Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

References

• Andersen, T.G., Bollerslev, T. and Diebold, F.X., Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. Rev. Econ. Stat., 2007, 89, 701–720.
   Web of Science ®Google Scholar
• Andersen, T.G., Bollerslev, T., Diebold, F.X. and Ebens, H., The distribution of realized stock return volatility. J. Financ. Econ., 2001a, 61, 43–76.
   Web of Science ®Google Scholar
• Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P., The distribution of exchange rate volatility. J. Am. Stat. Assoc., 2001b, 96, 42–55.
   Web of Science ®Google Scholar
• Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P., Modeling and forecasting realized volatility. Econometrica, 2003, 71, 579–625.
   Web of Science ®Google Scholar
• Beran, J., Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models. J. R. Stat. Soc., 1995, 57, 659–672.
   Google Scholar
• Bhattacharya, R., Gupta, V. and Waymire, E., The Hurst effect under trends. J. Appl. Probab., 1983, 20, 649–662.
   Web of Science ®Google Scholar
• Brockwell, P.J. and Davis, R.A., Time Series: Theory and Methods, 2nd ed., 1991 (Springer Verlag: New York).
   Google Scholar
• Chan, N.H. and Palma, W., State space modeling of long-memory processes. Ann. Stat., 1998, 26, 719–740.
   Web of Science ®Google Scholar
• Chen, C. and Tiao, G.C., Random level shift time series models, ARIMA approximations, and level-shift detection. J. Bus. Econ. Stat., 1990, 8, 83–97.
   Web of Science ®Google Scholar
• Chiriac, R. and Voev, V., Modelling and forecasting multivariate realized volatility. J. Appl. Econom., 2011, 28, 922–947.
   Web of Science ®Google Scholar
• Christensen, B.J. and Varneskov, R.T., Medium band least squares estimation of fractional cointegration in the presence of low-frequency contamination. J. Econometrics, 2017, 197, 218–244.
   Web of Science ®Google Scholar
• Corsi, F., A simple approximate long-memory model of realized volatility. J. Financ. Econom., 2009, 7, 174–196.
   Web of Science ®Google Scholar
• Deo, R.S., Hurvich, C.M. and Lu, Y., Forecasting realized volatility using a long memory stochastic volatility model: Estimation, prediction, and seasonal adjustment. J. Econometrics, 2006, 131, 29–58.
   Web of Science ®Google Scholar
• Diebold, F.X. and Inoue, A., Long memory and regime switching. J. Econometrics, 2001, 105, 131–159. Article 14
   Web of Science ®Google Scholar
• Doornik, J.A. and Ooms, M., Inference and forecasting for ARFIMA models with an application to US and UK inflation. Stud. Nonlinear Dyn. Econometrics, 2004, 8, 1–23. Article 14.
   Web of Science ®Google Scholar
• Engle, R., Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 1982, 50, 987–1007.
   Web of Science ®Google Scholar
• Engle, R.F. and Rangel, J.G., The Spline-GARCH model for low-frequency volatility and its global macroeconomic causes. Rev. Financ. Stud., 2008, 21, 1187–1222.
   Web of Science ®Google Scholar
• Gabriel, V.J. and Martins, L.F., On the forecasting ability of ARFIMA models when infrequent breaks occur. Econometrics J., 2004, 7, 455–475.
   Google Scholar
• Giacomini, R. and White, H., Tests of conditional predictive ability. Econometrica, 2006, 74, 1545–1578.
   Web of Science ®Google Scholar
• Granger, C.W.J. and Hyung, N., Occasional structural breaks and long memory with an application to the S &P 500 absolute stock returns. J. Empir. Financ., 2004, 11, 399–421.
   Google Scholar
• Granger, C.W.J. and Joyeux, R., Long memory relationships and the aggregation of dynamic models. J. Time Ser. Anal., 1980, 1, 15–29.
