In the context of dynamic factor models (DFM), it is known that, if the cross-sectional and time dimensions tend to infinity, the Kalman filter yields consistent smoothed estimates of the underlying factors. When looking at asymptotic properties, the cross- sectional dimension needs to increase...

In the context of linear state space models with known parameters, the Kalman filter (KF) generates best linear unbiased predictions of the underlying states together with their corresponding Prediction Mean Square Errors (PMSE). However, in practice, when the filter is run with the parameters...

The adequacy of GARCH models is often analyzed by comparing plug-in and sample kurtosis and autocorrelations of squares. We analyse the finite sample suitability of this comparison and show that it is not appropiate in general.

Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original...

In this paper, we show how to simplify the construction of bootstrap prediction densities in multivariate VAR models by avoiding the backward representation. Bootstrap prediction densities are attractive because they incorporate the parameter uncertainty a any particular assumption about the...

Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original...

This article compares multivariate and univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to forecast portfolio value-at-risk (VaR). We provide a comprehensive look at the problem by considering realistic models and diversified portfolios containing a large...

Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the variance as an unobservable variable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. Although it is not easy...

In this paper, we propose a new bootstrap procedure to obtain prediction intervals of future Value at Risk (VaR) and Expected Shortfall (ES) in the context of univariate GARCH models. These intervals incorporate the parameter uncertainty associated with the estimation of the conditional variance...

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage effect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH specication is the most exible while the GJR model may...