Jump detection in high-frequency financial data using wavelets

The presence of spikes or cusps in high-frequency return series might generate problems in terms of inference and estimation of the parameters in volatility models. For example, the presence of jumps in a time series can influence sample autocorrelations, which can cause misidentification or generate spurious ARCH effects. On the other hand, these jumps might also hide relevant heteroskedastic behavior of the dependence structure of a series, leading to identification issues and a poorer fit to a model. This paper proposes a wavelet-shrinkage method to separate out jumps in high-frequency financial series, fitting a suitable model that accounts for its stylized facts. We also perform simulation studies to assess the effectiveness of the proposed method, in addition to illustrating the effect of the jumps in time series. Lastly, we use the methodology to model real high-frequency time series of stocks traded on the Brazilian Stock Exchange and OTC and a series of cryptocurrencies trades.