMAX
from sklearn.metrics import mean_squared_error
import itertools
import statsmodels.api as sm
import warnings
# Define the p, d, q parameters to take any value between
p = d = q = range(0, 3)
# Generate all different combinations of p, d and q triplets
pdq = list(itertools.product(p, d, q))
# Generate all different combinations of seasonal p, d, q and quadruplets
seasonal_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, d, q))]
best_aic = np.inf
best_pdq = None
best_seasonal_pdq = None
temp_model = None
for param in pdq:
for param_seasonal in seasonal_pdq:
try:
temp_model = sm.tsa.statespace.SARIMAX(df['Close'],
order=param,
seasonal_order=param_seasonal,
enforce_stationarity=False,
enforce_invertibility=False)
results = temp_model.fit()
print(f"SARIMA{param}{param_seasonal} - AIC: {results.aic}")
if results.aic < best_aic:
best_aic = results.aic
best_pdq = param
best_seasonal_pdq = param_seasonal
except:
continue
print(f"Best SARIMA model - AIC: {best_pdq}, {best_seasonal_pdq}, {best_aic}")
SARIMA(0, 0, 0)(0, 0, 0, 12) - AIC: 2933.606783482486
SARIMA(0, 0, 0)(0, 0, 1, 12) - AIC: 2521.51081015389
SARIMA(0, 0, 0)(0, 0, 2, 12) - AIC: 2192.7449171077005
SARIMA(0, 0, 0)(0, 1, 0, 12) - AIC: 1814.2676132829092
SARIMA(0, 0, 0)(0, 1, 1, 12) - AIC: 1701.1750645358497
SARIMA(0, 0, 0)(0, 1, 2, 12) - AIC: 1600.0280415071468
SARIMA(0, 0, 0)(0, 2, 0, 12) - AIC: 1830.3018096808125
SARIMA(0, 0, 0)(0, 2, 1, 12) - AIC: 1666.3681520080168
SARIMA(0, 0, 0)(0, 2, 2, 12) - AIC: 1532.5873805062627
SARIMA(0, 0, 0)(1, 0, 0, 12) - AIC: 1817.1876688058792
SARIMA(0, 0, 0)(1, 0, 1, 12) - AIC: 1794.5007992416
SARIMA(0, 0, 0)(1, 0, 2, 12) - AIC: 1694.7482483569452
SARIMA(0, 0, 0)(1, 1, 0, 12) - AIC: 1724.2921969159556
SARIMA(0, 0, 0)(1, 1, 1, 12) - AIC: 1707.2610540400096
SARIMA(0, 0, 0)(1, 1, 2, 12) - AIC: 1601.4973489340196
SARIMA(0, 0, 0)(1, 2, 0, 12) - AIC: 1735.8045239527
SARIMA(0, 0, 0)(1, 2, 1, 12) - AIC: 1664.1931059076865
SARIMA(0, 0, 0)(1, 2, 2, 12) - AIC: 1534.569160596503
SARIMA(0, 0, 0)(2, 0, 0, 12) - AIC: 1724.2624510985056
SARIMA(0, 0, 0)(2, 0, 1, 12) - AIC: 1715.6675891135976
SARIMA(0, 0, 0)(2, 0, 2, 12) - AIC: 1694.3111780689833
SARIMA(0, 0, 0)(2, 1, 0, 12) - AIC: 1591.3916116603941
SARIMA(0, 0, 0)(2, 1, 1, 12) - AIC: 1588.5867175069225
SARIMA(0, 0, 0)(2, 1, 2, 12) - AIC: 1576.4153733129483
SARIMA(0, 0, 0)(2, 2, 0, 12) - AIC: 1557.5495455736523
SARIMA(0, 0, 0)(2, 2, 1, 12) - AIC: 1513.8591472528378
SARIMA(0, 0, 0)(2, 2, 2, 12) - AIC: 1485.6770796112
SARIMA(0, 0, 1)(0, 0, 0, 12) - AIC: 2593.563507205501
SARIMA(0, 0, 1)(0, 0, 1, 12) - AIC: 2201.5979265719643
SARIMA(0, 0, 1)(0, 0, 2, 12) - AIC: 1922.578320396512
SARIMA(0, 0, 1)(0, 1, 0, 12) - AIC: 1574.298265635709
SARIMA(0, 0, 1)(0, 1, 1, 12) - AIC: 1493.3206782590114
SARIMA(0, 0, 1)(0, 1, 2, 12) - AIC: 1402.6257177964408
SARIMA(0, 0, 1)(0, 2, 0, 12) - AIC: 1634.0844505911532
SARIMA(0, 0, 1)(0, 2, 1, 12) - AIC: 1453.606698026995
SARIMA(0, 0, 1)(0, 2, 2, 12) - AIC: 1350.302338739888
SARIMA(0, 0, 1)(1, 0, 0, 12) - AIC: 1586.204172323477
SARIMA(0, 0, 1)(1, 0, 1, 12) - AIC: 1574.7992635472951
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(0, 0, 1)(1, 0, 2, 12) - AIC: 1504.7698795401118
SARIMA(0, 0, 1)(1, 1, 0, 12) - AIC: 1510.1339768896778
SARIMA(0, 0, 1)(1, 1, 1, 12) - AIC: 1495.291202929871
SARIMA(0, 0, 1)(1, 1, 2, 12) - AIC: 1403.546710867597
SARIMA(0, 0, 1)(1, 2, 0, 12) - AIC: 1545.0455002725203
SARIMA(0, 0, 1)(1, 2, 1, 12) - AIC: 1455.5997777824196
SARIMA(0, 0, 1)(1, 2, 2, 12) - AIC: 1349.2954178480554
SARIMA(0, 0, 1)(2, 0, 0, 12) - AIC: 1511.7841767689597
SARIMA(0, 0, 1)(2, 0, 1, 12) - AIC: 1513.8948453782655
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(0, 0, 1)(2, 0, 2, 12) - AIC: 1487.2005482701595
SARIMA(0, 0, 1)(2, 1, 0, 12) - AIC: 1406.4454792281413
SARIMA(0, 0, 1)(2, 1, 1, 12) - AIC: 1406.9212528918436
SARIMA(0, 0, 1)(2, 1, 2, 12) - AIC: 1395.940627766261
SARIMA(0, 0, 1)(2, 2, 0, 12) - AIC: 1388.406264485038
SARIMA(0, 0, 1)(2, 2, 1, 12) - AIC: 1346.5048225950534
SARIMA(0, 0, 1)(2, 2, 2, 12) - AIC: 1354.2987292199916
SARIMA(0, 0, 2)(0, 0, 0, 12) - AIC: 2356.368129141507
SARIMA(0, 0, 2)(0, 0, 1, 12) - AIC: 1943.4376066755099
SARIMA(0, 0, 2)(0, 0, 2, 12) - AIC: 1755.2964124579848
SARIMA(0, 0, 2)(0, 1, 0, 12) - AIC: 1458.1886793037372
SARIMA(0, 0, 2)(0, 1, 1, 12) - AIC: 1381.8692466831221
SARIMA(0, 0, 2)(0, 1, 2, 12) - AIC: 1298.106271357512
SARIMA(0, 0, 2)(0, 2, 0, 12) - AIC: 1531.2373858869787
SARIMA(0, 0, 2)(0, 2, 1, 12) - AIC: 1347.976164420937
SARIMA(0, 0, 2)(0, 2, 2, 12) - AIC: 1253.8869004140624
SARIMA(0, 0, 2)(1, 0, 0, 12) - AIC: 1477.060835980769
SARIMA(0, 0, 2)(1, 0, 1, 12) - AIC: 1459.804732673664
SARIMA(0, 0, 2)(1, 0, 2, 12) - AIC: 1369.7078069080771
SARIMA(0, 0, 2)(1, 1, 0, 12) - AIC: 1402.7980688906387
SARIMA(0, 0, 2)(1, 1, 1, 12) - AIC: 1382.017785903155
SARIMA(0, 0, 2)(1, 1, 2, 12) - AIC: 1298.5679923435098
SARIMA(0, 0, 2)(1, 2, 0, 12) - AIC: 1450.0045883541902
SARIMA(0, 0, 2)(1, 2, 1, 12) - AIC: 1349.951890076526
SARIMA(0, 0, 2)(1, 2, 2, 12) - AIC: 1250.843467972781
SARIMA(0, 0, 2)(2, 0, 0, 12) - AIC: 1406.3075453208571
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(0, 0, 2)(2, 0, 1, 12) - AIC: 1409.057525860952
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(0, 0, 2)(2, 0, 2, 12) - AIC: 1401.3975095551875
SARIMA(0, 0, 2)(2, 1, 0, 12) - AIC: 1307.6617890391149
SARIMA(0, 0, 2)(2, 1, 1, 12) - AIC: 1308.7708149523505
SARIMA(0, 0, 2)(2, 1, 2, 12) - AIC: 1293.002863978336
