An integrated framework for visualizing and forecasting realized covariance matrices
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Statistics for High-Frequency Data
An integrated framework for visualizing and forecasting realized covariance matrices Hideto Shigemoto1 · Takayuki Morimoto2 Received: 27 August 2020 / Accepted: 7 November 2020 © Japanese Federation of Statistical Science Associations 2020
Abstract This paper proposes an integrated framework for visualizing and forecasting realized covariance matrices to enable the efficient construction and prediction of an optimal portfolio. Multivariate realized kernels are typically derived from intra-day high-frequency data, and are then used to estimate the realized covariance matrix via the graphical lasso algorithm. To forecast the realized covariances, we employ the conditional autoregressive Wishart model and its variants. Finally, we compute the Stein loss function and execute the model-confidence-set procedure to obtain the best model for optimal portfolio selection. Keywords High-frequency data · Multivariate realized kernel · Graphical lasso · Realized covariance · Conditional autoregressive Wishart (CAW )model · Stein loss · Model-confidence-set (MCS) · Optimal portfolio
1 Introduction Estimation and prediction of covariance are fundamental to financial practices such as asset allocation and risk management; however, the covariance of financial-asset returns cannot be observed directly. Most existing models can be divided into two categories; examples include the multivariate GARCH model, which treats past observations as measurable, and the multivariate stochastic volatility model, which treats the covariance matrix as if it consists of stochastic values. At present, covariance estimation and modeling approaches involve the construction of a realized * Takayuki Morimoto [email protected] Hideto Shigemoto h‑[email protected] 1
Graduate school of Science and Technology, Kwansei Gakuin University, 2‑1 Gakuen, Sanda, Hyogo 669‑1337, Japan
2
School of Science and Technology, Kwansei Gakuin University, 2‑1 Gakuen, Sanda, Hyogo 669‑1337, Japan
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Vol.:(0123456789)
Japanese Journal of Statistics and Data Science
covariance matrix that accurately estimates a covariance matrix over a fixed period constructed with high-frequency data. For example, Noureldin et al. (2012) incorporates ex-post covariance matrix estimates from high-frequency data into multivariate GARCH models. Similarly, the extension of realized stochastic volatility models in such a situation was proposed in Shirota et al. (2017) and Yamauchi and Omori (2020). Consistent estimation of large matrices based on high-dimensional data usually requires some sparsity, which may result from appropriate formulation of some lowdimensional structures within the high-dimensional data (Kim et al. 2018; Tao et al. 2013). Hence, Tao et al. (2013) and Kim et al. (2016, 2018) proposed procedures that require sparsity in the covariance matrix, which itself must be estimated. In Brownlees et al. (2018), realized networks that apply a graphical lasso (Friedman et al. 2008) to impose sparsity upon the precision matr
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