The study applied Autoregressive Integrated Moving Average Intervention in modelling crude oil prices in Nigeria spanning the period from January 1986 to June 2017. The time plot of the series showed an abrupt increase in the series and this called for intervention modelling. The data was divided into three set (actual series, pre-intervention and post-intervention series). The Augmented Dickey Fuller (ADF) was used to test for unit root on each of the series and were all found to be non-stationary at levels, they (actual, pre and post- intervention series) were however non stationary at first difference. Eighteen models were estimated and the best model was the pre-intervention model that minimise the Akaike information criterion (AIC) (ARIMA (111)) with AIC of (4.4.578). The plot of the residual correlogram showed adequacy of the model. The model was adequate since there was no spike that cut the level of the correlogram and the histogram of the residual was normally distributed with probability values (0.0000).

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Modelling the Nigeria Crude Oil Prices Using ARIMA, Pre-intervention and Post-intervention Model

This study compares the Seasonal autoregressive integrated moving average (SARIMA) model within Fourier time series model in modelling rainfall data in Port Harcourt Rivers State from 2000-2014. The time plot of the series showed Seasonality but a not obvious trend. The raw data is nonstationary at the level. Time plot of the seasonal differencing of rainfall at lag12 showed a stationary process with seasonality at lag 12 on the PACF and ACF of the series. The periodogram plot reveals that there exist both short and long term cycles within the period. The Fourier series and the seasonal autoregressive moving average models are reduced to 12month of seasonal component.(s = q = 12 ) The Akaike Information Criterion (AIC) was used to select better models. The best model is the model that minimises the information criterion. It was observed that SARIMA (1,0,1)(1,1,1)12 models have a minimum AIC value. Hence, SARIMA model performs better in modelling the rainfall data in Port Harcourt then the Fourier series models.

/pdf/a-comparative-study-of-fourier-series-models-and-seasonal-35r1s15vzr.pdf

A Comparative Study of Fourier Series Models and Seasonal -Autoregressive Integrated Moving Average Model of Rainfall Data in Port Harcourt

In this study we want to analyze effects of change in exchange rates on the export, import, product prices and others macroeconomic variables. The method which has been used in this study is based on co integration method and vector autoregressive method. In this study first the long-term relationships between variables are determined and then the short-term relationship between variables will be determined according to Impulse response functions.The results show that changes in exchange rates affect on macro economic variables, while there were no effects from exchange rate on macro economical variables.

/pdf/study-the-effect-of-trade-policies-on-export-and-import-in-4yojh3gcwt.pdf

Study the Effect of Trade Policies on Export and Import in Iran

The interdependence among oil prices, exchange rates and inflation rates, and their response to shocks, was a cause of concern. Unrestricted Vector Autoregression (UVAR) was employed to analyse this interactions as well as to investigate the pattern of causality among the study variable. Annual data spanning from 1981 to 2017 was sourced from the Statistical Bulletin of the Central Bank of Nigeria. Pre-estimation analysis showed that all variables were integrated of order one 1(1), and there no cointegrating relationship. The inverse root of AR characteristic polynomial showed a stable VAR model. All lag length selection criteria chose a lag length of 1. The UVAR estimates and the test of significance particularly the granger causality test indicated significant influence and uni-directional effect from oil price to exchange rates. The Wald statistics, showed significant own shocks, and the impulse response showed that all variables were instantaneously affected by own shocks. Exchange rate was instantaneously affected by oil price; however, it ruled out the response in inflation rate to contemporaneous shocks in oil price. The variance decomposition further showed that at least 93.1%, 97.1% and 92.4% of the impulse response in oil price, exchange rate, and inflation rate respectively were from own shocks in the long run. The post estimation analysis showed that the VAR model was multivariate normal, the residual was homoscedastic, and there was no serial autocorrelation. It was recommended that the government should diversify the national income stream and consider policies that will control inflation.

