Identifying jumps variations in high-frequency time series

• Autor(a) principal: Duran, William Gonzalo Rojas
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-09092022-194123/
• topic: Activity jumps; Cramér von Mises; Cramér-von Mises; Distribution function; função de distribuição; Itô semimartingal; Itô semimartingale; Saltos; variação de saltos; Variation jumps

Stochastic models based on diffusions are often used to describe complex dynamical systems in biology, engineering, finance, physics etc. However, these models, when applied in finance, for example, do not take into account possible price jumps during a business session on a stock exchange due to the arrival of market information. In diffusion models, price movements are conditionally Gaussian, so large and sudden movements do not occur. On the other hand, in practice, price jumps can give rise to substantial losses or gains. Therefore, it is important to analyze the functional volatility for high frequency data, taking into account the presence of these jumps. This work consist of two parts. The first part refers to detection of jumps in a time series using wavelets. The second part is devoted to studying a test statistic of the Cramér-Von Mises type test statistic to identify variations in time series jumps with high frequency data. The main result and contribution of this study shows that the distribution function of the proposed test statistic follows approximately a gamma distribution. This is of vital importance because it enables us to determine the critical region for the rejection of the null hypothesis of interest. We observe better results in comparison with the Kolmogorov-Smirnov (KS) test. Specifically, we show that the power and the error rate of the test using Cramér-von Mises (Cv-M) statistic is better than those using the KS test statistic, showing a higher detection power and lower error rate. We applied the proposed test to three real data sets, namely, the stock returns of Google, Apple and Goldman Sachs (GS), and found that the proposed test can capture the dynamics of the series.