This note is devoted to the application of copulas and linear autoregressive stochastic processes in time series analysis. Common processes like ARMA (autoregressive moving average) and GARCH (generalized autoregressive conditional heteroskedasticity) processes are discussed concerning stationarity and estimation. Especially for ARMA processes asymptotic normality of coefficient estimators of the maximum likelihood method is proved. This note analyses daily data sets of the MSCI index of Europe, Germany, North America and USA in the period 2005-2010 and data of the DAX index during 1995-2010 and fits ARMA processes to them. Furthermore weekly data of the stocks Addidas, Allianz, BMW, Eon, K+S and SAP during the period of 01.01.2003 - 28.03.2011 are used to demonstrate an algorithm which determines the VaR (Value-at-Risk) of the portfolios consisting of these stocks. To be more precise, it applies t copulas to model dependence of portfolio positions and ARMA-GARCH processes to describe the behaviour of return processes. Main results are that the 1% percentile is overestimated and violations of the lower VaR estimate occurs more often than for the upper VaR estimate. Latter suggests that the chosen model does not reflect the asymmetric behaviour of the return processes. Moreover model fitting fails in times of extreme volatility, e.g. in the recent financial crisis.     «

This note is devoted to the application of copulas and linear autoregressive stochastic processes in time series analysis. Common processes like ARMA (autoregressive moving average) and GARCH (generalized autoregressive conditional heteroskedasticity) processes are discussed concerning stationarity and estimation. Especially for ARMA processes asymptotic normality of coefficient estimators of the maximum likelihood method is proved. This note analyses daily data sets of the MSCI index of Europe,...     »