SARIMA(0, 0, 2)(2, 2, 0, 12) - AIC: 1306.4174086338487
SARIMA(0, 0, 2)(2, 2, 1, 12) - AIC: 1261.6640654231835
SARIMA(0, 0, 2)(2, 2, 2, 12) - AIC: 1232.979680456461
SARIMA(0, 1, 0)(0, 0, 0, 12) - AIC: 1232.8402196234074
SARIMA(0, 1, 0)(0, 0, 1, 12) - AIC: 1177.3521677023632
SARIMA(0, 1, 0)(0, 0, 2, 12) - AIC: 1119.56998719648
SARIMA(0, 1, 0)(0, 1, 0, 12) - AIC: 1323.4803493156328
SARIMA(0, 1, 0)(0, 1, 1, 12) - AIC: 1139.9864080516286
SARIMA(0, 1, 0)(0, 1, 2, 12) - AIC: 1091.5665594673019
SARIMA(0, 1, 0)(0, 2, 0, 12) - AIC: 1483.0328578444883
SARIMA(0, 1, 0)(0, 2, 1, 12) - AIC: 1225.3007862174807
SARIMA(0, 1, 0)(0, 2, 2, 12) - AIC: 1065.0316397130546
SARIMA(0, 1, 0)(1, 0, 0, 12) - AIC: 1182.2393944955986
SARIMA(0, 1, 0)(1, 0, 1, 12) - AIC: 1177.2831746978873
SARIMA(0, 1, 0)(1, 0, 2, 12) - AIC: 1120.4147434988622
SARIMA(0, 1, 0)(1, 1, 0, 12) - AIC: 1213.0260455767414
SARIMA(0, 1, 0)(1, 1, 1, 12) - AIC: 1141.9856451684714
SARIMA(0, 1, 0)(1, 1, 2, 12) - AIC: 1086.1462465592163
SARIMA(0, 1, 0)(1, 2, 0, 12) - AIC: 1327.277502181399
SARIMA(0, 1, 0)(1, 2, 1, 12) - AIC: 1189.9679830433784
SARIMA(0, 1, 0)(1, 2, 2, 12) - AIC: 1067.0306508756455
SARIMA(0, 1, 0)(2, 0, 0, 12) - AIC: 1123.0464120484326
SARIMA(0, 1, 0)(2, 0, 1, 12) - AIC: 1124.3133732820907
SARIMA(0, 1, 0)(2, 0, 2, 12) - AIC: 1121.875128999218
SARIMA(0, 1, 0)(2, 1, 0, 12) - AIC: 1113.8664119671212
SARIMA(0, 1, 0)(2, 1, 1, 12) - AIC: 1095.1552395299486
SARIMA(0, 1, 0)(2, 1, 2, 12) - AIC: 1085.8569603224876
SARIMA(0, 1, 0)(2, 2, 0, 12) - AIC: 1166.378473530242
SARIMA(0, 1, 0)(2, 2, 1, 12) - AIC: 1097.2931693347773
SARIMA(0, 1, 0)(2, 2, 2, 12) - AIC: 1093.4992403342876
SARIMA(0, 1, 1)(0, 0, 0, 12) - AIC: 1225.0029595564984
SARIMA(0, 1, 1)(0, 0, 1, 12) - AIC: 1172.9831477199925
SARIMA(0, 1, 1)(0, 0, 2, 12) - AIC: 1116.1070791021007
SARIMA(0, 1, 1)(0, 1, 0, 12) - AIC: 1314.1452781074313
SARIMA(0, 1, 1)(0, 1, 1, 12) - AIC: 1135.3861561080619
SARIMA(0, 1, 1)(0, 1, 2, 12) - AIC: 1087.9047161781
SARIMA(0, 1, 1)(0, 2, 0, 12) - AIC: 1476.8669722409315
SARIMA(0, 1, 1)(0, 2, 1, 12) - AIC: 1220.3147704699036
SARIMA(0, 1, 1)(0, 2, 2, 12) - AIC: 1059.28369904086
SARIMA(0, 1, 1)(1, 0, 0, 12) - AIC: 1182.3521869837734
SARIMA(0, 1, 1)(1, 0, 1, 12) - AIC: 1173.829257000661
SARIMA(0, 1, 1)(1, 0, 2, 12) - AIC: 1117.238009969493
SARIMA(0, 1, 1)(1, 1, 0, 12) - AIC: 1211.7907758230526
SARIMA(0, 1, 1)(1, 1, 1, 12) - AIC: 1137.3858865504208
SARIMA(0, 1, 1)(1, 1, 2, 12) - AIC: 1082.1761313609172
SARIMA(0, 1, 1)(1, 2, 0, 12) - AIC: 1327.2369651408112
SARIMA(0, 1, 1)(1, 2, 1, 12) - AIC: 1183.3084200127623
SARIMA(0, 1, 1)(1, 2, 2, 12) - AIC: 1079.6023769378305
SARIMA(0, 1, 1)(2, 0, 0, 12) - AIC: 1124.2876112450526
SARIMA(0, 1, 1)(2, 0, 1, 12) - AIC: 1125.3098568343016
SARIMA(0, 1, 1)(2, 0, 2, 12) - AIC: 1118.9833117071103
SARIMA(0, 1, 1)(2, 1, 0, 12) - AIC: 1113.2997848049426
SARIMA(0, 1, 1)(2, 1, 1, 12) - AIC: 1096.400204884703
SARIMA(0, 1, 1)(2, 1, 2, 12) - AIC: 1081.533305820415
SARIMA(0, 1, 1)(2, 2, 0, 12) - AIC: 1164.7096309550684
SARIMA(0, 1, 1)(2, 2, 1, 12) - AIC: 1096.5142551860536
SARIMA(0, 1, 1)(2, 2, 2, 12) - AIC: 1083.646618919271
SARIMA(0, 1, 2)(0, 0, 0, 12) - AIC: 1222.276339403938
SARIMA(0, 1, 2)(0, 0, 1, 12) - AIC: 1170.8465338125657
SARIMA(0, 1, 2)(0, 0, 2, 12) - AIC: 1113.0380053956
SARIMA(0, 1, 2)(0, 1, 0, 12) - AIC: 1310.8705608611692
SARIMA(0, 1, 2)(0, 1, 1, 12) - AIC: 1134.2908165469034
SARIMA(0, 1, 2)(0, 1, 2, 12) - AIC: 1083.842750097093
SARIMA(0, 1, 2)(0, 2, 0, 12) - AIC: 1471.083718998325
SARIMA(0, 1, 2)(0, 2, 1, 12) - AIC: 1215.8346218262504
SARIMA(0, 1, 2)(0, 2, 2, 12) - AIC: 1057.6923940592394
SARIMA(0, 1, 2)(1, 0, 0, 12) - AIC: 1184.165730308599
SARIMA(0, 1, 2)(1, 0, 1, 12) - AIC: 1171.7016456476927
SARIMA(0, 1, 2)(1, 0, 2, 12) - AIC: 1114.1602327638745
SARIMA(0, 1, 2)(1, 1, 0, 12) - AIC: 1213.7744778607716
SARIMA(0, 1, 2)(1, 1, 1, 12) - AIC: 1136.2905232084463
SARIMA(0, 1, 2)(1, 1, 2, 12) - AIC: 1078.8039320891185
SARIMA(0, 1, 2)(1, 2, 0, 12) - AIC: 1329.2341431082177
SARIMA(0, 1, 2)(1, 2, 1, 12) - AIC: 1179.7034405617933
SARIMA(0, 1, 2)(1, 2, 2, 12) - AIC: 1059.692194921274
SARIMA(0, 1, 2)(2, 0, 0, 12) - AIC: 1125.2219057199727
SARIMA(0, 1, 2)(2, 0, 1, 12) - AIC: 1126.30878001045
SARIMA(0, 1, 2)(2, 0, 2, 12) - AIC: 1115.413702148719
SARIMA(0, 1, 2)(2, 1, 0, 12) - AIC: 1114.1781943980936
SARIMA(0, 1, 2)(2, 1, 1, 12) - AIC: 1096.7064200727632
SARIMA(0, 1, 2)(2, 1, 2, 12) - AIC: 1077.3842210759367
SARIMA(0, 1, 2)(2, 2, 0, 12) - AIC: 1165.7271040214778
SARIMA(0, 1, 2)(2, 2, 1, 12) - AIC: 1097.4811105123517
SARIMA(0, 1, 2)(2, 2, 2, 12) - AIC: 1078.6304031534705
SARIMA(0, 2, 0)(0, 0, 0, 12) - AIC: 1374.4891198663067
SARIMA(0, 2, 0)(0, 0, 1, 12) - AIC: 1316.4205442579932
SARIMA(0, 2, 0)(0, 0, 2, 12) - AIC: 1256.5440106077917
SARIMA(0, 2, 0)(0, 1, 0, 12) - AIC: 1453.7331680681923
SARIMA(0, 2, 0)(0, 1, 1, 12) - AIC: 1272.0835091995423
SARIMA(0, 2, 0)(0, 1, 2, 12) - AIC: 1214.6530770646846
SARIMA(0, 2, 0)(0, 2, 0, 12) - AIC: 1616.253728341802
SARIMA(0, 2, 0)(0, 2, 1, 12) - AIC: 1350.2975368599416
SARIMA(0, 2, 0)(0, 2, 2, 12) - AIC: 1181.8854745078024
SARIMA(0, 2, 0)(1, 0, 0, 12) - AIC: 1321.2240043870056
SARIMA(0, 2, 0)(1, 0, 1, 12) - AIC: 1317.566256073661
SARIMA(0, 2, 0)(1, 0, 2, 12) - AIC: 1254.6600454159416
SARIMA(0, 2, 0)(1, 1, 0, 12) - AIC: 1334.508295785496
SARIMA(0, 2, 0)(1, 1, 1, 12) - AIC: 1274.0832622168905
SARIMA(0, 2, 0)(1, 1, 2, 12) - AIC: 1207.0573471700895
SARIMA(0, 2, 0)(1, 2, 0, 12) - AIC: 1445.282980077532