   Google Scholar
• Granger, C.W.J. and Morris, M.J., Time series modelling and interpretation. J. R. Stat. Soc. Ser. A., 1976, 139, 246–257.
   Web of Science ®Google Scholar
• Grassi, S. and de Magistris, P.S., When long memory meets the Kalman filter: A comparative study. Comput. Stat. Data Anal., 2014, 76, 301–319.
   Web of Science ®Google Scholar
• Haldrup, N. and Nielsen, M.O., Estimation of fractional integration in the presence of data noise. Comput. Stat. Data Anal., 2007, 51, 3100–3114.
   Web of Science ®Google Scholar
• Hamilton, J.D., Time Series Analysis, 1994b (Princeton University Press: Princeton, NJ).
   Google Scholar
• Hamilton, J.D., State space models. In Handbook of Econometrics, edited by R.F. Engle and D.L. McFadden, Vol. IV pp. 3041–3080, 1994a (Elsevier: North Holland).
   Google Scholar
• Hansen, P.R. and Lunde, A., Consistent ranking of volatility models. J. Econometrics, 2006, 131, 97–121.
   Web of Science ®Google Scholar
• Hansen, P.R. and Lunde, A., Estimating the persistence and the autocorrelation function of a time series that is measured with error. Economet. Theor., 2014, 30, 60–93.
   Web of Science ®Google Scholar
• Hansen, P.R., Lunde, A. and Nason, J.M., The model confidence set. Econometrica, 2011, 79, 453–497.
   Web of Science ®Google Scholar
• Harvey, A.C., Forecasting., Structural Time Series Models and the Kalman Filter, 1989 (Cambridge University Press: Cambridge, United Kingdom).
   Google Scholar
• Harvey, A.C. and Shephard, N., Estimation of an asymmetric stochastic volatility model for asset returns. J. Bus. Econ. Stat., 1996, 14, 429–434.
   Web of Science ®Google Scholar
• Hosking, J.R.M., Fractional differencing. Biometrika, 1981, 68, 165–176.
   Web of Science ®Google Scholar
• Hurvich, C.M. and Ray, B.K., The local whittle estimator of long-memory stochastic volatility. J. Financ. Economet., 2003, 1, 445–470.
   Google Scholar
• Koopman, S.J., Jungbacker, B. and Hol, E., Forecasting daily variability of the S &P 100 stock index using historical, realised and implied volatility measurements. J. Empir. Financ., 2005, 12, 445–475.
   Google Scholar
• Lobato, I. and Savin, N., Real and spurious memory long-memory properties of stock market data. J. Bus. Econ. Stat., 1998, 16, 261–268.
   Web of Science ®Google Scholar
• Lu, Y.K. and Perron, P., Modeling and forecasting stock return volatility using a random level shift model. J. Empir. Financ., 2010, 17, 138–156.
   Web of Science ®Google Scholar
• Martin, V.L. and Wilkins, N.P., Indirect estimation of ARFIMA and VARFIMA models. J. Econometrics, 1999, 93, 149–175.
   Web of Science ®Google Scholar
• McCloskey, A. and Hill, J.B., Parameter estimation robust to low frequency contamination. J. Bus. Econ. Stat., 2015. doi:10.1080/07350015.2015.1093948.
   Web of Science ®Google Scholar
• McCloskey, A. and Perron, P., Memory parameter estimation in the presence of level shifts and deterministic trends. Economet. Theor., 2013, 29, 1196–1237.
   Web of Science ®Google Scholar
• McCulloch, R. and Tsay, R., Bayesian inference and prediction for mean and variance shifts in autoregressive time series. J. Am. Stat. Assoc., 1993, 88, 968–978.
   Web of Science ®Google Scholar
• Meddahi, N., ARMA representation of integrated and realized variances. Econometrics J., 2003, 6, 334–379.
   Google Scholar
• Mikosch, T. and Stărică, C., Nonstationarities in financial time series, the long range dependence, and the IGARCH effects. Rev. Econ. Stat., 2004, 86, 378–390.
