Skip to main content
SpringerLink
Log in

Volatility Forecasting in a Data Rich Environment

  • Chapter
  • First Online:
Book cover Macroeconomic Forecasting in the Era of Big Data

Part of the book series: Advanced Studies in Theoretical and Applied Econometrics ((ASTA,volume 52))

  • 2901 Accesses

Abstract

This Chapter reviews the main classes of models that incorporate volatility, with a focus on the most recent advancements in the financial econometrics literature and on the challenges posed by the increased availability of data. There are limits to the feasibility of all models when the cross-sectional dimension diverges, unless strong restrictions are imposed on the model’s dynamics. In the latter case, the models might become feasible at the expense of reduced economic intuition that can be recovered from the model fit. In turn, this could have a negative impact on the forecast and the identification of its drivers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aguilar, O., & West, M. (2000). Bayesian dynamic factor models and portfolio allocation. Journal of Business & Economic Statistics, 18(3), 338–357.

    Google Scholar 

  • Aielli, G. P. (2013). Dynamic conditional correlation: On properties and estimation. Journal of Business & Economic Statistics, 31(3), 282–299.

    Article  Google Scholar 

  • Ait-Sahalia, Y., & Xiu, D. (2017). Using principal component analysis to estimate a high dimensional factor model with high-frequency data. Journal of Econometrics, 201(2), 384–399.

    Article  Google Scholar 

  • Ait-Sahalia, Y., & Xiu, D. (2019). Principal component analysis of high-frequency data. Journal of the American Statistical Association, 114, 287–303.

    Article  Google Scholar 

  • Alexander, C. (2001). Orthogonal GARCH. Upper Saddle River, NJ: Financial Times-Prentice Hall.

    Google Scholar 

  • Andersen, T. G., & Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4(2–3), 115–158.

    Article  Google Scholar 

  • Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39(4), 885–905.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579–625.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., & Dobrev, D. (2007). No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications. Journal of Econometrics, 138(1), 125–180.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Frederiksen, P., & Ørregaard Nielsen, M. (2010). Continuous-time models, realizedvolatilities, and testable distributional implications for daily stock returns. Journal of Applied Econometrics, 25(2), 233–261.

    Article  Google Scholar 

  • Andersen, T. G., & Sorensen, B. E. (1996). Gmm estimation of a stochastic volatility model: A monte carlo study. Journal of Business & Economic Statistics, 14(3), 328–352.

    Google Scholar 

  • Asai, M., & McAleer, M. (2006a). Asymmetric multivariate stochastic volatility. Econometric Reviews, 25(2–3), 453–473.

    Article  Google Scholar 

  • Asai, M., & McAleer, M. (2006b). Asymmetric multivariate stochastic volatility. Econometric Reviews, 25(2–3), 453–473.

    Article  Google Scholar 

  • Asai, M., & McAleer, M. (2009a). The structure of dynamic correlations in multivariate stochastic volatility models. Journal Econometrics, 150(2), 182–192.

    Article  Google Scholar 

  • Asai, M., & McAleer, M. (2009b). The structure of dynamic correlations in multivariate stochastic volatility models. Journal Econometrics, 150(2), 182–192.

    Article  Google Scholar 

  • Asai, M., McAleer, M., & Yu, J. (2006). Multivariate stochastic volatility: A review. Econometric Reviews, 25(2-3), 145–175.

    Article  Google Scholar 

  • Attanasio, O. P. (1991). Risk, time-varying second moments and market efficiency. The Review of Economic Studies, 58(3), 479–494.

    Article  Google Scholar 

  • Ball, C. A., & Torous, W. N. (1983). A simplified jump process for common stock returns. Journal of Financial and Quantitative Analysis, 18(1), 53–65.

    Article  Google Scholar 

  • Bandi, F. M., & Russel, J. R. (2006). Separating microstructure noise from volatility. Journal of Financial Economics, 79(3), 655–692.

    Article  Google Scholar 

  • Bandi, F. M., & Russell, J. R. (2005). Realized covariation, realized beta and microstructure noise. Unpublished paper.

