Autocovariances and Autocorrelation Properties of Diagonal Vector Autoregressive and Multivariate Autoregressive Distributed Lag Models

Abstract

The primary aim of this study was to conduct a comparative analysis of the performance of parsimonious models, specifically the Diagonal Vector Autoregressive (VAR) and Multivariate Autoregressive Distributed Lag (MARDL) Models, using their respective Autocovariance and Autocorrelation properties. This comparison was driven by the imposition of restrictions on parameters within the coefficient matrices, specifically limiting them to diagonal elements. To assess the efficacy of these novel multivariate lag models, we utilised data derived from key macroeconomic variables, including Nigeria's Gross Domestic Product (GDP), Crude Oil Petroleum (C/PET), Agriculture (AGRIC), and Telecommunication (TELECOM). The data was subjected to first-order differencing of the logarithm of the series to ensure stationarity. Subsequently, the models were estimated, and autocovariances and autocorrelations of the processes were derived for the analysis. The empirical findings revealed notable patterns, particularly the direct converse autocorrelation observed in both VAR and MARDL models. The negative autocorrelation identified in the macroeconomic variables suggests that periods of economic expansion were succeeded by contractions and vice versa. This implies a complementary relationship between the two models in effectively capturing the dynamics of multivariate lag variables. In conclusion, our study underscores the significance of considering the Diagonal Vector Autoregressive and Multivariate Autoregressive Distributed Lag Models with restricted parameters in the diagonal elements when modelling multivariate lag variables. These findings contribute to a nuanced understanding of the interplay between economic variables and provide valuable insights for researchers and practitioners in the field.