ABSTRACT
Autoregressive integrated moving average (ARIMA) method is a widely used time series forecasting technique. Most of the time, we try different combinations of parameters (p, d, q) and (P, D, Q) and select the best model mostly based on the likelihood score. The best model's performance with respect to the data is, however, measured in real-life applications usually using the mean absolute percentage error (MAPE) criterion. This chapter deals with ARIMA time series models. We present a multiobjective deterministic pseudo-evolutionary algorithm to generate offspring time series from a certain number of best performing parent models, based on criterion such as MAPE or maximum absolute percentage error, and using the relative fitness values of parents obtained deterministically. The best seasonal/nonseasonal ARIMA models become the parent models from which offspring time series are generated. We then obtain for the training data set a netfront containing the nondominated set of solutions derived from offspring and parent time series, and hence we obtain the nondominated set of forecasted time series for the user's test data set, by using the nondominated set of solutions obtained earlier for the training data set.
