Improvement of time series forecasting quality by means of multiple models prediction averaging

Abstract

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.

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

“…Among four tested models with orders q<4 there are signs of terms: 1 0   2 times and 1 0   also 2 times, 1 0   3 times (for ARIMA(1, 1, 0) it's zero), 2 0   for the both models with non-zero MA (2) term. Here, we expect that averaging is going to be good practice because signs of AR(1) part vary.…”

“…Also, again one can see that parameters of combined models are close to traits of the model with the highest order of moving average part. Various approaches to averaging technique have also been tested in [2].…”

“…Though, mathematical statement of this problem isn't researched well. There are attempts to choose the best model [1], to construct mean model [2], to implement bagging strategy to processed models of certain time series [3,4]. Selection of the best model is traditional way but in practice there's always a lot of models and there's no mathematically strict way to choose the best one.…”

Reduction of time series forecast variance by the case of ArDL(p, q) models

“…The main requirements to the series X, Y are the same as in the case of regression models [10,11]. Forecast is made just setting today values of time series into equation (1). Its variance calculation is based on the assumption of normally distributed error.…”

“…Nowadays combination of models belonging to one type has been handled well. The simplest combination function in case of time series processing is just averaging of all models' predictions or selection of the best one [1]. Approaches to implementation of the bagging and boosting principles [2,3] in order to construct better time series models than original ones (and usually implemented in time series analysis) have already been published [4][5][6][7].…”