Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya

Muthuri Evans Kithure; Anthony Waititu; Anthony Wanjoya

doi:doi:10.11648/j.sjams.20190701.11

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Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya

Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya

Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 1)

Received: 18 October 2018 Accepted: 8 November 2018 Published: 23 May 2019

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Abstract

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.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 1)
DOI	10.11648/j.sjams.20190701.11
Page(s)	1-7
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Autoregressive Conditional Heteroscedasticity (ARCH), Expected Shortfall (ES), Threshold Generalized Autoregressive Conditional Heteroscedasticity (TGARCH), Value at Risk (VaR)

References

[1]	G. C. &. N. R. D. Cornia, State tax revenue growth and volatility, Federal Reserve Bank of St. Louis Regional Economic Development, 2010.
[2]	ICPAK, "Kenya's revenue analysis 2010-2015," A Historical Perspective to, 2015.
[3]	R. A. R. Adhikari, An introductory study on time series modeling.
[4]	R. F. Engle, "Autoregressive conditional heteroscedasticity with estimates," Journal of the Econometric Society, pp. 987-1007, 1982.
[5]	T. Bollerslev, "Generalized autoregressive conditional heteroskedasticity," Journal of econometrics, pp. 307-327, 1986.
[6]	D. B. Nelson, "Conditional heteroskedasticity in asset returns," Journal of the Econometric Society, pp. 347-370, 1991.
[7]	G. e. a. Ali, "Egarch, gjr-garch, tgarch, avgarch, ngarch, igarch," Journal of Statistical and, pp. 57-73, 2013.
[8]	e. a. M. Gilli, "An application of extreme value theory for measuring financial rik," Computational Economics , pp. 207-228, 2006.
[9]	E. p. R. Norberg, "Modelling extremal events for insurance and finance," The Journal of the IAA, pp. 285-286, 1998.
[10]	D. E. G. F. Ren, "Extreme value analysis of daily canadian crude oil prices," Applied Financial Economics, p. 941-954, 2010.

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Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya. (2019). Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Science Journal of Applied Mathematics and Statistics, 7(1), 1-7. https://doi.org/10.11648/j.sjams.20190701.11

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ACS Style

Muthuri Evans Kithure; Anthony Waititu; Anthony Wanjoya. Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Sci. J. Appl. Math. Stat. 2019, 7(1), 1-7. doi: 10.11648/j.sjams.20190701.11

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AMA Style

Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya. Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Sci J Appl Math Stat. 2019;7(1):1-7. doi: 10.11648/j.sjams.20190701.11

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@article{10.11648/j.sjams.20190701.11,
  author = {Muthuri Evans Kithure and Anthony Waititu and Anthony Wanjoya},
  title = {Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.sjams.20190701.11},
  url = {https://doi.org/10.11648/j.sjams.20190701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190701.11},
  abstract = {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.},
 year = {2019}
}

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TY  - JOUR
T1  - Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya
AU  - Muthuri Evans Kithure
AU  - Anthony Waititu
AU  - Anthony Wanjoya
Y1  - 2019/05/23
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190701.11
DO  - 10.11648/j.sjams.20190701.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20190701.11
AB  - 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.
VL  - 7
IS  - 1
ER  -

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Author Information

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

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APA Style

Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya. (2019). Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Science Journal of Applied Mathematics and Statistics, 7(1), 1-7. https://doi.org/10.11648/j.sjams.20190701.11

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ACS Style

Muthuri Evans Kithure; Anthony Waititu; Anthony Wanjoya. Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Sci. J. Appl. Math. Stat. 2019, 7(1), 1-7. doi: 10.11648/j.sjams.20190701.11

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AMA Style

Muthuri Evans Kithure, Anthony Waititu, Anthony Wanjoya. Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya. Sci J Appl Math Stat. 2019;7(1):1-7. doi: 10.11648/j.sjams.20190701.11

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@article{10.11648/j.sjams.20190701.11,
  author = {Muthuri Evans Kithure and Anthony Waititu and Anthony Wanjoya},
  title = {Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.sjams.20190701.11},
  url = {https://doi.org/10.11648/j.sjams.20190701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190701.11},
  abstract = {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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya
AU  - Muthuri Evans Kithure
AU  - Anthony Waititu
AU  - Anthony Wanjoya
Y1  - 2019/05/23
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190701.11
DO  - 10.11648/j.sjams.20190701.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20190701.11
AB  - 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.
VL  - 7
IS  - 1
ER  -

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