/pdf/unrestricted-vector-autoregressive-modelling-of-the-2sw0sgrni7.pdf

Unrestricted Vector Autoregressive Modelling of the Interaction among Oil Price, Exchange Rate and Inflation in Nigeria (1981–2017)

To model Nigeria crude oil prices, this analysis compared univariate linear models to univariate nonlinear models. The data for this analysis was gathered from the Central Bank of Nigeria (CBN) Monthly Statistical Bulletin. The upward and downward movement in the series revealed by the time plot suggests that the series exhibit a regime-switching pattern: the cycle of expansion and contraction. At lag one, the Augmented Dickey-Fuller test was used to test for stationarity. For univariate linear ARIMA (p, d, q)) and univariate nonlinear MS-AR, seven models were estimated for the linear model and two for the non-linear model. The best model was chosen based on the criterion of least information criterion, AIC (2.006612), SC (2.156581), and the maximum log-likelihood of (-150.5480) for the crude oil prices were used to pick MS-AR (1) for the series. In analysing crude oil prices data, the MS-AR model proposed by Hamilton outperforms the linear autoregressive models proposed by BoxJenkins. The model was used to predict the series' values over a one-year cycle (12 months).

/pdf/linear-and-non-linear-modelling-of-nigerian-crude-oil-prices-1ybnrpqy4a.pdf

Linear and Non-Linear Modelling of Nigerian Crude Oil Prices

The dynamic behaviour of macroeconomic stability indicators particularly their; evolution, interaction and interdependence, obviously cause shocks among themselves. This study is a multivariate time-series modelling and investigation of the interaction and pattern of causality among exchange rates, inflation rate, interest rates, and implicit price deflator in Nigeria using unrestricted Variance Autoregression (VAR). Quarterly data on the variables spanning the period from 1981 to 2016 were sourced from CBN Statistical bulletin and used for the study. The study used both descriptive and analytical design. The result of the inverse root of AR characteristic polynomial indicated that the VAR model was stable. The Trace Statistics and Max Eigen result showed no co-integrating relationship. The Schwarz Information Criterion showed a lag length of 2. The VAR estimates indicated that the exchange rate was significantly affected by its first lag and second lag, while inflation rates was significantly affected by its first lag. The Wald statistics showed that both lags of each variable were jointly significant in affecting itself. The impulse response showed that all variables were instantaneously affected by own shocks, however, it ruled out the Original Research Article Tuaneh; AJEBA, 9(4): 1-17, 2018; Article no.AJEBA.46515 2 response in exchange rate to contemporaneous shocks in inflation rate, interest rate and implicit price deflator. The variance decomposition further showed that at least 80% of the impulse response were from own shocks. It was consequently recommended that government should regulates interest rates and exchange rates.

https://www.journalajeba.com/index.php/AJEBA/article/download/29140/54782

Vector Autoregressive Modelling of the Interaction among Macroeconomic Stability Indicators in Nigeria (1981-2016)

The risks associated with exchange rate and money market indicators have drawn the attentions of econometricians, researchers, statisticians, and even investors in deposit money banks in Nigeria. The study targeted at modeling exchange rate and Nigerian deposit banks money market dynamics using trivariate form of multivariate GARCH model. Data for the period spanning from 1991 to 2017 on exchange rate (Naira/Dollar) and money market indicators (Maximum and prime lending rate) were sourced for from the central bank of Nigeria (CBN) online statistical database. The study specifically investigated; the dynamics of the variance and covariance of volatility returns between exchange rate and money market indicators in Nigeria were examine whether there exist a linkage in terms of returns and volatility transmission between exchange rate and money market indicators in Nigeria and compared the difference in Multivariate BEKK GARCH considering restrictive indefinite under the assumption of normality and that of student’s –t error distribution.  Preliminary time series checks were done on the data and the results revealed the present of volatility clustering. Results reveal the estimate of the maximum lag for exchange rate and money market indicators were 4 respectively. Also, the results confirmed that there were two co-integrating equations in the relationship between the returns on exchange rate and money market indicators.  The results of the diagonal MGARCH –BEKK estimation  confirmed  that diagonal MGARCH –BEKK in students’-t was  the best fitted and an appropriate model for modeling exchange rate and Nigerian deposit money market dynamics using trivariate form of multivariate GARCH model. Also, the study confirmed presence of two directional volatility spillovers between the two sets of variables.

/pdf/modeling-exchange-rate-and-nigerian-deposit-money-market-2ip2h4ojjj.pdf

Godwin Lebari Tuaneh

Papers

Modelling the Nigeria Crude Oil Prices Using ARIMA, Pre-intervention and Post-intervention Model

Vector Autoregressive Modelling of the Interaction among Macroeconomic Stability Indicators in Nigeria (1981-2016)

Modeling Exchange Rate and Nigerian Deposit Money Market Dynamics Using Trivariate form of Multivariate GARCH Model