   Web of Science ®Google Scholar
• Nielsen, M.O., Asymptotics for the conditional-sum-of-squares estimator estimator in multivariate fractional time-series models. J. Time Ser. Anal., 2015, 36, 154–188.
   Web of Science ®Google Scholar
• Nunes, L.C., Newbold, P. and Kuan, C.-M., Spurious breaks. Economet. Theor., 1995, 11, 555–577.
   Google Scholar
• Ohanissian, A., Russell, J.R. and Tsay, R.S., True or spurious long memory? A new test. J. Bus. Econ. Stat., 2008, 26, 161–175.
   Web of Science ®Google Scholar
• Patton, A., Volatility forecast comparison using imperfect volatility proxies. J. Econometrics, 2011, 160, 246–256.
   Web of Science ®Google Scholar
• Perron, P., The great crash, the oil price shock and the unit root hypothesis. Econometrica, 1989, 57, 1361–1401.
   Web of Science ®Google Scholar
• Perron, P., Testing for a unit root in a time series regression with changing mean. J. Bus. Economic Stat., 1990, 8, 153–162.
   Web of Science ®Google Scholar
• Perron, P. and Qu, Z., An analytical evaluation of the log-periodogram estimate in the presence of level shifts. Unpublished Manuscript, Department of Economics, Boston University, 2007.
   Google Scholar
• Perron, P. and Qu, Z., Long memory and level shifts in the volatility of stock market return indices. J. Bus. Econ. Stat., 2010, 28, 275–290.
   Web of Science ®Google Scholar
• Perron, P. and Wada, T., Let’s take a break: Trends and cycles in US real DGP. J. Monetary Econ., 2009, 56, 749–765.
   Web of Science ®Google Scholar
• Pettenuzzo, D. and Timmermann, A., Predictability of stock returns and asset allocation under structural breaks. J. Econometrics, 2011, 164, 60–78.
   Web of Science ®Google Scholar
• Qu, Z., A test against spurious long memory. J. Bus. Econ. Stat., 2011, 29, 423–438.
   Web of Science ®Google Scholar
• Qu, Z. and Perron, P., A stochastic volatility model with random level shifts and its applications to S &P 500 and NASDAQ return indices. Econometrics J., 2013, 16, 300–339.
   Web of Science ®Google Scholar
• Ray, B.K. and Tsay, R.S., Bayesian methods for change-point detection in long-range dependent processes. J. Time Ser. Anal., 2002, 23, 687–705.
   Web of Science ®Google Scholar
• Smith, A., Level shifts and the illusion of long memory in economic time series. J. Bus. Econ. Stat., 2005, 23, 355–389.
   Web of Science ®Google Scholar
• Stărică, C. and Granger, C.W.J., Nonstationarities in stock returns. Rev. Econ. Stat., 2005, 87, 503–522.
   Web of Science ®Google Scholar
• Varneskov, R.T., Flat-top realized kernel estimation of quadratic covariation with non-synchronous and noisy asset prices. J. Bus. Econ. Stat., 2016b, 34, 1–22.
   Web of Science ®Google Scholar
• Varneskov, R.T., Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels. Economet. Theor., 2016a, doi:10.1017/S0266466616000475.
   Web of Science ®Google Scholar
• Varneskov, R.T. and Perron, P., Combining long memory and level shifts in modeling and forecasting the volatility of asset returns: Supplementary appendix. Unpublished Manuscript, Boston University, 2017.
   Google Scholar
• Varneskov, R.T. and Voev, V., The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts. J. Empir. Financ., 2013, 20, 83–95.
   Web of Science ®Google Scholar
• Xu, J. and Perron, P., Forecasting return volatility: Level shifts with varying jump probability and mean reversion. Int. J. Forecasting, 2014, 30, 449–463.
   Web of Science ®Google Scholar