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Archives of Business Research – Vol. 9, No. 10

Publication Date: October 25, 2021

DOI:10.14738/abr.910.11085.

Tuaneh, G. L., Essi, I. D., & Etuk, E. H. (2021). Markov-Switching Vector Autoregressive (MS-VAR) Modelling (Mean Adjusted):

Application to Macroeconomic data. Archives of Business Research, 9(10). 261-274.

Services for Science and Education – United Kingdom

Markov-Switching Vector Autoregressive (MS-VAR) Modelling

(Mean Adjusted): Application to Macroeconomic data

Tuaneh, Godwin Lebari

Dept. of Agricultural and Applied Economics

Rivers State University, PMB 5080, Port Harcourt, Nigeria

Essi,Isaac Didi

Dept. of Mathematics, Rivers State University

PMB 5080, Port Harcourt, Nigeria

Etuk, Ette Harrison

Dept. of Mathematics, Rivers State University

PMB 5080, Port Harcourt, Nigeria

ABSTRACT

Researchers very often model economic relationships using linear models. Even

when non-linear models are used, they hardly consider the possibility of regimes,

the transmission from one regime to another and also the duration of stay in a

particular regime. These are not captured by linear models. To address this, we

applied the Markov-Switching Mean Vector Autoregressive Model to model and

estimate the interdependence between macroeconomic variables (International

Trade and Macroeconomic Stability) within the context of the Nigerian economy.

Specifically, the study analyzed the trends of total export, total import, exchange

rate, and inflation rate in Nigeria within the study period, Estimated MSM-VAR

models on the study variables and selected the best model using information

criteria. The study empirically investigated the interdependence existing among

the study variables; determined the probabilities of transition from one regime to

another and the duration of stay in a regime; the study ascertained the relative

significance of each random innovation in affecting the study variables. Monthly

time series data of 246 months spanning through January 2000 to June 2020 were

collected from the Central Bank of Nigeria Statistical Bulletin. The study used the

Markov-Switching Mean Vector Autoression in the Analysis. The results showed

that all variables were stationary at first difference. The study chose 2 regimes and

the model selection criteria selected [MS(2)-MVAR(2)]. The variables were largely

self-explanatory and very strongly exogenous.

Keywords: Markov-Switching Variance Autoregressive Model (MS-VAR), MSM-VAR,

International Trade, Macroeconomic Stability, Nigeria

INTRODUCTION

The dynamic interdependence existing between two or more macroeconomic variables is

commonly modelled linearly without recourse to the existence of regimes. Consequently, the

models are inappropriate with incomplete structural inference. Tuaneh and Essi (2021)

reported that linear models ignore the unobservable state, regime switches and duration of stay

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Archives of Business Research (ABR) Vol. 9, Issue 10, October-2021

Services for Science and Education – United Kingdom

in a regime. The linear econometric methods often adopted by researchers suggest that the

variables considered are always increasing or always decreasing. The periods of normalcy are

not reflected. To bridge this gap in the literature, this study adopted a Multivariate Markov- Switching VAR (MS-VAR) model proposed by (Krolzig, 1997) to determine a regime-dependent

dynamic interdependence between total export, total import, exchange rate and inflation rate.

The MS-VAR is a flexible nonlinear multivariate framework that allows the parameters of the

model to vary over time and according to different regimes determined by an often disregarded

unobservable state variable.

There are basically two classes of the MS-VAR; the Markov-Switching Intercept VAR Model and

the Markov-Switching Mean VAR. Model. The main focus of the study was to apply the Markov- Switching Mean VAR Model, in modelling and estimating the interdependence between

macroeconomic variables (International Trade and Macroeconomic Stability) within the

context of the Nigerian economy. The study adopted total export and total import as proxies for

International trade while exchange rate and inflation rate were used as proxies for

Macroeconomic Stability Specifically, it is the objective of the study to analyze the trends of total

export, total import, exchange rate and inflation rate in Nigeria within the study period,

Estimate the MSM-VAR models of total export, total import, exchange rate and inflation rate,

and select the best model using information criteria, empirically investigate the

interdependence existing between exchange rate and inflation in Nigeria and determine the

probabilities of transition from one regime to another and the duration of stay in a regime. It is

also our view to ascertain the relative significance of each random innovation in affecting the

variables of the study.

MS-VAR models are used for prediction when there is state transmission (from an observable

state to an unobservable state). The model describes a non-linear data generation process as

piecewise linear through the restriction of the process to be linear in each state. The mechanism

that produces the state is stochastic and is assumed differently. MS-VAR is a generalization of

the basic finite VAR model of order p. the idea is that when the process is regime dependent,

the stable VAR model might be inappropriate. The MS-VAR class of models has an underlying

data generating process of an observed time series vector �! which depend upon an

unobservable regime �# . Observational equations do not completely describe the data- generating process. The models are formulated allowing deducing the evolution of regimes

(Clement and Krolzig, 2002)

LITERATURE

Markov Switching Vector Autoregressive (MS-VAR) models have been applied to complex

multivariate systems. In a series of papers, Krolzig (1997, 1998, 2000, and 2001) and Clement

and Krolzig (2002) discuss the characterization and the tested business cycle asymmetries

using the MS-VAR models. Series of authors, Krolzig (2001), Tilmann (2003) Chen and Shen

2007, Kiganda, Obange and Adhiambo 2017 used MS-VAR in macroeconomic research.

Tarsa and Bayat (2015) studied Inflation Targeting for Turkey, they analyzed the behaviour of

the inflation rate in Turkey using monthly data spanning from January 2003 to August 2014.

The study used the Markov Switching Intercept Autoregression (MSI-AR). The study identified

two regimes and the results showed that the regime changes were slow in turkey.