The correct implementation of the Durbin and Koopman simulation smoother is explained. A possible misunderstanding is pointed out and clarified for both the basic state space model with a non-zero mean of the initial state and with time-varying intercepts (mean adjustments).

The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In...

The rank of the spectral density matrix conveys relevant information in a variety of modelling scenarios. Phillips (1986) showed that a necessary condition for cointegration is that the spectral density matrix of the innovation sequence at frequency zero is of a reduced rank. In a recent paper...

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics...

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics...

It is widely known that significant in-sample evidence of predictability does not garantuee significant out-of-sample predictability. This is often interpreted as an indiciation that in-sample evidence is likely to be spurious and should be discounted. In this paper we question this conventional...

The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive de?nite matrix estimate...

When back-testing the calibration quality of rating systems two-sided statistical tests can detect over- and underestimation of credit risk. Some users though, such as risk-averse investors and regulators, are primarily interested in the underestimation of risk only, and thus require one-sided...

When back-testing the calibration quality of rating systems two-sided statistical tests can detect over- and under-estimation of credit risk. Some users though, such as risk-averse investors and regulators, are primarily interested in the under-estimation of risk only, and thus require one-sided...

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression eroor as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity....