z-Transform and identification of linear econometric models with autocorrelated errors

The paper consists of two main parts. In the first part we derive the solution of systems of linear stochastic difference equations by means of thez-transform. In the second part thisz-transform is used to treat the problem of identification of linear econometric systems (the term econometric is used to stress the special aspects of the identification problem dealt with in econometrics). It is shown, that under suitable restrictions observationally equivalent structures are related by unimodular matrices. Using this result, we state (rank-) conditions which ensure, that the unimodular matrices are constant, such that the classical econometric identification theorems can be applied. These conditions are given for stationary errors in the general case as well as in the MA, AR and ARMA case.     

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Struktur der österreichischen Industrieproduktion

Summary Spectral methods are applied to disaggregated production indices to analyze the structure of the Austrian industrial production with special emphasis on their business cycle behavior. In the model an additive partition of each series in a trend, long term, business cycle, seasonal, and disturbance component is used. The univariate analysis investigates the relative importance of each of these components. Lead-lag relationships with respect to a reference series are calculated in the bivariate analysis. Estimation by complex demodulates enables to check the stability of the frequency characteristics over time.     

Estimating the codifference function of linear time series models with infinite variance

We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetric α-stable innovations, 0 < α ≤ 2. In addition, we derive their limiting distribution. We present a simulation study showing the dependence of the estimator on certain design parameters. Finally, we provide an empirical example using some stocks from Indonesia Stock Exchange.     

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Identification of Factor Models for Forecasting Returns

A data-driven approach for forecasting returns of asset pricesis introduced. Special emphasis is given to data-driven specificationand to dimension reduction. Specification is performed by amodified AIC, BIC-based An-algorithm. Quasi-static principalcomponent analysis, quasi-static factor models with idiosyncraticerrors and reduced rank regression are considered. The forecastingresults obtained are compared.     

The uniqueness of the transfer function of linear systems from input-output observations

Summary Some problems preceding the estimation of the (rational) transfer function of a linear dynamical system are considered: Fairly general conditions under which these transfer functions are uniquely determined from the second moments of the observed processes and under which the relation between the second moments and the transfer functions is continuous are given. Most of these conditions include the non (asymptotically) stationary as well as the unstable case.

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Zusammenfassung Einige der Schätzung von (rationalen) Transferfunktionen linearer dynamischer Systeme vorgelagerte Probleme werden untersucht: Es werden relativ allgemeine Bedingungen angegeben unter denen diese Transferfunktionen eindeutig aus den zweiten Momenten der beobachteten Prozesse bestimmt werden können und es wird untersucht unter welchen Bedingungen diese Abhängigkeit stetig ist. Insbesondere ist sowohl der nicht (asymptotisch) stationäre als auch der nichtstabile Fall miteingeschlossen.

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This paper is an extension of a previous paper by the first and third author entitled Identifiability of Transfer Functions in Linear Systems (Research Memo. Inst. of Econometrics, University of Bonn, 1977).