Markov-Switching Vector Autoregressive (MS-VAR) Modelling (Mean Adjusted): Application to Macroeconomic data

This book chapter compares the out-of-sample forecast for inflation rates in Nigeria using ARIMAX and ARIMA models. To achieve this, Annual Data on Exchange Rate, Inflation Rate, Interest Rate and Unemployment Rate from 1981 to 2017 was sourced from Central Bank of Nigeria (CBN). The analysis used data from 1981 to 2010 while 2011 to 2017 was used to valid the forecast from the ARIMA and ARIMAX models. The preliminary analysis revealed that natural log transform of inflation rate is normally distributed and stationary at first difference while Exchange Rate, Inflation Rate, Interest Rate and Unemployment Rate were used as exogenous variables in the ARIMAX models. The following models ARIMA(1,1,0), ARIMA(1,1,1), ARIMA(0,1,1), ARIMAX(1,1,0), ARIMAX(1,1,1) and ARIMAX(0,1,1) were compared for both in-sample and out-of-sample forecasts. Using the Root Mean Square Error (RMSE) as selection criteria, ARIMAX(0,1,1) with RMSE of 0.6810 emerged as superior model for the in-sample forecast for forecasting inflation rate in Nigeria while ARIMA(1,1,1) emerged as a superior model for the out-of-sample forecast for inflation rate in Nigeria and its forecast for inflation revealed a negative growth in inflation in Nigeria. This study therefore recommended ARIMA(1,1,1) model be used for out-of-sample forecast for inflation rate in Nigeria.

Purpose. Chronic budget deficit and rising inflation have been the major problems of government in Nigeria with their implication for significant macroeconomic variables. The government’s efforts in curbing these problems have not yielded the expected result. Thus, this study investigated the inflationary effects of the budget deficit in Nigeria. Methodology. Augmented-Dickey Fuller test, Bound Test and Autoregressive Distributed Lag test (ARDL) were used for analysis. Data were sourced from Central Bank of Nigerian Statistical Bulletin from 1986 to 2019.Finding and Implication. A long-run dynamic relationship was established between the budget deficit and the inflation rate in Nigeria, Based on findings, long run movement was discovered between budget deficit and inflation in Nigeria. It was established that rising budget deficit lead to inflationary pressure in Nigeria. Thus, there is need for government to work assiduously and diligently in ensuring balance in national budget. Originality and Limitation. This study contributed to existing study by investigating the dynamic inflationary effects of budget deficit in Nigeria and the adoption of important deficit financing variables. This study mainly focused on inflation rate without looking at the effect of budget deficit on other macroeconomic variables. Thus, future studies should focus on other macroeconomic variables like unemployment rate and balance of payments.

This paper investigates the asymmetric exchange rate pass-through (ERPT) to inflation in Nigeria. The study employed Autoregressive Distributed Lag (ARDL) and Nonlinear ARDL (NARDL) models from 2010Q1 to 2024Q2. The analysis incorporates key policy changes, such as the 2023 exchange rate unification, and explores both the short- and long-run impacts of exchange rate fluctuations on food and headline inflation. In particular, the study highlights the response and pass-through periods of exchange rate shocks, with depreciation demonstrating a stronger and more immediate effect on inflation than on appreciation. Results reveal that exchange rate depreciation exerts significant cost-push pressures, with a pass-through effect observed within 3 to 4 quarters, while the effect of appreciation is weaker and more prolonged. This asymmetry is especially pronounced for food inflation, where the dependency on imported goods accelerates the transmission of exchange rate shocks to consumer prices. The study also finds that cumulative depreciation has a much more pronounced effect on inflation. At the same time, appreciation offers minimal relief, reflecting Nigeria’s vulnerability to exchange rate volatility due to its reliance on imports. The findings show the importance of managing exchange rate fluctuations to control inflation, particularly given the asymmetry in how depreciation and appreciation affect prices. By providing a comprehensive analysis of both long- and short-run dynamics, this study contributes to the understanding of ERPT in Nigeria, offering insights for policymakers to implement targeted interventions to mitigate inflationary pressures in the context of exchange rate instability.

