Spot Variance Path Estimation and Its Application to High Frequency Jump Testing

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Abstract
This paper considers spot variance path estimation from datasets of intraday high frequency asset prices in the presence of diurnal variance patterns, jumps, leverage effects and microstructure noise. We rely on parametric and nonparametric methods. The estimated spot variance path can be used to extend an existing high frequency jump test statistic, to detect arrival times of jumps and to obtain distributional characteristics of detected jumps. The effectiveness of our approach is explored through Monte Carlo simulations. It is shown that sparse sampling for mitigating the impact of microstructure noise has an adverse effect on both spot variance estimation and jump detection. In our approach we can analyze high frequency price observations that are contaminated with microstructure noise without the need for sparse sampling, say at fifteen minute intervals. An empirical illustration is presented for the intraday EUR/USD exchange rates. Our main finding is that fewer jumps are detected when sampling intervals increase.