Quantile Versions of Holt-winters Forecasting Algorithms

We propose new versions of Holt-Winters (HW) and seasonal Holt-Winters (SHW) time series forecasting algorithms. The exponential smoothing construct is identical to HW/SHW, except that the coefficients are estimated by minimizing a given quantile error criterion, instead of the usual squared errors. We call these versions quantile HW/SHW (QHW/QSHW), which amounts to performing HW/SHW under an asymmetric error loss function. We discuss best linear prediction (BLP) for ARIMA models, and highlight some models, where various versions of exponential smoothing are known to be optimal (in the BLP sense). This serves as a guide to models that we should focus on for a simulation study. The simulations compare scaled prediction errors between BLP and QHW, with models driven by Gaussian and Laplace noise. The results show that in most cases QHW gives similar forecasts to BLP. The advantage of QHW over BLP is that the user does not have to a-priori decided on a model for the data. The methodology is illustrated on some real data sets of interest in climatology and finance. A. ALEXANDRE TRINDADE and YANXUN XU 16