SARIMA(0, 2, 0)(1, 2, 1, 12) - AIC: 1304.840342325498
SARIMA(0, 2, 0)(1, 2, 2, 12) - AIC: 1183.884682549463
SARIMA(0, 2, 0)(2, 0, 0, 12) - AIC: 1260.8150507450673
SARIMA(0, 2, 0)(2, 0, 1, 12) - AIC: 1259.2830322709947
SARIMA(0, 2, 0)(2, 0, 2, 12) - AIC: 1256.6597862426395
SARIMA(0, 2, 0)(2, 1, 0, 12) - AIC: 1232.9107098485956
SARIMA(0, 2, 0)(2, 1, 1, 12) - AIC: 1224.9608696670948
SARIMA(0, 2, 0)(2, 1, 2, 12) - AIC: 1208.3365406437392
SARIMA(0, 2, 0)(2, 2, 0, 12) - AIC: 1271.6545952653635
SARIMA(0, 2, 0)(2, 2, 1, 12) - AIC: 1207.5912316958188
SARIMA(0, 2, 0)(2, 2, 2, 12) - AIC: 1197.9736310209314
SARIMA(0, 2, 1)(0, 0, 0, 12) - AIC: 1229.9271452309558
SARIMA(0, 2, 1)(0, 0, 1, 12) - AIC: 1175.0478037140892
SARIMA(0, 2, 1)(0, 0, 2, 12) - AIC: 1117.016387328761
SARIMA(0, 2, 1)(0, 1, 0, 12) - AIC: 1319.6847708176176
SARIMA(0, 2, 1)(0, 1, 1, 12) - AIC: 1142.106016572819
SARIMA(0, 2, 1)(0, 1, 2, 12) - AIC: 1091.6476719776
SARIMA(0, 2, 1)(0, 2, 0, 12) - AIC: 1477.259392230324
SARIMA(0, 2, 1)(0, 2, 1, 12) - AIC: 1228.272057945561
SARIMA(0, 2, 1)(0, 2, 2, 12) - AIC: 1066.4189794448907
SARIMA(0, 2, 1)(1, 0, 0, 12) - AIC: 1185.2534947365903
SARIMA(0, 2, 1)(1, 0, 1, 12) - AIC: 1174.481491981182
SARIMA(0, 2, 1)(1, 0, 2, 12) - AIC: 1118.042451272997
SARIMA(0, 2, 1)(1, 1, 0, 12) - AIC: 1215.9548901462672
SARIMA(0, 2, 1)(1, 1, 1, 12) - AIC: 1143.8806328272667
SARIMA(0, 2, 1)(1, 1, 2, 12) - AIC: 1082.6246227761176
SARIMA(0, 2, 1)(1, 2, 0, 12) - AIC: 1329.2396846847969
SARIMA(0, 2, 1)(1, 2, 1, 12) - AIC: 1190.7802073698379
SARIMA(0, 2, 1)(1, 2, 2, 12) - AIC: 1067.808104786408
SARIMA(0, 2, 1)(2, 0, 0, 12) - AIC: 1125.8678266244015
SARIMA(0, 2, 1)(2, 0, 1, 12) - AIC: 1127.1249164953779
SARIMA(0, 2, 1)(2, 0, 2, 12) - AIC: 1119.1677799028091
SARIMA(0, 2, 1)(2, 1, 0, 12) - AIC: 1117.02484114143
SARIMA(0, 2, 1)(2, 1, 1, 12) - AIC: 1099.8340730840819
SARIMA(0, 2, 1)(2, 1, 2, 12) - AIC: 1084.738931073058
SARIMA(0, 2, 1)(2, 2, 0, 12) - AIC: 1168.9383543409456
SARIMA(0, 2, 1)(2, 2, 1, 12) - AIC: 1102.3798656883405
SARIMA(0, 2, 1)(2, 2, 2, 12) - AIC: 1087.4299912485621
SARIMA(0, 2, 2)(0, 0, 0, 12) - AIC: 1225.854171855526
SARIMA(0, 2, 2)(0, 0, 1, 12) - AIC: 1170.5120234330327
SARIMA(0, 2, 2)(0, 0, 2, 12) - AIC: 1111.6427964569498
SARIMA(0, 2, 2)(0, 1, 0, 12) - AIC: 1313.478800995227
SARIMA(0, 2, 2)(0, 1, 1, 12) - AIC: 1137.7145543014176
SARIMA(0, 2, 2)(0, 1, 2, 12) - AIC: 1085.2121767675626
SARIMA(0, 2, 2)(0, 2, 0, 12) - AIC: 1472.2213206364918
SARIMA(0, 2, 2)(0, 2, 1, 12) - AIC: 1220.8588191755823
SARIMA(0, 2, 2)(0, 2, 2, 12) - AIC: 1061.0745617537489
SARIMA(0, 2, 2)(1, 0, 0, 12) - AIC: 1185.276112392676
SARIMA(0, 2, 2)(1, 0, 1, 12) - AIC: 1169.9772965381464
SARIMA(0, 2, 2)(1, 0, 2, 12) - AIC: 1113.3371042750948
SARIMA(0, 2, 2)(1, 1, 0, 12) - AIC: 1214.5263094643587
SARIMA(0, 2, 2)(1, 1, 1, 12) - AIC: 1139.568671088502
SARIMA(0, 2, 2)(1, 1, 2, 12) - AIC: 1075.256487137216
SARIMA(0, 2, 2)(1, 2, 0, 12) - AIC: 1329.03489515432
SARIMA(0, 2, 2)(1, 2, 1, 12) - AIC: 1182.9687209521737
SARIMA(0, 2, 2)(1, 2, 2, 12) - AIC: 1062.6020477611025
SARIMA(0, 2, 2)(2, 0, 0, 12) - AIC: 1127.220638014182
SARIMA(0, 2, 2)(2, 0, 1, 12) - AIC: 1128.374772738424
SARIMA(0, 2, 2)(2, 0, 2, 12) - AIC: 1114.3858841088982
SARIMA(0, 2, 2)(2, 1, 0, 12) - AIC: 1116.24154937127
SARIMA(0, 2, 2)(2, 1, 1, 12) - AIC: 1101.141769127622
SARIMA(0, 2, 2)(2, 1, 2, 12) - AIC: 1078.8614382571282
SARIMA(0, 2, 2)(2, 2, 0, 12) - AIC: 1167.0090254348424
SARIMA(0, 2, 2)(2, 2, 1, 12) - AIC: 1102.3436653782337
SARIMA(0, 2, 2)(2, 2, 2, 12) - AIC: 1081.0089282756576
SARIMA(1, 0, 0)(0, 0, 0, 12) - AIC: 1238.7813049498518
SARIMA(1, 0, 0)(0, 0, 1, 12) - AIC: 1183.2422925608466
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 0)(0, 0, 2, 12) - AIC: 1129.2626356215628
SARIMA(1, 0, 0)(0, 1, 0, 12) - AIC: 1322.908300404827
SARIMA(1, 0, 0)(0, 1, 1, 12) - AIC: 1145.5615891441084
SARIMA(1, 0, 0)(0, 1, 2, 12) - AIC: 1098.1825666919076
SARIMA(1, 0, 0)(0, 2, 0, 12) - AIC: 1478.3705714094522
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 0)(0, 2, 1, 12) - AIC: 1228.2414127490756
SARIMA(1, 0, 0)(0, 2, 2, 12) - AIC: 1070.042170152292
SARIMA(1, 0, 0)(1, 0, 0, 12) - AIC: 1183.99865297107
SARIMA(1, 0, 0)(1, 0, 1, 12) - AIC: 1183.2384828243028
SARIMA(1, 0, 0)(1, 0, 2, 12) - AIC: 1126.8687709025885
SARIMA(1, 0, 0)(1, 1, 0, 12) - AIC: 1210.3124591831918
SARIMA(1, 0, 0)(1, 1, 1, 12) - AIC: 1147.5585493902577
SARIMA(1, 0, 0)(1, 1, 2, 12) - AIC: 1092.3080510357588
SARIMA(1, 0, 0)(1, 2, 0, 12) - AIC: 1323.984756681787
SARIMA(1, 0, 0)(1, 2, 1, 12) - AIC: 1194.022932396092
SARIMA(1, 0, 0)(1, 2, 2, 12) - AIC: 1072.038213680441
SARIMA(1, 0, 0)(2, 0, 0, 12) - AIC: 1125.0196322027641
SARIMA(1, 0, 0)(2, 0, 1, 12) - AIC: 1126.305109128632
SARIMA(1, 0, 0)(2, 0, 2, 12) - AIC: 1128.2803240086873
SARIMA(1, 0, 0)(2, 1, 0, 12) - AIC: 1112.4400146740395
SARIMA(1, 0, 0)(2, 1, 1, 12) - AIC: 1096.026630556145
SARIMA(1, 0, 0)(2, 1, 2, 12) - AIC: 1092.033624364726
SARIMA(1, 0, 0)(2, 2, 0, 12) - AIC: 1163.7435098346516
SARIMA(1, 0, 0)(2, 2, 1, 12) - AIC: 1096.056275936577
SARIMA(1, 0, 0)(2, 2, 2, 12) - AIC: 1096.4661610795547
SARIMA(1, 0, 1)(0, 0, 0, 12) - AIC: 1234.420035560365
SARIMA(1, 0, 1)(0, 0, 1, 12) - AIC: 1179.5640890396603
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 1)(0, 0, 2, 12) - AIC: 1125.8802914274456
SARIMA(1, 0, 1)(0, 1, 0, 12) - AIC: 1315.491042374868
SARIMA(1, 0, 1)(0, 1, 1, 12) - AIC: 1141.3816685571664
SARIMA(1, 0, 1)(0, 1, 2, 12) - AIC: 1093.1759709147475
