Nonlinearities and regime shifts in financial time series

Abstract: This volume contains four essays on various topics in the field of financial econometrics. All four discuss the properties of high frequency financial data and its implications on the model choice when an estimate of the capital asset return volatility is in focus. The interest lies both in characterizing "stylized facts" in such series with time series models and in predicting volatility.The first essay, entitled A Survey of Recent Papers Considering the Standard & Poor 500 Composite Stock Index, presents recent empirical findings and stylized facts in the financial market from 1987 to 1996 and gives a brief introduction to the research field of capital asset return volatitlity models and properties of high frequency financial data. As the title indicates, the survey is restricted to research on the well known Standard & Poor 500 index.The second essay, with the title, Stylized Facts of Daily Return Series and the Hidden Markov Model, investigates the properties of the hidden Markov Model, HMM, and its capability of reproducing stylized facts of financial high frequency data.The third essay, Modelling the Conditional Mean and Conditional Variance: A combined Smooth Transition and Hidden Markov Approach with an Application to High Frequency Series, investigates the consequences of combining a nonlinear parameterized conditional mean with an HMM for the conditional variance when characterization of stylized facts is considered.Finally, the fourth essay entitled, Volatility Forecasting for Option Pricing on Exchange Rates and Stock Prices, investigates the volatility forecasting performance of some of the most frequently used capital asset return volatility models such as the GARCH with normal and t-distributed errors, the EGARCH and the HMM. The prediction error minimization approach is also investigated.Each essay is self-contained and could, in principle, be read in any order chosen by the reader. This, however, requires a working knowledge of the properties of the HMM. For readers less familiar with the research field the first essay may serve as an helpful introduction to the following three essays.