    Google Scholar 

  • Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2011). Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. Journal of Econometrics, 162(2), 149–169.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society: Series B, 64(2), 253–280.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2004). Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica, 72(3), 885–925.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics, 4(1), 1–30.

    Article  Google Scholar 

  • Bates, D. S. (2000). Post- ’87 crash fears in the s & p 500 futures option market. Journal of Econometrics, 94(1–2), 181–238.

    Article  Google Scholar 

  • Bauer, G., & Vorkink, K. (2011). Forecasting multivariate realized stock market volatility. Journal of Econometrics, 2(1), 93–101.

    Article  Google Scholar 

  • Bauwens, L., Grigoryeva, L., & Ortega, J.-P. (2016). Estimation and empirical performance of non-scalar dynamic conditional correlation models. Computational Statistics and Data Analysis, 100, 17–36.

    Article  Google Scholar 

  • Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: A survey. Journal of Applied Econometrics, 21(1), 79–109.

    Article  Google Scholar 

  • Bekierman, J., & Manner, H. (2018). Forecasting realized variance measures using time-varying coefficient models. International Journal of Forecasting, 34(2), 276–287.

    Article  Google Scholar 

  • Bhattacharya, A., & Dunson, D. B. (2011). Sparse Bayesian infinite factor models. Biometrika, 98(2), 291–306.

    Article  Google Scholar 

  • Billio, M., Caporin, M., Frattarolo, L., & Pelizzon, L. (2018). Networks in risk spillovers: A multivariate GARCH perspective. SAFE.

    Google Scholar 

  • Billio, M., Caporin, M., & Gobbo, M. (2006). Flexible dynamic conditional correlation multivariate GARCH models for asset allocation. Applied Financial Economics Letters, 2(2), 123–130.

    Article  Google Scholar 

  • Bitto, A., & Frühwirth-Schnatter, S. (2019). Achieving shrinkage in a time-varying parameter model framework. Journal of Econometrics, 210(1), 75–97.

    Article  Google Scholar 

  • Black, F. (1976). Studies of stock price volatility changes. In Proceedings of the 1976 Meetings of the American Statistical Association (pp. 171–181).

    Google Scholar 

  • Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637–654.

    Article  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

    Article  Google Scholar 

  • Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized arch model. The Review of Economics and Statistics, 72(3), 498–505.

    Article  Google Scholar 

  • Bollerslev, T. (2010). Glossary to ARCH GARCH. In R. Engle, M. Watson, T. Bollerslev, & J. Russell (Eds.), Volatility and time series econometrics: Essays in honour of Robert F. Engle. Advanced Texts in Econometrics. Oxford: Oxford University Press.

    Google Scholar 

  • Bollerslev, T., Chou, R. Y., & Kroner, K. F. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52(1–2), 5–59.

    Article  Google Scholar 

  • Bollerslev, T., Engle, R. F., & Nelson, D. B. (1994). Arch models. Handbook of Econometrics, 4, 2959–3038.

    Article  Google Scholar 

  • Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96(1), 116–131.

    Article  Google Scholar 

  • Bollerslev, T., Patton, A. J., & Quaedvlieg, R. (2016). Exploiting the errors: A simple approach for improved volatility forecasting. Journal of Econometrics, 192(1), 1–18.

    Article  Google Scholar 

  • Bonaccolto, G., & Caporin, M. (2016). The determinants of equity risk and their forecasting implications: A quantile regression perspective. Journal of Risk and Financial Management, 9(3), 8.

    Article  Google Scholar 

  • Bonato, M., Caporin, M., & Ranaldo, A. (2012). A forecast-based comparison of restricted wishart autoregressive models for realized covariance matrices. The European Journal of Finance, 18(9), 761–774.

    Article  Google Scholar 

  • Bonato, M., Caporin, M., & Ranaldo, A. (2013). Risk spillovers in international equity portfolios. Journal of Empirical Finance, 24, 121–137.

    Article  Google Scholar 

  • Callot, L. A. F., Kock, A. B., & Medeiros, M. C. (2017). Modeling and forecasting large realized covariance matrices and portfolio choice. Journal of Applied Econometrics, 32(1), 140–158.

