Testing for jumps in semi-martingales

Abstract

A test recently proposed by Ait-Sahalia and Jacod (2009) to check whether jumps are present in a discretely observed process is entertained. The test provided is a ratio test and when implementing it on discretely observed data, the convergence in probability is checked. If the test statistic tends to 1, then this would mean that the data contains jumps. However no jumps are present in the data if the test converges to another value. In this dissertation this test is carried out on both simulations done by MATLAB and on real stock price data. The data is taken every minute throughout four consecutive days for two different types of stock markets.