Improvement of time series forecasting quality by means of multiple models prediction averaging
2021
Construction of time series models is usually based on Akaike and Bayes information criteria.Requirement of model simplicity is built inside the information criteria structure and the best fitted models aren't always best in terms of criteria values.Often there are a few best models that fit investigated time series well and there's problem of choice between them.Usually information criteria values allow to choose among them.But if one needs the best model by forecasts quality, best fitted models, or there are other thoughts a research has to choose and test models manually.At the same time when a few models are chosen it's possible to construct their combination.The simplest way is to count mean value of their forecasts and to use it as a combined prediction.Practical researches confirm that forecast error gets lower in this approach.Also, more complex construction than averaging of forecasts can be used (for example, weighted voting that is widely used in bagging technique in solution of classification problems).But this approach hasn't got enough theoretical base.From theoretical point of view confidence intervals of time series forecasts (usually here they're considered as prediction intervals) is also very complex task.Intervals tend to be very wide even for models with good prediction quality in terms of mean forecast errors.Thus, prediction intervals are rare in use.In this paper a few time series models are constructed for wage and income indices of Russian macroeconomic time series.Their predictions are combined into one forecast and it's quality is compared to individual ones.Transformation of forecast variance and prediction intervals in case of simple (moving averages MA(q) and autoregressions AR(p) of low order) models is also considered but is a part of further work.