The prevailing occurrence of high inflation rates and unstable exchange rate in Nigeria have given rise to this topic "the interaction between inflation rate and exchange rate in Nigeria using autoregressive lagged ordered model (ARLOM)".The variables used are monthly time series data from 1995m1-2022m12.The analysis shows that the variables are stationary after first difference and there exist co-integration between variables as the estimated error term are stationary at level using Engle-Granger co-integration test.Also it was found that the short run error term (SRET) is statistically significant at 5% level indicating a short run interaction between the variables.In the long run, exchange rate has significant impact on inflation rate in Nigeria.Therefore, the study recommends that government should enact adequate monetary and structural policy especially in the aspect of corruption and insecurity.The implementation of these policies will attract foreign investors boost economic competitiveness and strengthen the naira in the global market.The outcome of these implementation will lead to stable exchange rate and pricing system in the country.

This study empirically analysed the effect of monetary policy on inflation in Nigeria; 1970 – 2018. The objective is to determine the effectiveness of monetary policy instruments on inflation in Nigeria. In doing this, relevant literature was reviewed and theoretical relationship between monetary policy and inflation was established following the quantity theory of money by Irving Fisher. The study employed time series data sourced from the statistical bulletin of Central bank of Nigeria (CBN) 2018. Stationarity test was also conducted on the time series data to determine the order of integration using Augmented Dickey Fuller (ADF) test. The unit root test revealed that inflation rate was stationary at level i.e. I(0) while monetary policy rate, treasury bill rate and cash reserve ratio were stationary at first difference i.e. I(1). The estimated results showed that there is cointegration between monetary policy variables and inflation rate in Nigeria. The results revealed that Monetary Policy Rate (MPR) was statistically significant in the short run after first difference, which indicates that monetary policy rate (MPR) exerts significant effect on inflation in Nigeria in the short run. Based on these findings, the study concluded that monetary policy variables alone are not sufficient enough in maintaining price stability in Nigeria. Therefore, the Federal government, Central Bank of Nigeria (CBN) and policy makers should simultaneously use monetary and fiscal policy instruments to maintain price stability in Nigeria.

The significant role of agricultural sector cannot be underestimated in any nation. It has been the source of feeding of the populace and income generation for other developmental activities. As a result, various governments have been making concerted efforts to improve economic growth and agricultural productivity through agricultural credit but rarely one can see any improvement in the sector. It is in line with these its fundamental role that this study makes a giant stride to examine the relationship between agricultural credit and economic growth in Nigeria. The study employed time series data from Central Bank of Nigeria, Statistical Bulletin and National Bureau of Statistics which spanned from 1986-2014. This study carried out Auto-Regressive Distributed Lag (ARDL) approach to investigate the variables. The findings showed that short and long run relationship existed between agricultural credit and economic growth in both short and long run respectively. Moreover, real exchange rate and private domestic investment as control variables had direct effect on economic growth whereas inflation rate revealed an inverse relationship in the model. The study concluded that economic growth is influenced by dynamic variables such as credit to agricultural sector, real exchange rate, real interest rate, private domestic investment and inflation rate in Nigeria. The study therefore suggested that concerted efforts should be made by policy makers to increase the level of productivity of agricultural sector in Nigeria through adequate credit to the sector so as to boost the growth of the economy.

