Predictive Model with Square-Root Variance Stabilizing Transformation for Nigeria Crude Oil Export to America
Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 5, October 2017, Pages: 174-180
Received: Jan. 20, 2017;
Accepted: Sep. 19, 2017;
Published: Nov. 5, 2017
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Obinna Adubisi, Department of Mathematics and Statistics, Faculty of Pure & Applied Sciences, Federal University Wukari, Wukari, Nigeria
Titus Terkaa Mom, Department of Mathematics and Statistics, Faculty of Pure & Applied Sciences, Federal University Wukari, Wukari, Nigeria
Chidi Emmanuel Adubisi, Department of Physics, Faculty of Physical Science, University of Ilorin, Ilorin, Nigeria
Phillip Luka, Department of Mathematics and Statistics, Faculty of Pure & Applied Sciences, Federal University Wukari, Wukari, Nigeria
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In the last few decades, crude oil has claimed the topmost position in Nigerian export list, constituting a very fundamental change in the structure of Nigerian international trade. In this study, secondary data on monthly crude oil export to the United States was obtained from the Energy Information Administration (EIA) database. Using the Box-Jenkins (ARIMA) methodology, the results showed that Seasonal ARIMA (0, 1, 1) (1, 0, 1)12 model had the least information criteria after the data was Square-Root transformed and non-seasonally first differenced in order to achieve series stationarity. The diagnostic tests on the selected model residuals revealed the residuals are normally distributed uncorrelated random shocks.
Transformation, SARIMA, Unit Root, Crude Oil Export, ARCH-LM
To cite this article
Titus Terkaa Mom,
Chidi Emmanuel Adubisi,
Predictive Model with Square-Root Variance Stabilizing Transformation for Nigeria Crude Oil Export to America, Science Journal of Applied Mathematics and Statistics.
Vol. 5, No. 5,
2017, pp. 174-180.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Central Intelligence Agency (2013). United States central Intelligence Agency (CIA) World Fact-book, www.cia.gov.
Vanguard Nigeria (2016): Importing Nigeria crude oil. http://www.vanguardngr.com/2016/us-importing-nigeria-crude-oil.
Adubisi (2016). Modelling the growth pattern of reserve currency in Nigeria. FUW Trends in Sciences & Technology Journal. 1(1): 130 – 133.
Iheanyichukwu S. Iwueze, Eleazar C. Nwogu and Valentine U. Nlebedim (2013). Time Series Modelling of Nigeria External Reserves. CBN Journal of Applied Statistics 4 (2).
Daniya Tiegenova (2014). Forecasting Exchange Rates Using Time Series Analysis. The sample of the currency of Kazakhstan.
Kumar Manoj and Anand Manhu (2012). An application of time Series ARIMA Forecasting model for predicting sugarcane production in India. Studies in Business and Economics. 81-94.
Adubisi and E. T. Jolayemi (2015). Estimating the impact on the Nigeria Crude oil Export from 2002 to 2013. (An ARIMA-Intervention Analysis). International Journal of Scientific and Engineering Research. 6(10): 878-886.
Smart (2013). Modelling and Forecasting Maternal Mortality; An Application of ARIMA Models, International Journal of Applied Science and Technology. 3(1): 19 – 28.
O. D. Adubisi, C. C. Eleke, T. T. Mom and C. E. Adubisi (2017). Application of SARIMA to modelling and forecasting money circulation in Nigeria. Asian Research Journal of Mathematics. 6(1): 1–10. DOI: 10.9734/ARJOM/2017/35555.
EIA (2009). Energy Information Administration (EIA); World oil statistics. OPEC, Zurich, Switzerland. Obtained from www.Eia.org on 24/8/2016.
Box G. E. P and Cox D. R (1964): An analysis of transformations. Journal of the Royal statistical society, series B 26(2): 211 – 252.
Yan L (2015): Variance stabilizing properties of Box-Cox transformation for dependent observations. Advances in science, Technology and Environmentology. B12 (3): 63 – 70.
Carroll R. J and Ruppert D (1960): On prediction and the power transformation family. Biometrika 68: 609 – 615.
Nishii R (2001): Box-Cox transformation Encyclopaedia of Mathematics, Springer, ISBN: 978-1-55-608-010-4.
Sakia R. M (1992): The Box-Cox transformation technique: A review. The statistician. 41: 169 – 178.
Bickel P. J and Doksum K. A (1981): An analysis of transformation revisited. Journal of the American statistical Association. 76(374): 296 – 311.
Box G. E. P & Jenkins G. M (1976). Time series Analysis Forecasting and Control, Revised edn. Holden-Day, San Francisco-USA. ISBN: 0816211043.
Box G. E. P, Jenkins G. M & Reinsel G. C (1994). Time series Analysis Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs, New Jersey-USA.
Pankratz, A. (1983). Forecasting with Univariate Box-Jenkins model: concepts and case, John Wiley and Sons, ISBN: 0471090239, New-York-USA.
Dickey D. A & Fuller W. A (1979). Distribution of the Estimators for Autoregressive time series with a unit root. Journal of the American statistics Association. 7(366): 427 431. JSTOR: 2286348.
Kwiatkowski D., Phillips, P. C. B, Schmidt P., and Shin Y. (1992). Testing the Null Hypothesis of Stationarity against the Alternative of a unit Root. Journal of Econometrics 54: 159-178.
Ljung G. M and Box G. E. P (1978). On a measure of a lack of fit in Time Series Models. Biometrika. 65 (2): 297 – 303. Doi: 10.1093/biomet/65.2.297
Shapiro, S. S., and Wilk, M. B. (1965): “An analysis of variance test for normality (complete samples). Biometrika 52(3-4): 591-611 doi 10.1093/biomet/52.3-4.591. JSTOR 2333709. MR205384. p. 593.
Engle R: (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, (50): 987-1008.