SARIMA(1, 0, 1)(0, 2, 0, 12) - AIC: 1471.135771298094
SARIMA(1, 0, 1)(0, 2, 1, 12) - AIC: 1221.2058988334907
SARIMA(1, 0, 1)(0, 2, 2, 12) - AIC: 1066.6407231700505
SARIMA(1, 0, 1)(1, 0, 0, 12) - AIC: 1184.1877273387533
SARIMA(1, 0, 1)(1, 0, 1, 12) - AIC: 1179.8722584002924
SARIMA(1, 0, 1)(1, 0, 2, 12) - AIC: 1123.6537151502962
SARIMA(1, 0, 1)(1, 1, 0, 12) - AIC: 1208.094309685178
SARIMA(1, 0, 1)(1, 1, 1, 12) - AIC: 1143.379245902223
SARIMA(1, 0, 1)(1, 1, 2, 12) - AIC: 1087.268577855265
SARIMA(1, 0, 1)(1, 2, 0, 12) - AIC: 1322.5024149135484
SARIMA(1, 0, 1)(1, 2, 1, 12) - AIC: 1185.4773888225677
SARIMA(1, 0, 1)(1, 2, 2, 12) - AIC: 1068.6380135110874
SARIMA(1, 0, 1)(2, 0, 0, 12) - AIC: 1126.2728509132507
SARIMA(1, 0, 1)(2, 0, 1, 12) - AIC: 1127.309406180747
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 1)(2, 0, 2, 12) - AIC: 1125.1746893782722
SARIMA(1, 0, 1)(2, 1, 0, 12) - AIC: 1111.1201858804334
SARIMA(1, 0, 1)(2, 1, 1, 12) - AIC: 1097.058271897616
SARIMA(1, 0, 1)(2, 1, 2, 12) - AIC: 1086.9458052058028
SARIMA(1, 0, 1)(2, 2, 0, 12) - AIC: 1160.8245679596291
SARIMA(1, 0, 1)(2, 2, 1, 12) - AIC: 1094.4884372158863
SARIMA(1, 0, 1)(2, 2, 2, 12) - AIC: 1088.8372651906607
SARIMA(1, 0, 2)(0, 0, 0, 12) - AIC: 1228.996604644098
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 2)(0, 0, 1, 12) - AIC: 1176.7021694083987
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 2)(0, 0, 2, 12) - AIC: 1122.8529132736276
SARIMA(1, 0, 2)(0, 1, 0, 12) - AIC: 1309.436631532708
SARIMA(1, 0, 2)(0, 1, 1, 12) - AIC: 1139.2344447260266
SARIMA(1, 0, 2)(0, 1, 2, 12) - AIC: 1090.6488170333712
SARIMA(1, 0, 2)(0, 2, 0, 12) - AIC: 1466.9930312494325
SARIMA(1, 0, 2)(0, 2, 1, 12) - AIC: 1217.554260003428
SARIMA(1, 0, 2)(0, 2, 2, 12) - AIC: 1062.8663201990967
SARIMA(1, 0, 2)(1, 0, 0, 12) - AIC: 1185.970508879208
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 2)(1, 0, 1, 12) - AIC: 1177.6455789722108
SARIMA(1, 0, 2)(1, 0, 2, 12) - AIC: 1120.3210091167143
SARIMA(1, 0, 2)(1, 1, 0, 12) - AIC: 1210.0237970818873
SARIMA(1, 0, 2)(1, 1, 1, 12) - AIC: 1141.2331874794304
SARIMA(1, 0, 2)(1, 1, 2, 12) - AIC: 1085.6957867139563
SARIMA(1, 0, 2)(1, 2, 0, 12) - AIC: 1323.941762389324
SARIMA(1, 0, 2)(1, 2, 1, 12) - AIC: 1181.9052018459072
SARIMA(1, 0, 2)(1, 2, 2, 12) - AIC: 1064.8655118723914
SARIMA(1, 0, 2)(2, 0, 0, 12) - AIC: 1127.1859603380499
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 2)(2, 0, 1, 12) - AIC: 1128.298112460137
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(1, 0, 2)(2, 0, 2, 12) - AIC: 1121.7182799641866
SARIMA(1, 0, 2)(2, 1, 0, 12) - AIC: 1112.54069974487
SARIMA(1, 0, 2)(2, 1, 1, 12) - AIC: 1097.6925870010818
SARIMA(1, 0, 2)(2, 1, 2, 12) - AIC: 1084.0987979230263
SARIMA(1, 0, 2)(2, 2, 0, 12) - AIC: 1162.466190906236
SARIMA(1, 0, 2)(2, 2, 1, 12) - AIC: 1095.9878461513727
SARIMA(1, 0, 2)(2, 2, 2, 12) - AIC: 1081.5460178439985
SARIMA(1, 1, 0)(0, 0, 0, 12) - AIC: 1232.5416167015276
SARIMA(1, 1, 0)(0, 0, 1, 12) - AIC: 1177.7473819747806
SARIMA(1, 1, 0)(0, 0, 2, 12) - AIC: 1120.756309838843
SARIMA(1, 1, 0)(0, 1, 0, 12) - AIC: 1322.878798472721
SARIMA(1, 1, 0)(0, 1, 1, 12) - AIC: 1141.146110267157
SARIMA(1, 1, 0)(0, 1, 2, 12) - AIC: 1092.032894717092
SARIMA(1, 1, 0)(0, 2, 0, 12) - AIC: 1484.1056199617842
SARIMA(1, 1, 0)(0, 2, 1, 12) - AIC: 1226.1095164037488
SARIMA(1, 1, 0)(0, 2, 2, 12) - AIC: 1067.4720486223648
SARIMA(1, 1, 0)(1, 0, 0, 12) - AIC: 1178.392974673179
SARIMA(1, 1, 0)(1, 0, 1, 12) - AIC: 1178.1300749068464
SARIMA(1, 1, 0)(1, 0, 2, 12) - AIC: 1121.4502548291343
SARIMA(1, 1, 0)(1, 1, 0, 12) - AIC: 1207.2253247026317
SARIMA(1, 1, 0)(1, 1, 1, 12) - AIC: 1143.1460517191144
SARIMA(1, 1, 0)(1, 1, 2, 12) - AIC: 1086.9080582810514
SARIMA(1, 1, 0)(1, 2, 0, 12) - AIC: 1320.8934932647362
SARIMA(1, 1, 0)(1, 2, 1, 12) - AIC: 1188.961024743413
SARIMA(1, 1, 0)(1, 2, 2, 12) - AIC: 1085.5698768130242
SARIMA(1, 1, 0)(2, 0, 0, 12) - AIC: 1119.8965277678105
SARIMA(1, 1, 0)(2, 0, 1, 12) - AIC: 1121.2240076966834
SARIMA(1, 1, 0)(2, 0, 2, 12) - AIC: 1123.21384046758
SARIMA(1, 1, 0)(2, 1, 0, 12) - AIC: 1108.9169098020889
SARIMA(1, 1, 0)(2, 1, 1, 12) - AIC: 1091.073747995279
SARIMA(1, 1, 0)(2, 1, 2, 12) - AIC: 1086.255931770739
SARIMA(1, 1, 0)(2, 2, 0, 12) - AIC: 1160.4090735963714
SARIMA(1, 1, 0)(2, 2, 1, 12) - AIC: 1092.0655961232787
SARIMA(1, 1, 0)(2, 2, 2, 12) - AIC: 1092.3362124681753
SARIMA(1, 1, 1)(0, 0, 0, 12) - AIC: 1226.973379103324
SARIMA(1, 1, 1)(0, 0, 1, 12) - AIC: 1174.9134357284593
SARIMA(1, 1, 1)(0, 0, 2, 12) - AIC: 1117.9477118058692
SARIMA(1, 1, 1)(0, 1, 0, 12) - AIC: 1316.0763392625572
SARIMA(1, 1, 1)(0, 1, 1, 12) - AIC: 1137.0631376376766
SARIMA(1, 1, 1)(0, 1, 2, 12) - AIC: 1089.8639339841957
SARIMA(1, 1, 1)(0, 2, 0, 12) - AIC: 1472.959900280736
SARIMA(1, 1, 1)(0, 2, 1, 12) - AIC: 1222.1976066273314
SARIMA(1, 1, 1)(0, 2, 2, 12) - AIC: 1060.138374025335
SARIMA(1, 1, 1)(1, 0, 0, 12) - AIC: 1180.2290817018957
SARIMA(1, 1, 1)(1, 0, 1, 12) - AIC: 1175.7426235523055
SARIMA(1, 1, 1)(1, 0, 2, 12) - AIC: 1117.1382569862647
SARIMA(1, 1, 1)(1, 1, 0, 12) - AIC: 1209.061918618745
SARIMA(1, 1, 1)(1, 1, 1, 12) - AIC: 1139.0629146338365
SARIMA(1, 1, 1)(1, 1, 2, 12) - AIC: 1083.950479702542
SARIMA(1, 1, 1)(1, 2, 0, 12) - AIC: 1325.954360310076
SARIMA(1, 1, 1)(1, 2, 1, 12) - AIC: 1185.0161430543046
SARIMA(1, 1, 1)(1, 2, 2, 12) - AIC: 1062.1381448471334
SARIMA(1, 1, 1)(2, 0, 0, 12) - AIC: 1121.7630902156934
SARIMA(1, 1, 1)(2, 0, 1, 12) - AIC: 1122.8779278547458
SARIMA(1, 1, 1)(2, 0, 2, 12) - AIC: 1120.7719149335076
SARIMA(1, 1, 1)(2, 1, 0, 12) - AIC: 1109.7034764157825
SARIMA(1, 1, 1)(2, 1, 1, 12) - AIC: 1092.552270386118
SARIMA(1, 1, 1)(2, 1, 2, 12) - AIC: 1083.3561426087292
SARIMA(1, 1, 1)(2, 2, 0, 12) - AIC: 1154.7506110263885
SARIMA(1, 1, 1)(2, 2, 1, 12) - AIC: 1092.842468827464
SARIMA(1, 1, 1)(2, 2, 2, 12) - AIC: 1085.2500552892948
SARIMA(1, 1, 2)(0, 0, 0, 12) - AIC: 1223.3988851647377
SARIMA(1, 1, 2)(0, 0, 1, 12) - AIC: 1171.473350743042
SARIMA(1, 1, 2)(0, 0, 2, 12) - AIC: 1113.8764681182197
SARIMA(1, 1, 2)(0, 1, 0, 12) - AIC: 1311.4689712526929
SARIMA(1, 1, 2)(0, 1, 1, 12) - AIC: 1135.991913974463
SARIMA(1, 1, 2)(0, 1, 2, 12) - AIC: 1084.9776173916896
SARIMA(1, 1, 2)(0, 2, 0, 12) - AIC: 1470.1746796464631
SARIMA(1, 1, 2)(0, 2, 1, 12) - AIC: 1216.388459621785
SARIMA(1, 1, 2)(0, 2, 2, 12) - AIC: 1059.63808405008
SARIMA(1, 1, 2)(1, 0, 0, 12) - AIC: 1180.944395768498
SARIMA(1, 1, 2)(1, 0, 1, 12) - AIC: 1173.0358335666674
SARIMA(1, 1, 2)(1, 0, 2, 12) - AIC: 1115.4370860412637
SARIMA(1, 1, 2)(1, 1, 0, 12) - AIC: 1210.8129176903367
SARIMA(1, 1, 2)(1, 1, 1, 12) - AIC: 1137.9915964098811
SARIMA(1, 1, 2)(1, 1, 2, 12) - AIC: 1078.8878181122593
SARIMA(1, 1, 2)(1, 2, 0, 12) - AIC: 1324.1935158484944
SARIMA(1, 1, 2)(1, 2, 1, 12) - AIC: 1181.4349429126928
SARIMA(1, 1, 2)(1, 2, 2, 12) - AIC: 1076.1189428614498
SARIMA(1, 1, 2)(2, 0, 0, 12) - AIC: 1121.764821224034
SARIMA(1, 1, 2)(2, 0, 1, 12) - AIC: 1123.3694375952498
SARIMA(1, 1, 2)(2, 0, 2, 12) - AIC: 1116.7972313569892
SARIMA(1, 1, 2)(2, 1, 0, 12) - AIC: 1111.1158306501698
SARIMA(1, 1, 2)(2, 1, 1, 12) - AIC: 1092.3660862654624
SARIMA(1, 1, 2)(2, 1, 2, 12) - AIC: 1079.0130249350134
SARIMA(1, 1, 2)(2, 2, 0, 12) - AIC: 1162.6774659761627
SARIMA(1, 1, 2)(2, 2, 1, 12) - AIC: 1094.317376279384
SARIMA(1, 1, 2)(2, 2, 2, 12) - AIC: 1080.5158193373125
SARIMA(1, 2, 0)(0, 0, 0, 12) - AIC: 1325.7493708745649
SARIMA(1, 2, 0)(0, 0, 1, 12) - AIC: 1269.8542150759474
SARIMA(1, 2, 0)(0, 0, 2, 12) - AIC: 1212.6685429922004
SARIMA(1, 2, 0)(0, 1, 0, 12) - AIC: 1412.7919429250555
SARIMA(1, 2, 0)(0, 1, 1, 12) - AIC: 1228.689590603405
SARIMA(1, 2, 0)(0, 1, 2, 12) - AIC: 1173.6661983250654
SARIMA(1, 2, 0)(0, 2, 0, 12) - AIC: 1577.0677346121922
SARIMA(1, 2, 0)(0, 2, 1, 12) - AIC: 1311.5678829622698
SARIMA(1, 2, 0)(0, 2, 2, 12) - AIC: 1145.4337229134599
SARIMA(1, 2, 0)(1, 0, 0, 12) - AIC: 1270.1063714392492
SARIMA(1, 2, 0)(1, 0, 1, 12) - AIC: 1271.1994090409003
SARIMA(1, 2, 0)(1, 0, 2, 12) - AIC: 1212.6980641180426
SARIMA(1, 2, 0)(1, 1, 0, 12) - AIC: 1288.1968461202648
SARIMA(1, 2, 0)(1, 1, 1, 12) - AIC: 1230.689541598925
SARIMA(1, 2, 0)(1, 1, 2, 12) - AIC: 1167.6627914605792
SARIMA(1, 2, 0)(1, 2, 0, 12) - AIC: 1397.9081407603167
SARIMA(1, 2, 0)(1, 2, 1, 12) - AIC: 1266.196321746363
SARIMA(1, 2, 0)(1, 2, 2, 12) - AIC: 1147.4341181051254
SARIMA(1, 2, 0)(2, 0, 0, 12) - AIC: 1212.4436653725024
SARIMA(1, 2, 0)(2, 0, 1, 12) - AIC: 1212.953426897719
SARIMA(1, 2, 0)(2, 0, 2, 12) - AIC: 1214.6979260538953
SARIMA(1, 2, 0)(2, 1, 0, 12) - AIC: 1192.0941081533642
SARIMA(1, 2, 0)(2, 1, 1, 12) - AIC: 1179.7515955975232
SARIMA(1, 2, 0)(2, 1, 2, 12) - AIC: 1169.311399066732
SARIMA(1, 2, 0)(2, 2, 0, 12) - AIC: 1234.5374576508407
SARIMA(1, 2, 0)(2, 2, 1, 12) - AIC: 1169.516629290918
SARIMA(1, 2, 0)(2, 2, 2, 12) - AIC: 1166.6056344345773
SARIMA(1, 2, 1)(0, 0, 0, 12) - AIC: 1230.7069089189795
SARIMA(1, 2, 1)(0, 0, 1, 12) - AIC: 1175.4821876441201
SARIMA(1, 2, 1)(0, 0, 2, 12) - AIC: 1118.3225862270142
SARIMA(1, 2, 1)(0, 1, 0, 12) - AIC: 1318.8299691007978
SARIMA(1, 2, 1)(0, 1, 1, 12) - AIC: 1142.4571776969935
SARIMA(1, 2, 1)(0, 1, 2, 12) - AIC: 1091.9262979598843
SARIMA(1, 2, 1)(0, 2, 0, 12) - AIC: 1478.2898575591194
SARIMA(1, 2, 1)(0, 2, 1, 12) - AIC: 1228.493803573788
SARIMA(1, 2, 1)(0, 2, 2, 12) - AIC: 1067.5789453391549
SARIMA(1, 2, 1)(1, 0, 0, 12) - AIC: 1180.7105053328264
SARIMA(1, 2, 1)(1, 0, 1, 12) - AIC: 1175.7438243985405
SARIMA(1, 2, 1)(1, 0, 2, 12) - AIC: 1119.3499514338105
SARIMA(1, 2, 1)(1, 1, 0, 12) - AIC: 1209.6465199748409
SARIMA(1, 2, 1)(1, 1, 1, 12) - AIC: 1145.8539126672968
SARIMA(1, 2, 1)(1, 1, 2, 12) - AIC: 1083.7393585926163
SARIMA(1, 2, 1)(1, 2, 0, 12) - AIC: 1323.3141503541124
SARIMA(1, 2, 1)(1, 2, 1, 12) - AIC: 1190.3113487800656
SARIMA(1, 2, 1)(1, 2, 2, 12) - AIC: 1069.106113485948
SARIMA(1, 2, 1)(2, 0, 0, 12) - AIC: 1122.7306101796435
SARIMA(1, 2, 1)(2, 0, 1, 12) - AIC: 1123.8622743951305
SARIMA(1, 2, 1)(2, 0, 2, 12) - AIC: 1120.8364391494822
SARIMA(1, 2, 1)(2, 1, 0, 12) - AIC: 1110.1421564663472
SARIMA(1, 2, 1)(2, 1, 1, 12) - AIC: 1095.1718447233357
SARIMA(1, 2, 1)(2, 1, 2, 12) - AIC: 1084.9599671028993
SARIMA(1, 2, 1)(2, 2, 0, 12) - AIC: 1160.8729919666405
SARIMA(1, 2, 1)(2, 2, 1, 12) - AIC: 1095.9273334534926
SARIMA(1, 2, 1)(2, 2, 2, 12) - AIC: 1086.9409862029274
SARIMA(1, 2, 2)(0, 0, 0, 12) - AIC: 1227.8340048264704
SARIMA(1, 2, 2)(0, 0, 1, 12) - AIC: 1172.4420973159768
SARIMA(1, 2, 2)(0, 0, 2, 12) - AIC: 1113.5899443653384
SARIMA(1, 2, 2)(0, 1, 0, 12) - AIC: 1315.4196943831123
SARIMA(1, 2, 2)(0, 1, 1, 12) - AIC: 1139.7130683019263
SARIMA(1, 2, 2)(0, 1, 2, 12) - AIC: 1087.081159616581
SARIMA(1, 2, 2)(0, 2, 0, 12) - AIC: 1474.0329351200155
SARIMA(1, 2, 2)(0, 2, 1, 12) - AIC: 1222.8148275231733
SARIMA(1, 2, 2)(0, 2, 2, 12) - AIC: 1062.8280374328024
SARIMA(1, 2, 2)(1, 0, 0, 12) - AIC: 1182.5184820415539
SARIMA(1, 2, 2)(1, 0, 1, 12) - AIC: 1171.8484857121114
SARIMA(1, 2, 2)(1, 0, 2, 12) - AIC: 1115.2272553566204
