Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice

In this paper we consider modeling and forecasting of large realized covariance matrices by penalized vector autoregressive models. We propose using Lasso-type estimators to reduce the dimensionality to a manageable one and provide strong theoretical performance guarantees on the forecast capability of our procedure. To be precise, we show that we can forecast future realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics for the realized covariance matrices of the 30 Dow Jones stocks and find that these dynamics are not stable as the data is aggregated from the daily to the weekly and monthly frequency. The theoretical performance guarantees on our forecasts are illustrated on the Dow Jones index. In particular, we can beat our benchmark by a wide margin at the longer forecast horizons. Finally, we investigate the economic value of our forecasts in a portfolio selection exercise and find that in certain cases an investor is willing to pay a considerable amount in order get access to our forecasts.

[1]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[2]  Fulvio Corsi,et al.  A Simple Long Memory Model of Realized Volatility , 2004 .

[3]  Paolo Santucci de Magistris,et al.  Chasing Volatility: A Persistent Multiplicative Error Model with Jumps , 2014 .

[4]  Jianqing Fan,et al.  Large covariance estimation by thresholding principal orthogonal complements , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[5]  Chris Kirby,et al.  The Economic Value of Volatility Timing , 2000 .

[6]  M. D. Cattaneo,et al.  Bootstrapping Kernel-Based Semiparametric Estimators , 2014 .

[7]  Mehmet Caner,et al.  Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso , 2014, 1410.4208.

[8]  Nikolaus Hautsch,et al.  A Blocking and Regularization Approach to High Dimensional Realized Covariance Estimation , 2010 .

[9]  George Kapetanios,et al.  Forecasting Medium and Large Datasets with Vector Autoregressive Moving Average (VARMA) Models , 2015 .

[10]  P. Bickel,et al.  SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR , 2008, 0801.1095.

[11]  Dennis Kristensen,et al.  ABC of SV: Limited Information Likelihood Inference in Stochastic Volatility Jump-Diffusion Models , 2015 .

[12]  N. Meinshausen,et al.  High-dimensional graphs and variable selection with the Lasso , 2006, math/0608017.

[13]  A. Belloni,et al.  Least Squares After Model Selection in High-Dimensional Sparse Models , 2009, 1001.0188.

[14]  Chris Kirby,et al.  The economic value of volatility timing using “realized” volatility ☆ , 2003 .

[15]  Shuzhong Shi,et al.  Estimating High Dimensional Covariance Matrices and its Applications , 2011 .

[16]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[17]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[18]  Asger Lunde,et al.  Factor Structure in Commodity Futures Return and Volatility , 2017, Journal of Financial and Quantitative Analysis.

[19]  C. Gouriéroux,et al.  The Wishart Autoregressive Process of Multivariate Stochastic Volatility , 2009 .

[20]  N. Hautsch,et al.  Do High-Frequency Data Improve High-Dimensional Portfolio Allocations? , 2013 .

[21]  Adam J. Rothman,et al.  Sparse estimation of large covariance matrices via a nested Lasso penalty , 2008, 0803.3872.

[22]  Tom Leonard,et al.  The Matrix-Logarithmic Covariance Model , 1996 .

[23]  P. Bickel,et al.  Regularized estimation of large covariance matrices , 2008, 0803.1909.

[24]  Francesco Audrino,et al.  Lassoing the Har Model: A Model Selection Perspective on Realized Volatility Dynamics , 2013 .

[25]  Roxana Halbleib,et al.  Modelling and Forecasting Multivariate Realized Volatility , 2008 .

[26]  Jianqing Fan,et al.  High dimensional covariance matrix estimation using a factor model , 2007, math/0701124.

[27]  Chris Kirby,et al.  The Economic Value of Volatility Timing Using 'Realized' Volatility , 2001 .

[28]  Bent Nielsen,et al.  Outlier Detection Algorithms for Least Squares Time Series Regression , 2014 .

[29]  Ke Yu,et al.  Journal of the American Statistical Association Vast Volatility Matrix Estimation Using High- Frequency Data for Portfolio Selection Vast Volatility Matrix Estimation Using High-frequency Data for Portfolio Selection , 2022 .

[30]  Vasyl Golosnoy,et al.  The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility , 2010 .

[31]  Marc Hallin,et al.  Discussion of ``Large covariance estimation by thresholding principal orthogonal complements", by J. Fan, Y. Liao, and M. Mincheva , 2013 .

[32]  Peng Zhao,et al.  On Model Selection Consistency of Lasso , 2006, J. Mach. Learn. Res..

[33]  A. Kock,et al.  Oracle Inequalities for High Dimensional Vector Autoregressions , 2012, 1311.0811.

[34]  Ke Yu,et al.  Constraints , 2019, Sexual Selection.

[35]  N. Shephard,et al.  Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice , 2016 .

[36]  Laurent Callot,et al.  Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy , 2014, 1411.0877.

[37]  Yazhen Wang,et al.  VAST VOLATILITY MATRIX ESTIMATION FOR HIGH-FREQUENCY FINANCIAL DATA , 2010, 1002.4754.

[38]  Jianqing Fan,et al.  High Dimensional Covariance Matrix Estimation in Approximate Factor Models , 2011, Annals of statistics.

[39]  Markku Lanne,et al.  Is the Quantity Theory of Money Useful in Forecasting U.S. Inflation , 2014 .

[40]  秀俊 松井,et al.  Statistics for High-Dimensional Data: Methods, Theory and Applications , 2014 .

[41]  F. Audrino,et al.  Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics , 2013 .

[42]  Gregory H. Bauer,et al.  Forecasting multivariate realized stock market volatility , 2011 .