Multivariate Time-Series Modelling

In the attempt to increase the production of the industrial sector to accommodate human needs; motor vehicles and power plants have led to the decline of air quality. The tremendous decline of air pollution levels can adversely affect human health, especially children, those elderly, as well as patients suffering from asthma and respiratory problems. As such, the air pollution modelling appears to be an important tool to help the local authorities in giving early warning, apart from functioning as a guide to develop policies in near future. Hence, in order to predict the concentration of air pollutants that involves multiple parameters, both artificial neural network (ANN) and principal component regression (PCR) have been widely used, in comparison to classical multivariate time series. Besides, this paper also presents comprehensive literature on univariate time series modelling. Overall, the classical multivariate time series modelling has to be further investigated so as to overcome the limitations of ANN and PCR, including univariate time series methods in short-term prediction of air pollutant concentrations.

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Multivariate Time Series Modelling with Seasonal Univariate Components; Evidence from Nigeria GDP

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2019/v5i430140 ◽

2019 ◽

pp. 1-20

Author(s):

Taofikat Abidemi Azeez ◽

Yusuf Olufemi Olusola ◽

Hamzat Kayode Idris ◽

Salawu Monsuru Micheal

Keyword(s):

Time Series ◽

Multivariate Time Series ◽

Positive Association ◽

Information Criteria ◽

Strong Positive Correlation ◽

Positive Correlation ◽

Pairwise Correlation ◽

Time Series Modelling ◽

Adf Test ◽

Time Plot

The patterns of GDP variables are graphically examined using time plot presented the time plot for the GDP variables concerning time presented a combined single time plot for all the considered GDP variables. The relationship, as well as the degree of relationship between/among the GDP variables, was further revealed by computing the pairwise correlation. Based on the output, each variable when crossed classified with itself have a strong positive correlation with an output of (1), while pairwise correlation reveals a positive figure with the least estimate being (0.3149), this implies that for all the variables there exist a positive correlation. All the pairwise relationship reveals a strong positive association with all the estimates revealing a value between (0.8-0.9) except ‘trade and industry' that shows a positive relationship but not strong with an estimate of (0.3149). The initial test in fitting a time series model is to examine the series for stationarity. The Augmented Dickey-Fuller test revealed that ‘Agriculture’, ‘Construction’, and Services’” satisfies the requirement of stationarity while the series ‘industry and “Trade” are non-stationary initially but later became stationary after the application of the first difference transformation which was confirmed after the application of the ADF test to the first differenced series. The Johansen co-integration's Trace test was employed to determine the order of co-integration and it was revealed that the series are cointegrated hence presentation of the equation of integration. We presented the lag length estimation criteria which revealed that the lag length of order 5 is appropriate for the VAR model as suggested by Akaike Information Criteria (AIC), Hannan-Quinn (HQ) Information Criteria, Schwarz Information Criteria (SC). The VAR(5) model was fitted for all the considered GDP variables.

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Multivariate Time Series Modelling of Nigerian Gross Domestic Product (GDP) and Some Macroeconomic Variables

African Journal of Mathematics and Statistics Studies ◽

10.52589/ajmss-0bvpbd9k ◽

2021 ◽

Vol 4 (3) ◽

pp. 12-31

Author(s):

Anthony U. ◽

Emediong U.

Keyword(s):

Time Series ◽

Gross Domestic Product ◽

Crude Oil ◽

Multivariate Time Series ◽

Domestic Product ◽

Economic Sectors ◽

Vector Autoregressive ◽

Macroeconomic Variables ◽

Distributed Lag ◽

Time Series Modelling

This paper focused on modelling Nigeria’s Gross Domestic Product and some macroeconomic variables, which include, Agriculture, Crude Oil/Mineral Gas and Telecommunication using different classes of multivariate time series models. Multi-Dependent Linear Regression Model (MLRM), Vector Autoregressive Model (VARM) and Multivariate Autoregressive Distributed Lag Models (MARDLM) have been fitted to the multivariate time series. The basic statistics of the estimates and errors reveal the competitiveness of VARM and MARDLM. This was also evidently using the model selection criteria. But the mean square error of forecast places VARM on a higher comparative advantage than MARDLM. The results of the Granger causality tests showed that Crude Oil/Mineral Gas granger causes Gross Domestic Product and also granger causes Agriculture, but not vice versa in each case. This paper establishes the fact that Crude Oil/Mineral Gas is a good predictor of Gross Domestic Product and Agriculture as a major contributor to the nation’s economic development. The need to consistently juxtapose causal relationships between major economic sectors and Gross Domestic Product is vehemently advocated for proper evaluation of sectorial contributions and formulation of economic driven policy in the country.

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