SARIMA(1, 2, 2)(1, 1, 0, 12) - AIC: 1211.5092718330209
SARIMA(1, 2, 2)(1, 1, 1, 12) - AIC: 1141.5608979859658
SARIMA(1, 2, 2)(1, 1, 2, 12) - AIC: 1076.7061249785338
SARIMA(1, 2, 2)(1, 2, 0, 12) - AIC: 1325.2463927749186
SARIMA(1, 2, 2)(1, 2, 1, 12) - AIC: 1184.9634753604282
SARIMA(1, 2, 2)(1, 2, 2, 12) - AIC: 1064.0806091623817
SARIMA(1, 2, 2)(2, 0, 0, 12) - AIC: 1124.4242016167684
SARIMA(1, 2, 2)(2, 0, 1, 12) - AIC: 1125.5740636388748
SARIMA(1, 2, 2)(2, 0, 2, 12) - AIC: 1116.2692478684787
SARIMA(1, 2, 2)(2, 1, 0, 12) - AIC: 1111.1494400383935
SARIMA(1, 2, 2)(2, 1, 1, 12) - AIC: 1096.6445255241945
SARIMA(1, 2, 2)(2, 1, 2, 12) - AIC: 1080.7195947237478
SARIMA(1, 2, 2)(2, 2, 0, 12) - AIC: 1155.0056115851626
SARIMA(1, 2, 2)(2, 2, 1, 12) - AIC: 1096.412148848525
SARIMA(1, 2, 2)(2, 2, 2, 12) - AIC: 1082.5726482227942
SARIMA(2, 0, 0)(0, 0, 0, 12) - AIC: 1234.4737227808619
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 0)(0, 0, 1, 12) - AIC: 1183.6764525315316
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 0)(0, 0, 2, 12) - AIC: 1132.073527790566
SARIMA(2, 0, 0)(0, 1, 0, 12) - AIC: 1315.56901185883
SARIMA(2, 0, 0)(0, 1, 1, 12) - AIC: 1146.3003941427974
SARIMA(2, 0, 0)(0, 1, 2, 12) - AIC: 1098.1674920647708
SARIMA(2, 0, 0)(0, 2, 0, 12) - AIC: 1471.2577684462226
SARIMA(2, 0, 0)(0, 2, 1, 12) - AIC: 1227.4696767345854
SARIMA(2, 0, 0)(0, 2, 2, 12) - AIC: 1072.1223309430657
SARIMA(2, 0, 0)(1, 0, 0, 12) - AIC: 1180.2498202932572
SARIMA(2, 0, 0)(1, 0, 1, 12) - AIC: 1179.9938265688925
SARIMA(2, 0, 0)(1, 0, 2, 12) - AIC: 1127.8329406425482
SARIMA(2, 0, 0)(1, 1, 0, 12) - AIC: 1203.1354072496913
SARIMA(2, 0, 0)(1, 1, 1, 12) - AIC: 1143.6215429447948
SARIMA(2, 0, 0)(1, 1, 2, 12) - AIC: 1092.6221564865612
SARIMA(2, 0, 0)(1, 2, 0, 12) - AIC: 1316.0506182669012
SARIMA(2, 0, 0)(1, 2, 1, 12) - AIC: 1185.4833169083936
SARIMA(2, 0, 0)(1, 2, 2, 12) - AIC: 1074.1222845156453
SARIMA(2, 0, 0)(2, 0, 0, 12) - AIC: 1121.8918857481635
SARIMA(2, 0, 0)(2, 0, 1, 12) - AIC: 1123.284299477989
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 0)(2, 0, 2, 12) - AIC: 1125.2545367058472
SARIMA(2, 0, 0)(2, 1, 0, 12) - AIC: 1106.9609339913445
SARIMA(2, 0, 0)(2, 1, 1, 12) - AIC: 1091.7790200491845
SARIMA(2, 0, 0)(2, 1, 2, 12) - AIC: 1087.1526087538375
SARIMA(2, 0, 0)(2, 2, 0, 12) - AIC: 1156.2644191645309
SARIMA(2, 0, 0)(2, 2, 1, 12) - AIC: 1090.0569786510987
SARIMA(2, 0, 0)(2, 2, 2, 12) - AIC: 1089.2769502228941
SARIMA(2, 0, 1)(0, 0, 0, 12) - AIC: 1236.4184803882538
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(0, 0, 1, 12) - AIC: 1181.5534298648479
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(0, 0, 2, 12) - AIC: 1128.1285293980322
SARIMA(2, 0, 1)(0, 1, 0, 12) - AIC: 1317.4543991806254
SARIMA(2, 0, 1)(0, 1, 1, 12) - AIC: 1143.1445007016184
SARIMA(2, 0, 1)(0, 1, 2, 12) - AIC: 1095.1645235665142
SARIMA(2, 0, 1)(0, 2, 0, 12) - AIC: 1473.1193681440404
SARIMA(2, 0, 1)(0, 2, 1, 12) - AIC: 1223.2058985500053
SARIMA(2, 0, 1)(0, 2, 2, 12) - AIC: 1067.5584382176062
SARIMA(2, 0, 1)(1, 0, 0, 12) - AIC: 1182.154704707992
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(1, 0, 1, 12) - AIC: 1181.8246535597557
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(1, 0, 2, 12) - AIC: 1125.773709753221
SARIMA(2, 0, 1)(1, 1, 0, 12) - AIC: 1205.0927852995296
SARIMA(2, 0, 1)(1, 1, 1, 12) - AIC: 1145.1427546227637
SARIMA(2, 0, 1)(1, 1, 2, 12) - AIC: 1089.0780088309346
SARIMA(2, 0, 1)(1, 2, 0, 12) - AIC: 1318.0506173737276
SARIMA(2, 0, 1)(1, 2, 1, 12) - AIC: 1187.4388819396472
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(1, 2, 2, 12) - AIC: 1069.5842776351064
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(2, 0, 0, 12) - AIC: 1123.824684756145
SARIMA(2, 0, 1)(2, 0, 1, 12) - AIC: 1125.3611248504046
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 1)(2, 0, 2, 12) - AIC: 1127.3185527428739
SARIMA(2, 0, 1)(2, 1, 0, 12) - AIC: 1108.166933167227
SARIMA(2, 0, 1)(2, 1, 1, 12) - AIC: 1093.277871804367
SARIMA(2, 0, 1)(2, 1, 2, 12) - AIC: 1088.8189090830706
SARIMA(2, 0, 1)(2, 2, 0, 12) - AIC: 1157.4105437579346
SARIMA(2, 0, 1)(2, 2, 1, 12) - AIC: 1091.2820669723576
SARIMA(2, 0, 1)(2, 2, 2, 12) - AIC: 1090.7116582223994
SARIMA(2, 0, 2)(0, 0, 0, 12) - AIC: 1229.1133724928159
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(0, 0, 1, 12) - AIC: 1178.0868543984877
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(0, 0, 2, 12) - AIC: 1134.9045079599427
SARIMA(2, 0, 2)(0, 1, 0, 12) - AIC: 1311.3636071083588
SARIMA(2, 0, 2)(0, 1, 1, 12) - AIC: 1141.1349275595355
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(0, 1, 2, 12) - AIC: 1090.2270108714952
SARIMA(2, 0, 2)(0, 2, 0, 12) - AIC: 1468.613132499469
SARIMA(2, 0, 2)(0, 2, 1, 12) - AIC: 1219.1340999408199
SARIMA(2, 0, 2)(0, 2, 2, 12) - AIC: 1064.6180103162555
SARIMA(2, 0, 2)(1, 0, 0, 12) - AIC: 1182.8264899704004
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(1, 0, 1, 12) - AIC: 1180.5877768893554
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(1, 0, 2, 12) - AIC: 1122.3114746897104
SARIMA(2, 0, 2)(1, 1, 0, 12) - AIC: 1206.9510357069962
SARIMA(2, 0, 2)(1, 1, 1, 12) - AIC: 1143.1700746926876
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(1, 1, 2, 12) - AIC: 1086.125918309167
SARIMA(2, 0, 2)(1, 2, 0, 12) - AIC: 1319.3007287220341
SARIMA(2, 0, 2)(1, 2, 1, 12) - AIC: 1183.809783625461
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(1, 2, 2, 12) - AIC: 1066.6190737881673
