Volume 7, Issue 1, February 2019, Page: 1-7
Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya
Muthuri Evans Kithure, Faculty of Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Waititu, Faculty of Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya, Faculty of Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Oct. 18, 2018;       Accepted: Nov. 8, 2018;       Published: May 23, 2019
DOI: 10.11648/j.sjams.20190701.11      View  531      Downloads  112
Taxation is one of the means by which governments finance their expenditure by imposing charges on citizens and corporate entities. Kenya Revenue Authority (KRA) is the agency responsible for the assessment, collection and accounting for of all revenues that are due to government. Volatile government revenue is a challenge for fiscal policy makers since it creates risks to government service provision and can make planning difficult, as revenue falls short of expenditure needs both frequently and unexpectedly. The main objective of this study was to model and forecast the volatility of VAT revenue collected in Kenya as well as computing its value at risk and the expected shortfall. Secondary data on daily VAT revenue collections for a period of 3 years was analyzed. The first step was to model the mean equation of the return series using the ARIMA model and ARIMA(3,0,3) was identified to be the most suitable since it had the least values of AIC and BIC. The Lagrange Multiplier test confirmed the presence of ARCH effects using the residuals of the mean equation. A number of heteroscedastic models were fitted and the TGARCH family (ARIMA(3,0,3)/TGARCH(1,2)) was preferred to fit the volatility of the returns. One step ahead forecasting of volatility of the returns was done using the model which gave a value of 7.212. Estimation of value at risk and expected shortfall involved use of POT method by fitting a GPD function to the return data series. The first step was determination of threshold by use of MRL plot and later fitting a GPD function to the return data series using the threshold. The shape, location and scale parameters were estimated using MLE and they were later used to compute the VaR loss and ES at 95% and 99% confidence intervals. The VaR at 95% and 99% was 1.45% and 1.49% respectively while the ES at both the intervals was 0.04% and 0.1% respectively. This study concluded that volatility is persistent in the daily VAT revenue collections and it can easily be modelled using conditional heteroscedastic models.
Autoregressive Conditional Heteroscedasticity (ARCH), Expected Shortfall (ES), Threshold Generalized Autoregressive Conditional Heteroscedasticity (TGARCH), Value at Risk (VaR)
To cite this article
Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya, Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya, Science Journal of Applied Mathematics and Statistics. Vol. 7, No. 1, 2019, pp. 1-7. doi: 10.11648/j.sjams.20190701.11
Copyright © 2019 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/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
G. C. &. N. R. D. Cornia, State tax revenue growth and volatility, Federal Reserve Bank of St. Louis Regional Economic Development, 2010.
ICPAK, "Kenya's revenue analysis 2010-2015," A Historical Perspective to, 2015.
R. A. R. Adhikari, An introductory study on time series modeling.
R. F. Engle, "Autoregressive conditional heteroscedasticity with estimates," Journal of the Econometric Society, pp. 987-1007, 1982.
T. Bollerslev, "Generalized autoregressive conditional heteroskedasticity," Journal of econometrics, pp. 307-327, 1986.
D. B. Nelson, "Conditional heteroskedasticity in asset returns," Journal of the Econometric Society, pp. 347-370, 1991.
G. e. a. Ali, "Egarch, gjr-garch, tgarch, avgarch, ngarch, igarch," Journal of Statistical and, pp. 57-73, 2013.
e. a. M. Gilli, "An application of extreme value theory for measuring financial rik," Computational Economics , pp. 207-228, 2006.
E. p. R. Norberg, "Modelling extremal events for insurance and finance," The Journal of the IAA, pp. 285-286, 1998.
D. E. G. F. Ren, "Extreme value analysis of daily canadian crude oil prices," Applied Financial Economics, p. 941-954, 2010.
Browse journals by subject