Application of the Family of Sign RCA Models for Obtaining the Selected Risk Measures

Joanna Górka



Accurate modelling of risk is very important in finance. There are many alternative risk measures, however none of them is dominating. This paper proposes to use the family of Sign RCA models to obtain the Value-at-Risk (VaR) and Expected Shortfall (ES) measures. For models from the family of Sign RCA models and AR-GARCH model the one-step forecasts of VaR were calculated based on rolling estimates from the given model using different window sizes. To obtain the VaR and ES measures the filtered historical simulation was used in new version proposed by Christoffersen. The results were verified using backtesting and the loss function.


Family of Sign RCA Models, risk measures, Value at Risk, Expected Shortfall

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Acerbi, C., Tasche, D. (2002), Expected Shortfall: A Natural Coherent Alternative to Value at Risk, Economic Notes, 31, 379–388.

Angelidis, T., Degiannakis, S. (2006), Backtesting VaR Models: An Expected Shortfall Approach, Working Paper Series, (2.09.2009).

Appadoo, S., Thavaneswaran, A., Singh J. (2006), RCA Models with Correlated Errors Applied Mathematics Letters, 19, 824–829. DOI:

Aue, A. (2004), Strong Approximation for RCA(1) Time Series with Applications, Statistics & Probability Letters, 68, 369–382.

Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroscedasticity, Journal of Econometrics, 31, 307–327. DOI:

Christoffersen, P. F. (2009), Value-at-Risk Models, in Andersen, T. G., Davis, R. A., Kreiss, J.-P., Mikosch, T. (ed.), Handbook of Financial Time Series, Springer Verlag. DOI:

Dowd, K. (2002), Measuring Market Risk, John Wiley & Sons, ltd.

Engle, R. F. (1982), Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987–1006.

Górka, J. (2008), Description the kurtosis of distributions by selected models with sing function, Dynamic Econometric Models, vol.8, Toruń

Nicholls, D., Quinn, B. (1982), Random Coefficient Autoregressive Models: An Introduction, Springer, New York.

Thavaneswaran, A., Appadoo, S. (2006), Properties of a New Family of Volatility Sing Models, Computers and Mathematics with Applications, 52, 809–818.

Thavaneswaran, A., Appadoo, S., Bector, C. (2006), Recent Developments in Volatility Modeling and Application, Journal of Applied Mathematics and Decision Sciences, 1–23.

Thavaneswaran, A., Peiris, S., Appadoo, S. (2008), Random Coefficient Volatility Models, Statistics & Probability Letters, 78, 582–593. DOI:

Thavaneswaran, S., Appadoo, S., i Ghahramani, M. (2009), RCA models with GARCH innovations, Applied Mathematics Letters, 22, 110–114.

Yamai, Y., Yoshiba, T. (2002), Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition and Optimization, Monetary and Economic Studies, 20(1), 87–121.

ISSN (print) 1234-3862
ISSN (online) 2450-7067

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