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(2, 0, 0, 12) - AIC: 1124.528963257328
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(2, 0, 1, 12) - AIC: 1125.6698086900142
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(2, 0, 2, 12) - AIC: 1124.1261079952676
SARIMA(2, 0, 2)(2, 1, 0, 12) - AIC: 1109.784081250805
SARIMA(2, 0, 2)(2, 1, 1, 12) - AIC: 1093.4973476194903
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 0, 2)(2, 1, 2, 12) - AIC: 1085.8666426946988
SARIMA(2, 0, 2)(2, 2, 0, 12) - AIC: 1159.3053444352508
SARIMA(2, 0, 2)(2, 2, 1, 12) - AIC: 1092.9663724171105
SARIMA(2, 0, 2)(2, 2, 2, 12) - AIC: 1083.5318341321686
SARIMA(2, 1, 0)(0, 0, 0, 12) - AIC: 1226.652153135218
SARIMA(2, 1, 0)(0, 0, 1, 12) - AIC: 1179.1290766204374
SARIMA(2, 1, 0)(0, 0, 2, 12) - AIC: 1121.5870345182193
SARIMA(2, 1, 0)(0, 1, 0, 12) - AIC: 1315.0748695917077
SARIMA(2, 1, 0)(0, 1, 1, 12) - AIC: 1142.180273415232
SARIMA(2, 1, 0)(0, 1, 2, 12) - AIC: 1093.490250931649
SARIMA(2, 1, 0)(0, 2, 0, 12) - AIC: 1476.4228963292512
SARIMA(2, 1, 0)(0, 2, 1, 12) - AIC: 1226.7602172707534
SARIMA(2, 1, 0)(0, 2, 2, 12) - AIC: 1068.2586184962834
SARIMA(2, 1, 0)(1, 0, 0, 12) - AIC: 1174.961361643169
SARIMA(2, 1, 0)(1, 0, 1, 12) - AIC: 1175.4649302831672
SARIMA(2, 1, 0)(1, 0, 2, 12) - AIC: 1122.1897319113118
SARIMA(2, 1, 0)(1, 1, 0, 12) - AIC: 1203.5773109380345
SARIMA(2, 1, 0)(1, 1, 1, 12) - AIC: 1140.216409309934
SARIMA(2, 1, 0)(1, 1, 2, 12) - AIC: 1088.2095841986775
SARIMA(2, 1, 0)(1, 2, 0, 12) - AIC: 1316.6553052603958
SARIMA(2, 1, 0)(1, 2, 1, 12) - AIC: 1185.0854936668115
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 0)(1, 2, 2, 12) - AIC: 1070.2577134283777
SARIMA(2, 1, 0)(2, 0, 0, 12) - AIC: 1116.17435270023
SARIMA(2, 1, 0)(2, 0, 1, 12) - AIC: 1117.6086983929195
SARIMA(2, 1, 0)(2, 0, 2, 12) - AIC: 1119.552583132843
SARIMA(2, 1, 0)(2, 1, 0, 12) - AIC: 1103.576039136915
SARIMA(2, 1, 0)(2, 1, 1, 12) - AIC: 1086.2578622937235
SARIMA(2, 1, 0)(2, 1, 2, 12) - AIC: 1082.799761604168
SARIMA(2, 1, 0)(2, 2, 0, 12) - AIC: 1151.935587540022
SARIMA(2, 1, 0)(2, 2, 1, 12) - AIC: 1084.7340730693015
SARIMA(2, 1, 0)(2, 2, 2, 12) - AIC: 1084.7981403903998
SARIMA(2, 1, 1)(0, 0, 0, 12) - AIC: 1226.985042993016
SARIMA(2, 1, 1)(0, 0, 1, 12) - AIC: 1176.1366803550386
SARIMA(2, 1, 1)(0, 0, 2, 12) - AIC: 1117.8016495428715
SARIMA(2, 1, 1)(0, 1, 0, 12) - AIC: 1315.5196241022359
SARIMA(2, 1, 1)(0, 1, 1, 12) - AIC: 1139.7965463011192
SARIMA(2, 1, 1)(0, 1, 2, 12) - AIC: 1090.8002115624267
SARIMA(2, 1, 1)(0, 2, 0, 12) - AIC: 1471.318344544196
SARIMA(2, 1, 1)(0, 2, 1, 12) - AIC: 1221.0539162694295
SARIMA(2, 1, 1)(0, 2, 2, 12) - AIC: 1062.1383599710043
SARIMA(2, 1, 1)(1, 0, 0, 12) - AIC: 1175.7155894656398
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 1)(1, 0, 1, 12) - AIC: 1176.7056030519157
SARIMA(2, 1, 1)(1, 0, 2, 12) - AIC: 1119.1407553188437
SARIMA(2, 1, 1)(1, 1, 0, 12) - AIC: 1205.8692063931876
SARIMA(2, 1, 1)(1, 1, 1, 12) - AIC: 1141.7949552967493
SARIMA(2, 1, 1)(1, 1, 2, 12) - AIC: 1084.3688089108164
SARIMA(2, 1, 1)(1, 2, 0, 12) - AIC: 1318.304769001128
SARIMA(2, 1, 1)(1, 2, 1, 12) - AIC: 1186.4919041408853
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 1)(1, 2, 2, 12) - AIC: 1064.7066990493372
SARIMA(2, 1, 1)(2, 0, 0, 12) - AIC: 1117.0318902388801
SARIMA(2, 1, 1)(2, 0, 1, 12) - AIC: 1118.6536734665808
SARIMA(2, 1, 1)(2, 0, 2, 12) - AIC: 1120.6044167535777
SARIMA(2, 1, 1)(2, 1, 0, 12) - AIC: 1105.7004145099177
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 1)(2, 1, 1, 12) - AIC: 1086.8089066297653
SARIMA(2, 1, 1)(2, 1, 2, 12) - AIC: 1083.805542911227
SARIMA(2, 1, 1)(2, 2, 0, 12) - AIC: 1148.5359148216837
SARIMA(2, 1, 1)(2, 2, 1, 12) - AIC: 1086.472184264438
SARIMA(2, 1, 1)(2, 2, 2, 12) - AIC: 1088.134307811798
SARIMA(2, 1, 2)(0, 0, 0, 12) - AIC: 1225.6592861330573
SARIMA(2, 1, 2)(0, 0, 1, 12) - AIC: 1171.6114256652722
SARIMA(2, 1, 2)(0, 0, 2, 12) - AIC: 1110.226043238397
SARIMA(2, 1, 2)(0, 1, 0, 12) - AIC: 1298.943303904589
SARIMA(2, 1, 2)(0, 1, 1, 12) - AIC: 1131.5111285543576
SARIMA(2, 1, 2)(0, 1, 2, 12) - AIC: 1083.2054306704345
SARIMA(2, 1, 2)(0, 2, 0, 12) - AIC: 1460.7749946611225
SARIMA(2, 1, 2)(0, 2, 1, 12) - AIC: 1206.3083397680296
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 2)(0, 2, 2, 12) - AIC: 1055.2972871173502
SARIMA(2, 1, 2)(1, 0, 0, 12) - AIC: 1177.0050739268477
SARIMA(2, 1, 2)(1, 0, 1, 12) - AIC: 1170.514701084226
SARIMA(2, 1, 2)(1, 0, 2, 12) - AIC: 1111.3371178085433
SARIMA(2, 1, 2)(1, 1, 0, 12) - AIC: 1205.1129920404896
SARIMA(2, 1, 2)(1, 1, 1, 12) - AIC: 1133.5154690106974
SARIMA(2, 1, 2)(1, 1, 2, 12) - AIC: 1076.7412573222732
SARIMA(2, 1, 2)(1, 2, 0, 12) - AIC: 1307.4872279987694
SARIMA(2, 1, 2)(1, 2, 1, 12) - AIC: 1180.6231990942083
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 2)(1, 2, 2, 12) - AIC: 1062.3118070138007
SARIMA(2, 1, 2)(2, 0, 0, 12) - AIC: 1114.3291463097487
SARIMA(2, 1, 2)(2, 0, 1, 12) - AIC: 1116.3076187550137
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 2)(2, 0, 2, 12) - AIC: 1113.2509236154876
SARIMA(2, 1, 2)(2, 1, 0, 12) - AIC: 1106.303379061537
SARIMA(2, 1, 2)(2, 1, 1, 12) - AIC: 1086.1172459241416
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 1, 2)(2, 1, 2, 12) - AIC: 1072.3731261132823
SARIMA(2, 1, 2)(2, 2, 0, 12) - AIC: 1158.0411819678154
SARIMA(2, 1, 2)(2, 2, 1, 12) - AIC: 1090.3492691608772
SARIMA(2, 1, 2)(2, 2, 2, 12) - AIC: 1082.0624600759452
SARIMA(2, 2, 0)(0, 0, 0, 12) - AIC: 1303.7871443590668
SARIMA(2, 2, 0)(0, 0, 1, 12) - AIC: 1252.9166721476558
