Grid Search for SARIMAX Parameters for Photovoltaic Time Series Modeling

Abstract

The SARIMAX (Seasonal Autoregressive Integrated Moving Average with eXogenous regressors) model is a time series model that can be used to forecast future values of a time series, given its past values. It is beneficial for modeling time series data that exhibits seasonality and incorporating additional exogenous variables (variables that are not part of the time series itself but may affect it). One way to optimize the performance of a SARIMAX model is to use a grid search approach to find the best combination of hyperparameters for the model. A grid search involves specifying a set of possible values for each hyperparameter and then training and evaluating the model using all possible combinations of these values. The combination of hyperparameters that results in the best model performance can then be chosen as the final model. To perform a grid search for a SARIMAX model, you must define the grid of hyperparameters you want to search over. This will typically include the values of the autoregressive (AR) and moving average (MA) terms and the values of any exogenous variables you want to include in the model. We will also need to define a metric to evaluate the model's performance, such as mean absolute or root mean squared error. Once we have defined the grid of hyperparameters and the evaluation metric, you can use a grid search algorithm (such as a brute force search or a more efficient method such as random search or Bayesian optimization) to evaluate the performance of the model using all possible combinations of hyperparameters. The combination of hyperparameters that results in the best model performance can then be chosen as the final model. In this article, we will explore the potential of SARIMAX for PV time series modeling. The objective is to find the optimal set of hyperparameters. Grid Search passes all hyperparameter combinations through the model individually and checks the results. Overall, it returns the collection of hyperparameters that yield the most outstanding results after running the model. One of the most optimal SARIMAX (p,d,q) x (P, D, Q,s) combinations is SARIMAX (0,0,1) x (0,0,0,4).