Modeling the Residuals of Financial Time Series with Missing Values for Risk Measures Using R
American Journal of Theoretical and Applied Statistics
Volume 7, Issue 6, November 2018, Pages: 247-255
Received: Nov. 30, 2018;
Accepted: Dec. 14, 2018;
Published: Jan. 10, 2019
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Udokang Anietie Edem, Department of Mathematics and Statistics, School of Applied Science and Technology, Federal Polytechnic, Offa, Nigeria
Ugwuowo Fidelis Ifeanyi, Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria
This paper is to fit an appropriate model on the returns of daily stock price and determine the appropriate model for the residuals in order to compute some risk measures. The daily stock price of First Bank Nigeria, Plc was collected from Nigerian Stock Exchange Market. The methods of weekly average, regression imputation and repetition were used in computing the missing values. Also, adopted was deleting days with missing values. The method of transformation was determined in each of the series and log transformation was adopted for the four series. In the model selection, the ARMA+GARCH model of the repetition had the minimum AIC as compared to other methods of dealing with missing values. The distribution of the residuals was found to be suitable to the Generalized Parato Distribution (GPD). The parameters of this distribution were used in computation of risk measures. The computed Value at Risk (VaR) has a value of 49438.79 and that of the Expected Shortfall (ES) as 49291.24 with position of 1,000,000. This is an indication that the risk of investing in the stock of the First Bank Nigeria, Plc is eminent.
Udokang Anietie Edem,
Ugwuowo Fidelis Ifeanyi,
Modeling the Residuals of Financial Time Series with Missing Values for Risk Measures Using R, American Journal of Theoretical and Applied Statistics.
Vol. 7, No. 6,
2018, pp. 247-255.
Copyright © 2018 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.
R. S. Tsay, Analysis of Financial Time Series. 2nd ed. John Wiley & Sons Inc: New Jersey; 2005.
Hamadu, D, & Mojekwu, J. N. An investigation of nigerian insurance stock options prices. International Business Management year, 2010.
Honaker, J. & King, G. What to do about missing values in time-series cross-section data. American Journal of Political Science, 2010.
Shukur, O. B. & Lee, M. H. (2015). Imputation of missing values in daily wind speed data using hybrid AR-ANN method. Modern Applied Science,2015.
Chow, G. C. & Lawler C. C. A time series analysis of the shanghai and new york stock price indices, 2003. www. Princeton.edu/-gchow/lawler.pdf.
Ajie, H. A. & Nenbee, S. G. An econometric analysis of monetary policy and stock prices in nigeria. International Journal of Economic Development Research and Investment, 2010.
Ferreiro, O. Methodologies for the estimation of missing observations in time series. Statistics & Probability Letters, 1987.
Kabaila, P & Mainzer, R. Estimation risk for value-at-risk and estimated shortfall. Journal of Risk, 20(3), 29-47.
Stavroyiannis, S. Value–at-risk and expected shortfall for the major digital currencies, SSRN Electronic Journal, August 2017.
Abad, P., Benito, S. and López, C. A comprehensive review of value at risk methodologies. The Spanish review of financial economics, 12 (2014), 15–32.
Velicer, W. F. & Colby, S. M. A Comparison of Missing-Data Procedures for ARIMA Time Series Analysis. SAGE Journals: Educational and Psychological Measurement. August, 2005.
Cameron, A. C. & Trivedi, P. K. Microeconometrics: Methods and Applications. Cambridge University Press. New York, 2005.
Soley – Bori, M. Dealing with Missing Data: Key Assumptions Methods for Applied Analysis. Technical Report No. 4; May, 2013.
Cryer, J. D. & Chan, K. Time Series Analysis with Applications in R. 2nd ed. Springer: New York, 2008.
A. McNeil, R. Frey, P. Embrechts. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press: New Jersey; 2005.
Davison, A. C. and Smith, R. L. (1990). Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society Series, B 52: 393–442.
Smith, R. L. (1989). Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone (with discussion). Statistical Science, 4, 367–393.
R Core Team. R: A language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria; 2015, URL https://www.R-project.org/.
J. Y. Campbell, A. W. Lo and A. C. MacKinlay. The Econometrics of Financial Markets. Princeton University Press, Princeton, NJ. 1997.
H. N. E. Bystrom. Extreme Value Theory and Extremely Large Electricity Price Changes. International Review of Economics and Finance-INT REV ECO FINANC. 2001.14;1: 41- 55.