SARIMA(2, 2, 0)(0, 0, 2, 12) - AIC: 1194.984868376605
SARIMA(2, 2, 0)(0, 1, 0, 12) - AIC: 1394.6700635978577
SARIMA(2, 2, 0)(0, 1, 1, 12) - AIC: 1212.306751813165
SARIMA(2, 2, 0)(0, 1, 2, 12) - AIC: 1157.5599909594816
SARIMA(2, 2, 0)(0, 2, 0, 12) - AIC: 1560.2270439190875
SARIMA(2, 2, 0)(0, 2, 1, 12) - AIC: 1299.8792257591012
SARIMA(2, 2, 0)(0, 2, 2, 12) - AIC: 1129.2285087320465
SARIMA(2, 2, 0)(1, 0, 0, 12) - AIC: 1248.6176088775087
SARIMA(2, 2, 0)(1, 0, 1, 12) - AIC: 1250.0352296547742
SARIMA(2, 2, 0)(1, 0, 2, 12) - AIC: 1194.3897764966998
SARIMA(2, 2, 0)(1, 1, 0, 12) - AIC: 1267.4168336106686
SARIMA(2, 2, 0)(1, 1, 1, 12) - AIC: 1209.1480415398169
SARIMA(2, 2, 0)(1, 1, 2, 12) - AIC: 1152.7195515533922
SARIMA(2, 2, 0)(1, 2, 0, 12) - AIC: 1382.1959839343892
SARIMA(2, 2, 0)(1, 2, 1, 12) - AIC: 1246.2476779863619
SARIMA(2, 2, 0)(1, 2, 2, 12) - AIC: 1131.228345981539
SARIMA(2, 2, 0)(2, 0, 0, 12) - AIC: 1189.247814669478
SARIMA(2, 2, 0)(2, 0, 1, 12) - AIC: 1189.1011018039435
SARIMA(2, 2, 0)(2, 0, 2, 12) - AIC: 1190.9882000370958
SARIMA(2, 2, 0)(2, 1, 0, 12) - AIC: 1164.1596210108619
SARIMA(2, 2, 0)(2, 1, 1, 12) - AIC: 1156.344760371727
SARIMA(2, 2, 0)(2, 1, 2, 12) - AIC: 1144.603928050347
SARIMA(2, 2, 0)(2, 2, 0, 12) - AIC: 1204.7719500132466
SARIMA(2, 2, 0)(2, 2, 1, 12) - AIC: 1140.3556020030596
SARIMA(2, 2, 0)(2, 2, 2, 12) - AIC: 1136.901142531931
SARIMA(2, 2, 1)(0, 0, 0, 12) - AIC: 1229.8751511515952
SARIMA(2, 2, 1)(0, 0, 1, 12) - AIC: 1176.8031634502445
SARIMA(2, 2, 1)(0, 0, 2, 12) - AIC: 1118.9428544540708
SARIMA(2, 2, 1)(0, 1, 0, 12) - AIC: 1319.539027595026
SARIMA(2, 2, 1)(0, 1, 1, 12) - AIC: 1143.3002623952054
SARIMA(2, 2, 1)(0, 1, 2, 12) - AIC: 1093.3476888821942
SARIMA(2, 2, 1)(0, 2, 0, 12) - AIC: 1477.7450658857758
SARIMA(2, 2, 1)(0, 2, 1, 12) - AIC: 1229.5302711239397
SARIMA(2, 2, 1)(0, 2, 2, 12) - AIC: 1068.272685884125
SARIMA(2, 2, 1)(1, 0, 0, 12) - AIC: 1177.6263784487192
SARIMA(2, 2, 1)(1, 0, 1, 12) - AIC: 1177.1730230146827
SARIMA(2, 2, 1)(1, 0, 2, 12) - AIC: 1119.7127318389892
SARIMA(2, 2, 1)(1, 1, 0, 12) - AIC: 1206.0747737164563
SARIMA(2, 2, 1)(1, 1, 1, 12) - AIC: 1145.296804778968
SARIMA(2, 2, 1)(1, 1, 2, 12) - AIC: 1085.0387299846002
SARIMA(2, 2, 1)(1, 2, 0, 12) - AIC: 1319.4685216549947
SARIMA(2, 2, 1)(1, 2, 1, 12) - AIC: 1191.9578006118022
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 2, 1)(1, 2, 2, 12) - AIC: 1070.2237885843485
SARIMA(2, 2, 1)(2, 0, 0, 12) - AIC: 1118.039761416192
SARIMA(2, 2, 1)(2, 0, 1, 12) - AIC: 1119.3268083319424
SARIMA(2, 2, 1)(2, 0, 2, 12) - AIC: 1121.323235617162
SARIMA(2, 2, 1)(2, 1, 0, 12) - AIC: 1104.8008215179802
SARIMA(2, 2, 1)(2, 1, 1, 12) - AIC: 1089.7554681606362
SARIMA(2, 2, 1)(2, 1, 2, 12) - AIC: 1086.1884795010092
SARIMA(2, 2, 1)(2, 2, 0, 12) - AIC: 1152.2774885500357
SARIMA(2, 2, 1)(2, 2, 1, 12) - AIC: 1086.5119744092508
SARIMA(2, 2, 1)(2, 2, 2, 12) - AIC: 1086.449655839379
SARIMA(2, 2, 2)(0, 0, 0, 12) - AIC: 1228.1481818009315
SARIMA(2, 2, 2)(0, 0, 1, 12) - AIC: 1173.318748356809
SARIMA(2, 2, 2)(0, 0, 2, 12) - AIC: 1112.0945246508286
SARIMA(2, 2, 2)(0, 1, 0, 12) - AIC: 1314.5602084902791
SARIMA(2, 2, 2)(0, 1, 1, 12) - AIC: 1141.014053431779
SARIMA(2, 2, 2)(0, 1, 2, 12) - AIC: 1087.447647446746
SARIMA(2, 2, 2)(0, 2, 0, 12) - AIC: 1469.55702610512
SARIMA(2, 2, 2)(0, 2, 1, 12) - AIC: 1225.0395260079865
SARIMA(2, 2, 2)(0, 2, 2, 12) - AIC: 1064.6614027495798
SARIMA(2, 2, 2)(1, 0, 0, 12) - AIC: 1179.1794687141619
SARIMA(2, 2, 2)(1, 0, 1, 12) - AIC: 1173.843410145089
SARIMA(2, 2, 2)(1, 0, 2, 12) - AIC: 1113.732761686236
SARIMA(2, 2, 2)(1, 1, 0, 12) - AIC: 1206.2683168899355
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 2, 2)(1, 1, 1, 12) - AIC: 1144.1510209267649
SARIMA(2, 2, 2)(1, 1, 2, 12) - AIC: 1078.7058496716413
SARIMA(2, 2, 2)(1, 2, 0, 12) - AIC: 1321.736186992774
SARIMA(2, 2, 2)(1, 2, 1, 12) - AIC: 1185.9298055267136
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
SARIMA(2, 2, 2)(1, 2, 2, 12) - AIC: 1066.3971899598587
SARIMA(2, 2, 2)(2, 0, 0, 12) - AIC: 1118.3849469381053
SARIMA(2, 2, 2)(2, 0, 1, 12) - AIC: 1119.7640781447465
SARIMA(2, 2, 2)(2, 0, 2, 12) - AIC: 1115.1871622240242
SARIMA(2, 2, 2)(2, 1, 0, 12) - AIC: 1107.6700023955286
SARIMA(2, 2, 2)(2, 1, 1, 12) - AIC: 1089.9734207392398
SARIMA(2, 2, 2)(2, 1, 2, 12) - AIC: 1081.8522223744822
SARIMA(2, 2, 2)(2, 2, 0, 12) - AIC: 1148.4782608982675
SARIMA(2, 2, 2)(2, 2, 1, 12) - AIC: 1083.5731869065223
SARIMA(2, 2, 2)(2, 2, 2, 12) - AIC: 1083.8394403537395
Best SARIMA model - AIC: (2, 1, 2), (0, 2, 2, 12), 1055.2972871173502
/usr/local/lib/python3.10/dist-packages/statsmodels/base/model.py:607: ConvergenceWarning:
Maximum Likelihood optimization failed to converge. Check mle_retvals
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-16-0ee908b777d3> in <cell line: 49>()
47 predictions = model_fit.predict(len(df['Close']), len(df['Close'])+29)
48
---> 49 predictions.summary()
50
51
/usr/local/lib/python3.10/dist-packages/pandas/core/generic.py in __getattr__(self, name)
5900 ):
5901 return self[name]
-> 5902 return object.__getattribute__(self, name)
5903
5904 def __setattr__(self, name: str, value) -> None:
AttributeError: 'Series' object has no attribute 'summary'
# plot the predictions
plt.figure(figsize=(10, 5))
plt.plot(df["Close"], label='Actual')
plt.plot(predictions, color="red", label='Predicted')
plt.xlabel('Date')
plt.ylabel('Close Price')
plt.title(f'{ticker} Stock Price')
plt.legend(loc='upper left')
plt.show()