The study examines the elements of real exchange rate in Nigeria. The ADF and KPSS stationarity tests were employed to examine the stationary process of each series and it shows that the macroeconomic variables under study have no stochastic trends, hence, are stationary in leves. The result from Johansen cointegration showed a long-run relationship between real exchange rate and the five explanatory variables. R2 of the estimated Fully Modified Ordinary Least Squares (FMOLS) model shows that about 73.39% of the total variability in real exchange rate has been explained by the independent variables and it further revealed that inflation rate and government expenditure contribute more to exchange rate volatility. Our model adjust its prior periods dis-equilibrium at a speed of 56.98% annually with the ec(-1) coefficient value -0.5698; also to achieve long term equilibrium stable state, the VECM shows a significant speed of correction of about 56.98% for adjusting dis-equilibrium annually. The VECM is well specified and its parameter coefficients are not biased because the ARCH test indicates that it is free from serial correlation and heteroscedasticity. Finally, the strong forces that influence real exchange rate fluctuations in Nigeria as revealed bythe Granger causility test are: government expenditure, money supply growth, inflation and real interest rates.

Purpose This study aims to investigate the effect of CBDC issuance on economic growth rate and inflation rate in Nigeria. We are interested in determining whether the rate of economic growth and inflation changed significantly after the issuance of a non-interest bearing CBDC in Nigeria. Design/methodology/approach Two-stage least squares regression and granger causality test were used to analyze the data. Findings Inflation significantly increased in the CBDC period, implying that CBDC issuance did not decrease the rate of inflation in Nigeria. Economic growth rate significantly increased in the CBDC period, implying that CBDC issuance improved economic growth in Nigeria. The financial sector, agricultural sector and manufacturing sector witnessed a much stronger contribution to gross domestic product (GDP) after CBDC issuance. There is one-way granger causality between CBDC issuance and monthly inflation, implying that CBDC issuance causes a significant change in monthly inflation in Nigeria. The implication of the result is that the non-interest bearing eNaira CBDC is not able to solve the twin economic problem of “controlling inflation which stifles economic growth” and “stimulating economic growth which leads to more inflation.” Policy makers should therefore use the eNaira CBDC alongside other monetary policy tools at their disposal to control inflation while stimulating growth in the economy. Originality/value There are no empirical studies on the effect of CBDC issuance on economic growth or inflation using real-world data. We add to the monetary economics literature by analyzing the effect of CBDC issuance on economic growth and inflation.

The impact of oil price shocks on Tehran Stock Exchange returns: Application of the Markov switching vector autoregressive models

This study investigates the relationship between food price indices and inflation in Nigeria, highlighting the significant impact of food price volatility on inflation and economic stability. Annual data from 2008 to 2024 sourced from the Food and Agriculture Organization (FAO) and the Central Bank of Nigeria was used for the analysis. Descriptive analytical tools, multiple linear regression, and time series models were used for the findings. Results showed that the trend of food was upward from 2021, there was significant reduction in the consumption of meat and dairy as revealed by negative skewness of their price indices and the significant difference from the regression outcomes. The findings highlight the importance of addressing price fluctuations to enhance economic resilience and mitigate rising inflation, particularly in a predominantly agrarian economy like Nigeria.

The challenges imposed by the rising cases of unemployment, inflationary rate and less purchasing power in households have stirred considerable interest amongst researchers and actors in contemporary times in designing agreeable mechanism that engenders economic growth. This paper examined the impact of unemployment, inflation and household’s consumption on economic growth for 1960 to 2018. OLS estimation technique was adopted. From the findings, unemployment, inflation and household’s consumption impacted on economic growth. But it was observed that inflation (INF) significantly influence economic growth in Nigeria. However, controlling for the influence of consumer price index (CPI), we observed that it is a key determinant of economic growth. The study therefore recommends for efficient and effective policy mix that may monitor the inflation rate in Nigeria.

This first chapter is devoted to a general introduction into the Markov-switching vector autoregressive (MS-VAR) time series model. In Section 1.2 we present the fundamental assumptions constituting this class of models. The discussion of the two components of MS-VAR processes will clarify their on time invariant vector auto-regressive and Markov-chain models. Some basic stochastic properties of MS-VAR processes are presented in Section 1.3. Finally, MS-VAR models are compared to alternative non-normal and non-linear time series models proposed in the literature. As most non-linear models have been developed for univariate time series, this discussion is restricted to this case. However, generalizations to the vector case are also considered.

