Bootstrapped Holt Method with Autoregressive Coefficients Based on Harmony Search Algorithm

Abstract

Exponential smoothing methods are one of the classical time series forecasting methods. It is well known that exponential smoothing methods are powerful forecasting methods. In these methods, exponential smoothing parameters are fixed on time, and they should be estimated with efficient optimization algorithms. According to the time series component, a suitable exponential smoothing method should be preferred. The Holt method can produce successful forecasting results for time series that have a trend. In this study, the Holt method is modified by using time-varying smoothing parameters instead of fixed on time. Smoothing parameters are obtained for each observation from first-order autoregressive models. The parameters of the autoregressive models are estimated by using a harmony search algorithm, and the forecasts are obtained with a subsampling bootstrap approach. The main contribution of the paper is to consider the time-varying smoothing parameters with autoregressive equations and use the bootstrap method in an exponential smoothing method. The real-world time series are used to show the forecasting performance of the proposed method.