    Article  Google Scholar 

  • Caporin, M., & McAleer, M. (2010). A scientific classification of volatility models. Journal of Economic Surveys, 24(1), 191–195.

    Google Scholar 

  • Caporin, M., & McAleer, M. (2012). Do we really need both BEKK and DCC? A tale of two multivariate GARCH models. Journal of Economic Surveys, 26(4), 736–751.

    Article  Google Scholar 

  • Caporin, M., & Paruolo, P. (2015). Proximity-structured multivariate volatility models. Econometric Reviews, 34(5), 559–593.

    Article  Google Scholar 

  • Caporin, M., & Poli, F. (2017). Building news measures from textual data and an application to volatility forecasting. Econometrics, 5(35), 1–46.

    Google Scholar 

  • Caporin, M., & Velo, G. G. (2015). Realized range volatility forecasting: Dynamic features and predictive variables. International Review of Economics & Finance, 40, 98–112.

    Article  Google Scholar 

  • Cappiello, L., Engle, R. F., & Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics, 4(4), 537–572.

    Article  Google Scholar 

  • Chib, S., & Greenberg, E. (1996). Markov chain monte carlo simulation methods in econometrics. Econometric Theory, 12(3), 409–431.

    Article  Google Scholar 

  • Chib, S., Nardari, F., & Shephard, N. (2002). Markov chain monte carlo methods for stochastic volatility models. Journal of Econometrics, 108(2), 281–316.

    Article  Google Scholar 

  • Chib, S., Nardari, F., & Shephard, N. (2006). Analysis of high dimensional multivariate stochastic volatility models. Journal of Econometrics, 134(2), 341–371.

    Article  Google Scholar 

  • Chiriac, R., & Voev, V. (2011). Modelling and forecasting multivariate realized volatility. Journal of Applied Econometrics, 26(6), 893–1057.

    Article  Google Scholar 

  • Christiansen, C., Schmeling, M., & Schrimpf, A. (2012). A comprehensive look at financial volatility prediction by economic variables. Journal of Applied Econometrics, 27(6), 956–977.

    Article  Google Scholar 

  • Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1, 223–236.

    Article  Google Scholar 

  • Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics, 7(2), 174–196.

    Article  Google Scholar 

  • Corsi, F., Pirino, D., & Renò, R. (2010). Threshold bipower variation and the impact of jumps on volatility forecasting. Journal of Econometrics, 159(2), 276–288.

    Article  Google Scholar 

  • Danielsson, J. (1998). Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models. Journal of Empirical Finance, 5(2), 155–173.

    Article  Google Scholar 

  • Dhaene, G., Sercu, P., & Wu, J. (2017). Multi-market volatility spillovers in equities: A sparse multivariate GARCH approach. Working paper.

    Google Scholar 

  • Diebold, F., & Nerlove, M. (1989). The dynamics of exchange rate volatility: A multivariate latent factor arch model. Journal of Applied Econometrics, 4(1), 1–21.

    Article  Google Scholar 

  • Ding, Z., & Engle, R. F. (2001). Large scale conditional covariance matrix modeling, estimation and testing. Academia Economic Papers, 29, 157–184.

    Google Scholar 

  • Ding, Z., Granger, C. W., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1(1), 83–106.

    Article  Google Scholar 

  • Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6), 1343–1376.

    Article  Google Scholar 

  • Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350.

    Article  Google Scholar 

  • Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.

    Article  Google Scholar 

  • Engle, R. F., & Gallo, G. M. (2006). A multiple indicators model for volatility using intra-daily data. Journal of Econometrics, 131(1–2), 3–27.

    Article  Google Scholar 

  • Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized arch. Econometric Theory, 11(1), 122–150.

    Article  Google Scholar 

  • Engle, R. F., & Russell, J. R. (1998). Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica, 66(5), 1127–1162.

    Google Scholar 

  • Engle, R. F., & Sokalska, M. E. (2012). Forecasting intraday volatility in the US equity market. Multiplicative component GARCH. Journal of Financial Econometrics, 10(1), 54–83.

