Theis Lange Asymptotic Theory in Financial Time Series Models with Conditional Heteroscedasticity

The present thesis deals with asymptotic analysis of financial time series models with conditional heteroscedasticity. It is well-established within financial econometrics that most financial time series data exhibit time varying conditional volatility, as well as other types of non-linearities. Reflecting this, all four essays of this thesis consider models allowing for time varying conditional volatility, or heteroscedasticity. Each essay is described in detail below. In the first essay a novel estimation technique is suggested to deal with estimation of parameters in the case of heavy tails in the autoregressive (AR) model with autoregressive conditional heteroscedastic (ARCH) innovations. The second essay introduces a new and quite general nonlinear multivariate error correction model with regime switching and discusses a theory for inference. In this model cointegration can be analyzed with multivariate ARCH innovations. In the third essay properties of the much applied heteroscedastic robust Wald test statistic is studied in the context of the ARARCH model with heavy tails. Finally, in the fourth essay, it is shown that the stylized fact that almost all financial time series exhibit integrated GARCH (IGARCH), can be explained by assuming that the true data generating mechanism is a continuous time stochastic volatility model. Lange, Rahbek & Jensen (2007): Estimation and Asymptotic Inference in the AR-ARCH Model. This paper studies asymptotic properties of the quasimaximum likelihood estimator (QMLE) and of a suggested modified version for the parameters in the AR-ARCH model. The modified QMLE (MQMLE) is based on truncation of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We