Analysis of the high order ADL(<i>p, q</i>) models used to describe connections between time series

Abstract

In the paper the mathematical models describing connection between two time series are researched. At first each of them is investigated separately, and the ARIMA(p, d, q) model is constructed. These models are based on the time series characteristics obtained during the analysis stage. The connection between two time series is confirmed with the aid of cointegration statistical tests. Then the mathematical model of the connection between series is constructed. The ADL(p, q) model describes this dependence. It’s shown that for the time series under investigation the orders p, q of the ADL(p, q) model are connected with the ARIMA(p, d, q) orders of the describing each series separately. This step makes the set of the investigated ADL(p, q) models much smaller. In the previous papers it was also shown that the ARIMA(p, d, q) automatical fitting functions in popular packages use limitations on the p, q orders of the time series process: q ≤ 5, p ≤ 5. The wish to use the simplest models is also built in the structure of the Akaike (AIC) and Bayes (BIC) informational criteria. In the paper the maximal values of the ADL(p, q) model orders are supposed to be the orders of the appropriate ARIMA(p, d, q) series. In the previous work it was shown that using high order ARIMA(p, d, q) it is possible to fit the models better. In this paper the experiments on the ADL(p, q) models construction are presented. The wage index and money income index time series pair is researched, and also the gas, water and energy production and consumption index/real agricultural production index pair is investigated. The data in the 2000–2018 time period is taken from the dynamic series of macroeconomic statistics of the Russian Federation.

Keywords

• dynamic series of macroeconomic statistics of the russian federation
• arima
• adl
• ardl
• cointergration
• time series
• akaike informational criterion