Currency fluctuations and inflation are the natural norm for most major economies. Numerous factors influence economic growth, including a country’s exchange rate system performance, the outlook for inflation, and interest rate differentials. These are the most significant factors that hinder the economic growth of every nation. As a result, this analysis investigates the impact of exchange rate and inflation on Nigeria’s growth performance from 1986 to 2021. Impulse response and variance decomposition were estimated. The real gross domestic product (RGDP) was used as a proxy for growth performance, while the inflation rate (IFNR), real exchange rate (REXR), and interest rate (INTR) were also used as proxies. The results of impulse response and variance decomposition estimates in the short-run (third quarter) and long-run (tenth quarter) show that real exchange rate D(REXR), INTR, and IFNR all have a positive impact on RGDP variation, with values of 13.38%, 31.88%, and 22.40%, respectively, in the third quarter. In the long run (the 10th quarter), REXR contributed approximately 28.76% of the variation in RGDP. The interest rate contributed 24.14%, while the IFNR has contributed about 28.27% of the variation in RGDP in the long run. Therefore, summing the contributions of REXR, INTR, and INFR to RGDP, these variables contributed about 81.17% of the variation in RGDP in the long run. Hence, the research concluded that REXR, INTR, and IFNR have a positive effect on growth performance as proxied by RGDP in Nigeria within the period of the research. The research recommended that the government should provide a policy that will reduce the excess growth of aggregate demand (AD) in the economy, which will reduce inflationary pressure, in order to achieve the sustainable development goals (SDGs) of 2030 in Nigeria, which include restoring economic growth and macroeconomic stability through macroeconomic variables such as the exchange rate, inflation, and other significant variables.

Monetary policy can be so dicey or delicate that it requires great tact from the monetary authority. Contractionary monetary policy, when pushed too far, drags the economy to recession while` extreme expansionary monetary policy sinks the economy to liquidity trap. Central banks are in charge and are expected to favorably run the monetary policy by adjusting interest rates, influencing local lending rates, buying foreign currency, printing money, and use of other tools to modulate currency exchange rates, manage inflation, etcetera, with a sole target of creating a healthy economy. This study looks into the effect of money supply rate, exchange rate and interest rate on inflation rate in Nigerian economy between 1991 and 2021. With secondary data, the variables are found to be of mixed order of integration and, therefore, the ARDL model is our parameter estimator. Our model is found to be stable and our empirical investigation reveals that both money supply rate and interest rate in Nigeria have no significant effect on Nigeria’s inflation rate while exchange `rate has a significant inverse effect on Nigeria’s inflation rate – the less favorable the exchange rate, the more biting the inflation. The study is wrapped up `with a recommendation that Nigerian government/authorities should rise up to occasion of fixing the insecurity challenges of the nation so as to create safe environment that can attract local investments as well as foreign direct investments which, among other benefits, will be favorable to Nigeria in exchange rate.

The stability of exchange rate in Nigeria is a significant monetary policy target. The fact that monetary authorities in Nigeria have over the years made various efforts to minimize the huge divergence between the official, interbank/autonomous and parallel/ Bureau De change rates in Nigerian foreign exchange market through different exchange rates regimes such as the overall fixed and flexible exchange rates regimes overtime. Accordingly, this paper investigates the comparative analysis of the impact of fixed and flexible exchange rates management policies on economic growth of Nigeria for the period of 1980A-2016A: using vector error correction model (VECM). The empirical results indicated evidence of long run relationship among the variable of interest in the study and in all there is a positive impact of exchange rates management policies on economic growth of Nigeria. Another finding from the Granger causality test confirms a unidirectional short run causality that runs from real effective exchange rate (REER) to economic growth (RGDP). In addition, unidirectional causality that runs from oil price (OPR) to real interest rate (RIR) in Nigeria also exists. However, the need for policy intervention to review and correct the foreign exchange market segments distortions is highly recommended. Again, the Nigerian economy needs a standard set of export base diversification from its mono cultural oil export in order to boost the foreign exchange earnings of the Nigerian economy.