A Theoretical Analysis of the Stationarity of an Unrestricted Autoregression Process

TL;DR

This paper provides a theoretical framework for understanding the stationarity conditions of high-dimensional autoregressive models with time-dependent coefficients, highlighting how parameter choices influence stationarity and model predictability.

Contribution

It offers a novel theoretical analysis of stationarity conditions for autoregressive processes with increasing lag dependence and variable coefficients, extending existing econometric models.

Findings

Stationarity depends on specific relations between coefficients and model dimension.

Parameter $oldsymbol{eta}$ bounds are determined by the choice of $oldsymbol{eta}$ and $oldsymbol{eta}$.

The bounds on $oldsymbol{eta}$ influence the number of lags used for prediction.

Abstract

The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive process of dimension $k>1$ having a sequence of coefficients $\beta$ multiplied by successively increasing powers of $0<\delta<1$. The theorem gives the conditions of stationarity in simple relations between the coefficients and $k$ in terms of $\delta$. Computationally, the evidence of stationarity depends on the parameters. The choice of $\delta$ sets the bounds on $\beta$ and the number of time lags for prediction of the model.