GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY WITH APPLICATIONS IN FINANCE (ARCH, CORRELATION STRUCTURE, GARCH, T-DISTRIBUTION, CAPM)

While conventional time series and econometric models operate under an assumption of constant variance, the Autoregressive Conditional Heteroskedastic (ARCH) process allows the conditional variance to change over time as a function of past squared errors leaving the unconditional variance constant. This type of model has proven useful in modelling several different economic phenomena, including models for the inflation rate, the term structure and foreign exchange rates.

In the first paper a natural generalization of the ARCH process is introduced which allows for past conditional variances in the current conditional variance equation. The extension of the ARCH process to the Generalized ARCH (GARCH) bears much resemblance to the extension of the standard time series AR process to the ARMA process and permits a more parsimonious description in many situations. The statistical properties of this new class of models are discussed along with an empirical example for the inflation rate.

Like in the ARMA analogue the autocorrelation and partial autocorrelation for the squared process may prove helpful in identifying and checking GARCH behavior in the conditional variance. In the second paper simulation experiments are used to study the applicability of the theoretical results. An illustrative example for the Box and Jenkins' IBM stock market price series is presented.

The Capital Asset Pricing Model (CAPM) provides a theoretical structure for the pricing of assets with uncertain returns. The premium to induce risk averse investors to bear the risk is proportional to the non-diversifiable risk. In the third paper a multivariate GARCH model in which the expected return of each asset is proportional to the conditional covariance of that asset with a fully diversified or market portfolio is estimated. The results are encouraging, although not definitive.

The fourth paper postulates that the conditional distribution, instead of being normal, is a standardized Student-t with unknown degrees of freedom. By estimating the degrees of freedom along with the other GARCH parameters, the model allows for a distinction between conditionally heteroskedasticity and a conditionally leptokurtic distribution. When estimating a model for stock returns this leads to major improvements.