MODELING NONSTATIONARY AND LEPTOKURTIC FINANCIAL TIME SERIES
Ying Chen and
Econometric Theory, 2015, vol. 31, issue 4, 703-728
Financial time series is often assumed to be stationary and has a normal distribution in the literature. Both assumptions are however unrealistic. This paper proposes a new methodology with a focus on volatility estimation that is able to account for nonstationarity and heavy tails simultaneously. In particular, a local exponential smoothing (LES) approach is developed, in which weak estimates with different memory parameters are aggregated in a locally adaptive way. The procedure is fully automatic and the parameters are tuned by a new propagation approach. The extensive and practically oriented numerical results confirm the desired properties of the constructed estimate: it performs stable in a nearly time homogeneous situation and is sensitive to structural shifts. Our main theoretical â€œoracleâ€ result claims that the aggregated estimate performs as good as the best estimate in the considered family. The results are stated under realistic and unrestrictive assumptions on the model.
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