In this paper it is shown that the number of latent factors in a multiple multivariate regression model need not be larger than the number of the response variables in order to achieve an optimal prediction. The practical importance of this lemma is outlined and an application of such a...

This paper deals with the problem of the discrimination between stable and unstable time series. One criterion for the seperation is given by the size of the Lyapunov exponent, which was originally defined for deterministic systems. However, this paper will show, that the Lyapunov exponent can...

When trying to interpret estimated parameters the researcher is interested in the (relative) importance of the individual predictors. However, if the predictors are highly correlated, the interpretation of coefficients, e.g. as economic ?multipliers?, is not applicable in standard regression or...

This paper analyses the influence of 13 stylized facts of the German economy on the West German business cycles from 1955 to 1994. The method used in this investigation is Statistical Experimental Design with orthogonal factors. We are looking for all existing Plackett-Burman designs realizable...

When analyzing business cycle data, one observes that the relevant predictor variables are often highly correlated. This paper presents a method to obtain measures of importance for the classification of data in which such multicollinearity is present. In systems with highly correlated variables...

Linear Discriminant Analysis (LDA) performs well for classifica- tion of business phases – even though the premises of an LDA are not met. As the variables are highly correlated there are numerical as well as interpretational shortcomings. By transforming the classification problem to a...

In this paper we compare the predictive abilility of Stochastic Volatility (SV)models to that of volatility forecasts implied by option prices. We develop anSV model with implied volatility as an exogeneous var able in the varianceequation which facilitates the use of statistical tests for...

The linear Gaussian state space model for which the common variance istreated as a stochastic time-varying variable is considered for themodelling of economic time series. The focus of this paper is on thesimultaneous estimation of parameters related to the stochasticprocesses of the mean part...

We provide a detailed discussion of the time series modelling of daily tax revenues. The mainfeature of daily tax revenue series is the pattern within calendar months. Standard seasonal timeseries techniques cannot be used since the number of banking days per calendar month varies andbecause...

We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over...