Forecasting realized volatility with long memory time series models using high frequency financial data: Estimation, prediction, seasonal adjustment and computation

This dissertation concentrates on the realized volatility measure constructed from time series of high frequency financial returns. Realized volatility has strong long memory and can be predicted using long memory time series models.; First, the optimal linear forecasts from a long memory stochastic volatility (LMSV) model are constructed in daily, weekly and monthly horizons to predict the realized volatility of the S&P 500 index constructed with 30-minute squared returns of the index. Along with the new forecasting method, a new frequency-domain seasonally adjustment method for the 30-minute returns volatility is proposed.; Computational efficiency is particularly important for high frequency modeling. The fast solution of the large Toeplitz covariance system from a long memory time series is desirable in both financial econometric application of volatility forecasting and pure statistical application such as Gaussian likelihood estimation of a time series with long memory. We theoretically justify the efficiency of the Preconditioned Conjugate Gradient (PCG) algorithm for solving such Toeplitz system and successfully apply the PCG algorithm to volatility forecasting and smoothing with high frequency data. A new method of approximating the determinant of the Toeplitz covariance matrix along with the PCG algorithm also improves the Gaussian likelihood estimation of a long memory time series.; Furthermore, in order to exploit the additional information in the tick-by-tick ultra-high frequency transaction-level financial data for forecasting the realized volatility, we studied the duration between consecutive trades or quote changes, the transaction volume of such trades and the realized volatility constructed from 5-minute squared returns for 10 stocks in the Dow Jones Industrial Average index. Long memory is again a strong stylized facts in these financial statistics. Motivated by the existing studies, long memory stochastic latent variable models are proposed and the estimation and forecasting for such models are successfully implemented. The PCG algorithm is again the key for the efficient computation in the empirical studies.; It is found that long memory should be incorporated when forecasting realized volatility, trade counts, quote counts or trade volume. Higher frequency data do provide extra information to forecast realized volatility even though there seems to be limited advantage of modeling the high frequency returns directly versus modeling the realized volatility itself as a long memory time series when forecasting the realized volatility is the sole purpose. Future research directions are also discussed.