Modeling of forecasts variance reduction at multiple time series prediction averaging with ARMA (1, q) functions

Abstract

Combination of time series forecasts is usually considered as good technique in practice. But it has got weak theoretical explanation. In this research variance of time series forecasts and variance of combined models are considered. One is interested in the view of variance of forecasts function over one, two and three periods. Conditions which can lead to improvement of averaged time series predictions are in scope of this research. In this paper a few examples of the most popular time series models are observed: the moving average models MA(q), the autoregressions AR(p) models and their combination in the form of ARIMA(p, d, q) or ARMA(p, q) model. In particular, AR(1) and ARMA(1, q) are investigated. Nowadays there are researches about time series averaging. Approaches based on bagging and boosting are implemented very often in classification and regressions. It’s very appealing to use such strategy in tine series modeling. At the same time it’s easy to construct learning set and test set in classification tasks. But it’s a complex task in case of time series processing. There’s a need of two sets: to train time series models and to construct their combinations. Thus nowadays combination of time series models, combination of their forecasts or of their prediction intervals are in scope of view of a few complex researches. In this paper we investigate behaviour of time series predictions’ variance in order to have another useful approach in time series prediction averaging. Russian macroeconomical time series statistics is used as experimental time series.