Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in ANDERS B. KOCKAarhus University, CREATES, Denmark. MARCELO C. MEDEIROSDepartment of Economics, Pontifical Catholic University of Rio de Janeiro, Brazil.Abstract. 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.

L_1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations

“…In this case, handling non-Gaussian conditional heteroskedastic errors is of great importance. Other applications include the selection of factors in approximate factor models, as in Bai and Ng (2002), Cheng and Hansen (2012), and Cheng et al (2013); variable selection in non-linear models (Rech et al 2001); forecast combination of many forecasters (Issler andLima 2009, Samuels andSekkel 2013); time-series network models (Barigozzi andBrownlees 2013, Lam andSouza 2014a,b); and forecasting large covariance matrices as in Callot et al (2014). Finally, instrumental variable estimation in a data rich environment with dependent data is also a potential application; see Belloni et al (2012).…”