Parameter Estimation of the Exponential Smoothing with Independent Regressors Using R

Abstract

As an extension to the state space approach of the exponential smoothing methods, Osman and King recently introduced a new class of exponential smoothing methods by integrating regressors into the model. For the model to be utilized successfully, it requires a proper estimation procedure. The parameter estimation can be done through optimization using the “optim” function available in R statistical software. The objective of this paper is to discuss the effective use of the “optim” function in estimating parameters of the state space model of the exponential smoothing method augmented with regressors. The study started by considering several sets of optimization R codes to be supplied to the “optim” function. These codes use different set of initial values as the starting points for the optimization routine. The other difference between optimization codes is also in terms of restrictions imposed on the optimization routine. The second phase of the study was done by generating a number of simulated time series data with predetermined parameter values. The final phase of the study was then conducted by applying the optimization codes on all simulated series. By analyzing the performance of each of the optimization codes to accurately estimate parameters, a guideline or suggestion on how to effectively execute “optim” function in R with respect to the use of the new forecasting approach then outlined.