    Article  Google Scholar 

  • Epps, T. W. (1979). Comovements in stock prices in the very short run. Journal of the American Statistical Association, 74(366), 291–298.

    Article  Google Scholar 

  • Eraker, B., Johannes, M. S., & Polson, N. G. (2003). The impact of jumps in returns and volatility. Journal of Finance, 53(3), 1269–1300.

    Article  Google Scholar 

  • Fan, J., Furger, A., & Xiu, D. (2016). Incorporating gloabl industrial classification standard into portfolio allocation: A simple factor-based large covariance matrix estimator with high-frequency data. Journal of Business and Economic Statistics, 34, 489–503.

    Article  Google Scholar 

  • Fleming, J., Kirby, C., & Ostdiek, B. (2008). The specification of GARCH models with stochastic covariates. Journal of Future Markets, 28(10), 922–934.

    Article  Google Scholar 

  • Forsberg, L., & Ghysels, E. (2007). Why do absolute returns predict volatility so well? Journal of Financial Econometrics, 5(1), 31–67.

    Article  Google Scholar 

  • Frühwirth-Schnatter, S., & Wagner, H. (2010). Stochastic model specification search for Gaussian and partial non-Gaussian state space models. Journal of Econometrics, 154(1), 85–100.

    Article  Google Scholar 

  • Ghysels, E., Harvey, A., & Renault, E. (1996). Stochastic volatility. In G. S. Maddala & C. R. Rao (Eds.), Handbook of statistics statistical methods in finance (Vol. 14). Amsterdam: North-Holland.

    Google Scholar 

  • Ghysels, E., & Jasiak, J. (1998). GARCH for irregularly spaced financial data: The ACD-GARCH model. Studies in Nonlinear Dynamics & Econometrics, 2(4).

    Google Scholar 

  • Ghysels, E., P., S.-C., & Valkanoy, R. (2006). Predicting volatility: Getting the most out of return data sampled at different frequencies. Journal of Econometrics, 131(1–2), 59–95.

    Google Scholar 

  • Ghysels, E., Santa-Clara, P., & Valkanov, R. (2004). The MIDAS touch: Mixed data sampling regression models. Montreal, QC: CIRANO.

    Google Scholar 

  • Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779–1801.

    Article  Google Scholar 

  • Golosnoy, V., Gribisch, B., & Liesenfeld, R. (2012). The conditional autoregressive Wishart model for multivariate stock market volatility. Journal of Econometrics, 167(1), 211–223.

    Article  Google Scholar 

  • Gourieroux, C. (2006). Continuous time Wishart process for stochastic risk. Economic Review, 25(2–3), 177–217.

    Article  Google Scholar 

  • Gourieroux, C., Jasiak, J., & Sufana, R. (2009a). The Wishart autoregressive process of multivariate stochastic volatility. Journal of Econometrics, 150(2), 167–181.

    Article  Google Scholar 

  • Gourieroux, C., Jasiak, J., & Sufana, R. (2009b). The Wishart autoregressive process of multivariate stochastic volatility. Journal of Econometrics, 150(2), 167–181.

    Article  Google Scholar 

  • Gourieroux, C., & Sufana, R. (2010). Derivative pricing with Wishart multivariate stochastic volatility. Journal of Business & Economic Statistics, 28(3), 438–451.

    Article  Google Scholar 

  • Gourieroux, C., & Sufana, R. (2011). Discrete time Wishart term structure models. Journal of Economic Dynamics and Control, 35(6), 815–824.

    Article  Google Scholar 

  • Gribisch, B. (2016). Multivariate Wishart stochastic volatility and changes in regime. AStA Advances in Statistical Analysis, 100(4), 443–473.

    Article  Google Scholar 

  • Griffin, J. E., & Brown, P. J. (2010). Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5(1), 171–188.

    Article  Google Scholar 

  • Hansen, P. R., Huang, Z., & Shek, H. H. (2012). Realized GARCH: A joint model for returns and realized measures of volatility. Journal of Applied Econometrics, 27(6), 877–906.

    Article  Google Scholar 

  • Hansen, P. R., & Lunde, A. (2006). Realized variance and market microstructure noise. Journal of Business and Economic Statistics, 24(2), 127–161.

    Article  Google Scholar 

  • Harvey, A., Ruiz, E., & Shephard, N. (1994). Multivariate stochastic variance models. The Review of Economic Studies, 61(2), 247–264.

    Article  Google Scholar 

  • Hasbrouck, J. (2006). Empirical market microstructure. The institutions, economics, and econometrics of securities trading. New York, NY: Oxford University Press.

    Google Scholar 

  • Hautsch, N., & Ou, Y. (2008). Discrete-time stochastic volatility models and MCMC-based statistical inference. SFB 649 Discussion Papers, Humboldt University, Berlin, Germany.

    Google Scholar 

  • Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2), 327–343.

    Article  Google Scholar 

  • Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42(2), 281–300.

    Article  Google Scholar 

  • Jacquier, E., Polson, N. G., & Rossi, P. (1999a). Stochastic volatility: Univariate and multivariate extensions. Computing in Economics and Finance, 1999, 112.

    Google Scholar 

  • Jacquier, E., Polson, N. G., & Rossi, P. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics, 122(1), 185–212.

    Article  Google Scholar 

  • Jacquier, E., Polson, N. G., & Rossi, P. E. (1994). Bayesian analysis of stochastic volatility models. Journal of Business & Economic Statistics, 12(4), 371–389.

    Google Scholar 

  • Jacquier, E., Polson, N., & Rossi, P. (1999b). Stochastic volatility: Univariate and multivariate extensions (Working paper No. 99). Montreal, QC: CIRANO.

    Google Scholar 

  • Jarrow, R. A., & Rosenfeld, E. R. (1984). Jump risks and the intertemporal capital asset pricing model. Journal of Business, 57, 337–351.

    Article  Google Scholar 

  • Jin, X., Maheu, J. M., & Yang, Q. (2019). Bayesian parametric and semiparametric factor models for large realized covariance matrices. Journal of Applied Econometrics, 34(5), 641–660.

    Article  Google Scholar 

  • Jorion, P. (1988). On jump processes in the foreign exchange and stock markets. Review of Financial Studies, 1(4), 427–445.

    Article  Google Scholar 

  • Kastner, G. (2018). Sparse Bayesian time-varying covariance estimation in many dimensions. Journal of Econometrics.

    Google Scholar 

  • Kastner, G., Frühwirth-Schnatter, S., & Lopes, H. F. (2017). Efficient Bayesian inference for multivariate factor stochastic volatility models. Journal of Computational and Graphical Statistics, 26(4), 905–917.

    Article  Google Scholar 

  • Kim, S., Shephard, N., & Chib, S. (1998a). Stochastic volatility: Likelihood inference and comparison with ARCH models. The Review of Economic Studies, 65(3), 361–393.

    Article  Google Scholar 

  • Kim, S., Shephard, N., & Chib, S. (1998b). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies, 65(3), 361–393.

    Article  Google Scholar 

  • Lam, C., Feng, P., & Hu, C. (2017). Nonlinear shrinkage estimation of large integrated covariance matrices. Biometrika, 104, 481–488.

    Article  Google Scholar 

  • Lee, S. S., & Mykland, P. A. (2008). Jumps in financial markets: A new nonparametric test and jump dynamics. Review of Financial Studies, 21(6), 2535–2563.

    Article  Google Scholar 

  • Liesenfeld, R., & Richard, J.-f. (2003). Univariate and multivariate stochastic volatility models: Estimation and diagnostics. Journal of Empirical Finance, 10(4), 505–531.

    Google Scholar 

  • Ling, S., & McAleer, M. (2002). Necessary and sufficient moment conditions for the GARCH(r, s) and asymmetric power GARCH(r, s) models. Econometric Theory, 18(3), 722–729.

    Article  Google Scholar 

  • Lopes, H. F., McCulloch, R. E., & Tsay, R. S. (2014). Parsimony inducing priors for large scale state-space models. Technical report.

    Google Scholar 

  • Marcus, M., & Minc, H. (1992). A survey of matrix theory and matrix inequalities (Vol. 14). New York, NY: Dover.

