How to determine the values for seasonal order P, D, Q, s in SARIMAX model

Determining the optimal values for seasonal order (P, D, Q, s) in your SARIMAX model requires an iterative approach involving data exploration, diagnostics, and model fitting. Here's a breakdown of each parameter and considerations for finding their values:

Seasonal Order (P, D, Q, s):

P (Seasonal Autoregressive): This parameter captures the seasonality pattern in the lags of the dependent variable. Determining P involves examining the autocorrelation function (ACF) and partial autocorrelation function (PACF) at seasonal lags (multiples of the seasonality period). Look for significant spikes at these lags to identify the appropriate P value.

D (Seasonal Differencing): Similar to differencing for trend removal, seasonal differencing eliminates non-stationary seasonality. Analyze the ACF and PACF at seasonal lags after applying differencing. If these functions show no significant spikes, you may have reached the desired level of seasonal stationarity.

Q (Seasonal Moving Average): This parameter accounts for the seasonality in the error terms. Examine the ACF and PACF of the residuals after fitting a tentative model with P and D values. Look for significant spikes to determine the appropriate Q value.

s (Seasonality): This parameter represents the length of the seasonal period. It should be based on the known seasonality in your data (e.g., daily, weekly, monthly, yearly).

Steps to Determine Seasonal Order:

Visualize autocorrelation and partial autocorrelation: Plot the ACF and PACF of your data to identify potential seasonality patterns. Look for spikes at seasonal lags (multiples of s).

Start with tentative values: Begin with P=0, D=0, and Q=0.

Fit a model with tentative values: Fit a SARIMAX model with the chosen P, D, and Q values.

Analyze residuals: Examine the ACF and PACF of the residuals after fitting the model.

Iterate and adjust: Based on the ACF and PACF of the residuals, adjust P, D, and Q accordingly. If significant spikes remain, increase P or Q. If differencing appears necessary, increase D.

Compare models: Fit models with different seasonal order combinations and compare their performance using metrics like AIC, BIC, or RMSE. Choose the model with the lowest information criterion or error.

Additional Tips:

Utilize tools like statsmodels.tsa.seasonal to decompose your data into trend, seasonal, and residual components.

Consider using automated methods like statsmodels.tsa.statespace.sarimax.autofit for initial parameter suggestions (be cautious and evaluate their suggestions).

Experiment with different seasonal periods (s) based on your data domain knowledge.

Remember, the best seasonal order depends on the specific characteristics of your time series data.

references:

Gemini, ChatGPT