New 2-parameter families of advanced forecasting functions: seasonal/nonseasonal models, comparison to the exponential smoothing and ARIMA models, and application to stock market data
Nabil Kahouadji, Associate Professor of Mathematics, Northeastern Illinois University
Abstract: We introduce twenty-four new two-parameter families of advanced time series forecasting functions, using three forecast estimate methods along with eight optimization criteria. We also introduce the concept of powering and derive non-seasonal and seasonal time series models with examples in education, sales, economics, industry and finance. We compare the performance of our twenty-four functions/models to both exponential smoothing and ARIMA models using non-seasonal and seasonal time series. We show in particular that our models not only do not require a decomposition of a seasonal time series into trend, seasonal and random components, but also leads to substantially lower sum of absolute error and a higher number of closer forecasts than both Holt--Winters and ARIMA models. Finally, we apply and compare the performance of our twenty-four models using five-year stock market data of 467 companies of the S&P500.