    Google Scholar 

  • McAleer, M., & Medeiros, M. (2006). Realized volatility: A review. Econometric Reviews, 27(1–3), 10–45.

    Google Scholar 

  • Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45(1–2), 239–265.

    Article  Google Scholar 

  • Meucci, A. (2010). Review of discrete and continuous processes in finance: Theory and applications. Working paper.

    Google Scholar 

  • Morimoto, T., & Nagata, S. (2017). Robust estimation of a high-dimensional integrated covariance matrix. Communications in Statistics - Simulation and Computation, 46(2), 1102–1112.

    Article  Google Scholar 

  • Muller, U., Dacorogna, M., Dav, R., Pictet, O., Olsen, R., & Ward, J. (1993). Fractals and intrinsic time - A challenge to econometricians. In XXXIXth International AEA Conference on Real Time Econometrics, Luxembourg.

    Google Scholar 

  • Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370.

    Article  Google Scholar 

  • Noureldin, D., Shephard, N., & Sheppard, K. (2014). Multivariate rotated arch models. Journal of Econometrics, 179(1), 16–30.

    Article  Google Scholar 

  • Pakel, C., Shephard, N., Sheppard, K., & Engle, R. F. (2017). Fitting vast dimensional time-varying covariance models. NYU Working paper.

    Google Scholar 

  • Philipov, A., & Glickman, M. E. (2006a). Factor multivariate stochastic volatility via Wishart processes. Econometric Review, 25(2–3), 311–334.

    Article  Google Scholar 

  • Philipov, A., & Glickman, M. E. (2006b). Multivariate stochastic volatility via Wishart processes. Journal of Business & Economic Statistics, 24(3), 313–328.

    Article  Google Scholar 

  • Pitt, M. K., & Shephard, N. (1999). Time-varying covariances: A factor stochastic volatility approach. In Bayesian statistics (pp. 547–570). Oxford: Oxford University Press.

    Google Scholar 

  • Shen, K., Yao, J., & Li, W. K. (2018). Forecasting high-dimensional realized volatility matrices using a factor model. Quantitative Finance, forthcoming.

    Google Scholar 

  • Shepard, N., & Sheppard, K. (2010). Realising the future: Forecasting with high-frequency-based volatility (heavy) models. Journal of Applied Econometrics, 25, 197–231.

    Article  Google Scholar 

  • Shephard, N. (1996). Statistical aspects of arch and stochastic volatility. In Time series models in econometrics (pp. 1–67). London: Chapman & Hall.

    Google Scholar 

  • Shephard, N., & Pitt, M. K. (2004). Erratum: Likelihood analysis of non-Gaussian measurement time series’. Biometrika, 91(1), 249–250.

    Article  Google Scholar 

  • Shephard, N., & Sheppard, K. (2010). Realising the future: Forecasting with high-frequency-based volatility (heavy) models. Journal of Applied Econometrics, 25(2), 197–231.

    Article  Google Scholar 

  • Sheppard, K. (2006). Realized covariance and scrambling. Unpublished manuscript.

    Google Scholar 

  • Sheppard, K., & Xu, W. (2019). Factor high-frequency-based volatility (heavy) models. Journal of Financial Econometrics, 17, 33–65.

    Article  Google Scholar 

  • Silvennoinen, A., & Teräsvirta, T. (2009). Multivariate GARCH models. In Handbook of financial time series (pp. 201–229). Berlin: Springer.

    Chapter  Google Scholar 

  • Smith, M., & Pitts, A. (2006). Foreign exchange intervention by the bank of Japan: Bayesian analysis using a bivariate stochastic volatility model. Econometric Reviews, 25(2–3), 425–451.

    Article  Google Scholar 

  • So, M. K. P., & Kwok, S. W. Y. (2006). A multivariate long memory stochastic volatility model. Physica A: Statistical Mechanics and its Applications, 362(2), 450–464.

    Article  Google Scholar 

  • So, M. K. P., Li, W. K., & Lam, K. (1997). Multivariate modelling of the autoregressive random variance process. Journal of Time Series Analysis, 18(4), 429–446.

    Article  Google Scholar 

  • Tao, M., Wang, Y., & Chen, X. (2013). Fast convergence rates in estimating large volatility matrices using high-frequency financial data. Econometric Theory, 29, 838–856.

    Article  Google Scholar 

  • Tao, M., Wang, Y., Yao, Q., & Zou, J. (2011). Large volatility matrix inference via combining low-frequency and high-frequency approaches. Journal of the American Statistical Association, 106, 1025–1040.

    Article  Google Scholar 

  • Tao, M., Wang, Y., & Zhou, H. H. (2013). Optimal sparse volatility matrix estimation for high-dimensional Ito processes with measurement error. Annals of Statistics, 41, 1816–1864.

    Article  Google Scholar 

  • Taylor, S. J. (1986). Modelling financial time series. Chichester: Wiley.

    Google Scholar 

  • Taylor, S. J. (1994). Modelling stochastic volatility: A review and comparative study. Mathematical Finance, 4(2), 183–204.

    Article  Google Scholar 

  • Teräsvirta, T. (2009). An introduction to univariate GARCH models. In Handbook of financial time series (pp. 17–42).

    Chapter  Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B, 58(1), 267–288.

    Google Scholar 

  • Tsay, R. S. (2010). Analysis of financial time series (3rd ed.). Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Van der Weide, R. (2002). GO-GARCH: A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics, 17(5), 549–564.

    Article  Google Scholar 

  • Violante, F., & Laurent, S. (2012). Volatility forecasts evaluation and comparison. In L. Bauwens, C. Hafner, & S. Laurent (Eds.), Handbook of volatility models and their applications. London: Wiley.

    Google Scholar 

  • Yamauchi, Y., & Omori, Y. (2018). Multivariate stochastic volatility model with realized volatilities and pairwise realized correlations. Journal of Business and Economic Statistics, forthcoming.

    Google Scholar 

  • Yu, J., & Meyer, R. (2006a). Multivariate stochastic volatility models: Bayesian estimation and model comparison. Econometric Reviews, 25(2–3), 361–384.

    Article  Google Scholar 

  • Yu, J., & Meyer, R. (2006b). Multivariate stochastic volatility models: Bayesian estimation and model comparison. Econometric Review, 25(2–3), 361–384.

    Article  Google Scholar 

  • Yu, P. L. H., Li, W. K., & Ng, F. C. (2017). The generalized conditional autoregressive Wishart model for multivariate realized volatility. Journal of Business & Economic Statistics, 35(4), 513–527.

    Article  Google Scholar 

  • Yu, Y., & Meng, X.-l. (2011). To center or not to center: That is not the question—an ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC efficiency. Journal of Computational and Graphical Statistics, 20(3), 531–570.

    Google Scholar 

  • Zhang, L., Mykland, P. A., & Ait-Sahalia, Y. (2005). A tale of two time scales. The Journal of the American Statistical Association, 100(472), 1394–1411.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistical Sciences, University of Padova and Istituto per le Applicazioni del Calcolo “Mauro Picone” - CNR, Roma, Italy

    Mauro Bernardi

  2. School of Economics and Law, University of Enna Kore, Enna, Italy

    Giovanni Bonaccolto

  3. Department of Statistical Sciences, University of Padova, Padova, Italy

    Massimiliano Caporin

  4. SAFE, Goethe University Frankfurt, Frankfurt, Germany

    Michele Costola

Authors
  1. Mauro Bernardi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giovanni Bonaccolto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Massimiliano Caporin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michele Costola
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimiliano Caporin .

Editor information

Editors and Affiliations

  1. UHERO and Department of Economics, University of Hawaii at Manoa, Honolulu, HI, USA

    Peter Fuleky

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bernardi, M., Bonaccolto, G., Caporin, M., Costola, M. (2020). Volatility Forecasting in a Data Rich Environment. In: Fuleky, P. (eds) Macroeconomic Forecasting in the Era of Big Data. Advanced Studies in Theoretical and Applied Econometrics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-31150-6_5

Download citation

Publish with us

Policies and ethics

Search

Navigation