Evaluating Realized Volatility Models with Higher Order Cumulants: HAR-RV Versus ARIMA-RV

  • Sanja DudukovicEmail author
Conference paper
Part of the Eurasian Studies in Business and Economics book series (EBES, volume 10/2)


The objective of this paper is to introduce a new Realized Volatility (RV) Model. The model solves the problems of capturing long memory and heavy tales, which persist in current Heterogeneous Auto Regressive Realized Volatility Models (HAR-RV). First, an extensive empirical analysis of the classical RV model is provided by coupling Digital Signal Processing (DSP), Non Gaussian Time Series Analyses (NG-TSA) and volatility forecasting concepts. All models are built and tested on 30 min quotations of closing spot prices: USD/JPY, CHF/USD, JPY/EUR USD/GBP and GBP/EUR for the period from May 14, 2013 to July 31, 2015, taken from Bloomberg. The independence of the model’s innovations is tested by using the second, third and fourth cumulants, known as Higher Order Cumulants (HOC).Two tests are used, the Box-Ljung (B-Lj) test and Hinich test. The model is compared with the more natural Autoregressive Moving Average model (ARMA-RV). The empirical analysis shows that neither classic HAR-RV nor ARMA-RV models produce independent residuals. In addition, DSP recent findings are used to build a new HOC-ARMA-RV model. It was shown that only HOC-ARMA model fully captures fat tails and the long memory of FX returns.


Realized volatility HAR-RV model HOC-ARMA model Extended Box-Jenkins method Model testing Volatility forecasting 


  1. Amemiya, T., & Wu, R. Y. (1972). The effect of aggregation on prediction in the autoregressive models. Journal of American Statistical Association, 67(9), 628–632.CrossRefGoogle Scholar
  2. Andersen, T., Bollerslev, T., Diebold, F., & Labys, P. (2000). Exchange rate returns standardized by realized volatility are nearly Gaussian. Multinational Financial Journal, 4(3&4), 159–179.CrossRefGoogle Scholar
  3. Andersen, T. G., Bollerslev, T., Frederiksen, P., & Nielsen, M. O. (2010). Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns. Journal of Applied Econometrics, 25(2), 233–261.CrossRefGoogle Scholar
  4. Andreou, E., Pittis, N., & Spanos, A. (2001). On modelling speculative prices: The empirical literature. Journal of Economic Surveys, 15(2), 187–220.CrossRefGoogle Scholar
  5. Audrino, F., & Knaus, S. (2016). Lassoing the HAR model: A model selection perspective on realized volatility dynamics. Econometric Reviews, 35(8–10), 1485–1521.CrossRefGoogle Scholar
  6. Bai, N., Russell, J. R., & Tiao, G. C. (2003). Kurtosis of GARCH and stochastic volatility models with non-normality. Journal of Econometrics, 114(2), 349–360.CrossRefGoogle Scholar
  7. Barndorff-Nielsen, O., & Shephard, N. (2004). Power and bepower variation with stochastic volatility and jumps. Journal of Financial Econometrics, 2(1), 1–37. Scholar
  8. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. In R. Engle (Ed.), ARCH selected readings (pp. 42–60). Oxford: Oxford University Press.Google Scholar
  9. Box, G., & Jenkins, G. (1970). Time series analysis, forecasting and control. San Francisco: Holden-Day.Google Scholar
  10. Cheong, C. W. (2016). Heterogeneous market hypothesis evaluations using various jump-robust realized volatility. Romanian Journal of Economic Forecasting, 19(4), 51–64.Google Scholar
  11. Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7(2), 174–196. Scholar
  12. Corsi, F., Dacorogna, M., Műller, U., & Zumbach, G. (2001). Consistent high-precision volatility from high-frequency data. Economic Notes, 30(2), 183–204.CrossRefGoogle Scholar
  13. Corsi, F., Kretschmer, U., Mittnik, S., & Pigorsch, C. (2008). The volatility of realized volatility. Economic Review, 27(1–3), 1–33.Google Scholar
  14. Engel, E. (1984). A unified approach to the study of sums, products, time-aggregation and other functions of ARMA processes. Journal of Time Series Analysis, 5(3), 159–171.CrossRefGoogle Scholar
  15. Giannakis, G., & Mendel, J. (1989). Identification of non-minimum phase systems using higher-order statistics. IEEE Transactions on Acoustics. Speech and Signal Processing, 37(3), 360–377.CrossRefGoogle Scholar
  16. Giannakis, G., & Swami, A. (1992). Identifiability of general ARMA processes using linear cumulant-based estimators. Automatica, 28(4), 771–779. Scholar
  17. Hinich, M. (1996). Testing for dependence in the input to a linear time series model. Journal of Nonparametric Statistics, 6(2–3), 205–221. Scholar
  18. Lim, K. P., Hinich, M. J., & Liew, V. K. S. (2005). Statistical Inadequacy of GARCH models for Asian stock markets: Evidence and implications. Journal of Emerging Market Finance, 4(3), 263–279. Scholar
  19. Műller, U., Dacorogna, M., Davé, R., Olsen, R., Pietet, O., & Veizsack, V. (1997). Volatilities of different time resolutions—analyzing the dynamics of market components. Journal of Empirical Finance, 4(2–3), 213–239.CrossRefGoogle Scholar
  20. Pagano, M. (1974). Estimation of models of autoregressive signal plus white noise. The Annals of Statistics, 2(1), 99–108.CrossRefGoogle Scholar
  21. Seďa, P. (2012). Performance of heterogeneous autoregressive models of realized volatility: Evidence from U.S. stock market. International Journal of Economics and Management Engineering, 6(12), 3421–3424.Google Scholar
  22. Swami, A., & Mendel, J. (1989). Closed form estimation of MA coefficients using autocorrelations and third-order cumulants. IEEE Transactions on Acoustics. Speech and Signal Processing, 37(11), 1794–1797.CrossRefGoogle Scholar
  23. Swami, A., Mendel, J., & Nikias, C. (1995). Higher-order spectral analysis toolbox: For use with Matlab. E-book math works. Accessed May 20, 2016, from
  24. Teräsvirta, T., & Zhao, Z. (2011). Stylized facts of return series, robust estimates, and three popular models of volatility. Applied Financial Economics, 21(1&2), 67–94.CrossRefGoogle Scholar
  25. Wild, P., Foster, J., & Hinich, M. (2010). Identifying nonlinear serial dependence in volatile, high-frequency time series and its implications for volatility modeling. Macroeconomic Dynamics, 14(1), 88–110.CrossRefGoogle Scholar
  26. Zhang, L., Mykland, P. A., & Ait-Sahalia, Y. (2011). Edgeworth expansions for realized volatility and related estimators. Journal of Econometrics, 160(1), 190–203.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.International Management DepartmentFranklin University SwitzerlandSorengoSwitzerland

Personalised recommendations