engleski

Realized density estimation using intraday prices

Although it is essential to make assumption about the true probability distribution of underlying asset returns, it still remains unknown. Moreover, the assumption that underlying distribution is time-invariant makes traditional forecasting models, especially parametric ones, inappropriate. The objective is to provide the best data-driven proxy of the unknown distribution of returns using high frequency data (with application to DAX intraday price observations on various trading days). Availability of high-frequency data, accordance with IT developments, enabled the use of more information to estimate not only daily mean and variance (volatility) but also higher moments and entire realized distribution of returns. Kernel estimation technique is used which balances between the bias and the variance according to the selection of the sampling frequency at slow-time scale, while the fast-time scale sampling frequency is fixed. Results show that slow-time scale frequency do not vary much across trading days and that optimal Kernel bandwidth depends on the optimal two-time scale estimation of realized variance (standard deviation). Kernel density estimation obtained in this way enables a trade-off between the bias and the variance and thus all realized moments (mean, variance, kurtosis and skewness) are free from microstructure noise. Limitation of the research is that considers only developed market. The obtained findings offer valuable information to market participants by pinpointing how often high- frequency data should be sampled to obtain unbiased and consistent estimation of entire probability density function for a given trading day using Kernel approach which is nonparametric. It also gives better insights in issues when dealing with high-frequency data, and supports previous findings that returns are not identically distributed and unlikely Gaussian. To the best of the authors’ knowledge, previous studies have not considered finding the appropriate data-driven Kernel bandwidth to estimate the true but unknown probability density function of DAX returns. This study also enriches the literature by providing an optimal slow-time scale frequency when applying two-time scale estimator.

Kernel density estimation ; bandwidth selection ; optimal slow-time scale ; high-frequency

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