It is widely known that conditional covariances of asset returns change over time.

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SUMMARY. This paper discusses an econometric technique based on optimal control theory which, by employing a variation of the near-neighbourhood search problem, is seen to be suitable for the type of research that requires estimating time-varying parameters for linear regression models. The methodology is based on the characterization of the time-varying parameter (TVP) problem as an optimal control problem, with an explicit allowance for welfare loss considerations, which leads to an algorithm capable of updating the values of the time-varying parameters as well as their covariance matrices. The technique adopts an instruments-targets approach, with the initial condition and the emphasis on parameter flexibility being the instruments; and the total welfare loss and the norm of the error vector being the targets. The methodology is a blend of the flexible least squares and Kalman filter techniques. By determining all the required priors endogenously, it is seen to overcome some of the drawbacks associated with these two earlier approaches to the TVP problem. The method works on the premise that the dynamics of the system are determined by the system itself without being specified by the user in an arbitrary fashion. 1.

Abstract. Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses this problem for small and medium sized samples and heavy tailed noise. In particular, we assume that the noise is regularly varying, i.e., the tails of the noise distribution exhibit power law behavior. Then the distributions of the regression estimators are heavy tailed themselves. This is relevant for regressions involving financial data which are typically heavy tailed. In medium sized samples and with some dependency in the noise structure, the regression coefficient estimators can deviate considerably from their true values. The relevance of the theory is demonstrated for the highly variable cross country estimates of the expectations coefficient in yield curve regressions. 1. Some motivation Estimators of the coefficients in equations of regression type which involve financial data are often found to vary considerably across different samples. This observation pertains to finance models like the CAPM beta regression, the forward premium equation and the yield curve regression. In economics, macro models like the monetary model of the foreign exchange rate often yield regression coefficients which significantly deviate from the unitary coefficient on money which is based on the theoretical assumption that money is neutral. The uncertainty in CAPM regressions was reviewed

Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions.