Essays in Financial Time Series

Abstract

This thesis consists of three essays on topics in financial time series with particular emphases on specification testing, structural breaks and long memory. The first essay develops an asymptotically valid specification testing framework for the Realised GARCH model of Hansen et al. (2012). The misspecification tests account for the joint dependence between return and the realised measure of volatility and thus extend the existing literature for testing the adequacy of GARCH models. The testing procedure is constructed based on the conditional moment principle and the first-order asymptotic theory. Our Monte Carlo results reveal good finite sample size and power properties. In the second essay, a Monte Carlo experiment is conducted to investigate the relative out-of-sample predictive ability of a class of conditional variance models when either a structural break or long memory is allowed. Our Monte Carlo results reveal that if the true volatility process is stationary short memory and its persistence level is not too high, but is contaminated by a structural break, the presence of the structural break is of importance in choosing a proper size of estimation window in the short-run forecast. If the persistence level is very high, spurious long memory may often dominate the true structural break in the longer-run forecast. For data generation processes without any structural break, the forecasting models, which can characterise the properties of the true conditional variance process, are favourable. In the last essay, we analyse the properties of the S&P 500 stock index return volatility process using historical and realised measures of volatility. We investigate a true property of the stochastic volatility processes by means of econometric tests, which may disentangle true or spurious long memory. The realised variance and realised kernel of the US stock market return exhibit true long memory. However, the historical volatility process shows some evidence of spurious long memory. We examine relative out-of-sample performance of one-day-ahead forecasts, with emphasis on the predictive content of structural changes and long memory. A class of ARFIMA models consistently produces the best-performing forecasts compared to a class of GARCH models. Among the GARCH models, it is shown that a rolling window GARCH forecast and GARCH forecasts which account for breaks outperform the long memory-based GARCH models even with the long memory proxy process.