Abstract: The selection of high-frequency data based covariance matrix estimators and forecasting models, jointly influence the forecasting performance of covariance, which therefore influences the performance of volatility timing portfolio strategies. When the number of assets is large, a lot of intraday data are not utilized in common high-frequency data based covariance matrix estimators due to non-synchronous trading, implying a loss of efficiency in information usage. Therefore, the KEM estimator which employs all the intraday price information is used to construct the high dimensional covariance matrix estimator in China's stock market, and its performance is compared, with two commonly used estimators. In addition, each of these three estimators is used in five forecasting models, namely the multivariate heterogeneous autoregressive model, the exponentially weighted moving average model, and the short-term, medium-term and long-term moving average models, and their economic performance under three risk-based portfolio strategies is compared. Empirical experiments with the tick-by-tick high-frequency data for 20 constituent stocks of the SSE 50 index show that: (1) The long-term moving average model is the best choice to forecast high-dimensional covariance estimators, since it achieves the lowest cost and the highest return for all the volatility timing strategies, no matter the market is stable or extremely volatile. (2) The KEM estimator is the best choice to estimate high-dimensional covariance matrix when the market is stable, since it achieves the lowest cost and the highest return for all the volatility timing strategies. However, the KEM estimator only achieves the lowest cost when the market is extremely volatile. (3) Among the volatility timing strategies, the equal risk contribution portfolio strategy always achieves the lowest cost, while the global minimum variance portfolio strategy always achieves the highest return, regardless of the market condition. The research not only for the first time evaluates the effectiveness of the KEM estimator in common volatility timing strategies, but for the first time empirically proves that the easily implemented long-term moving average model has significant superiority in high dimensional covariance matrix forecasting, and thus is of critical importance for applications such as investment decision making and risk management.

Key words: covariance matrix forecasting, intraday high-frequency data, KEM algorithm, moving average model, volatility timing