In this paper we introduce time-varying parameters in the dynamic Nelson-Siegel yield curve model for the simultaneous analysis and forecasting of interest rates of different maturities, known as the term structure. The Nelson-Siegel model has been recently reformulated as a dynamic factor model where the latent factors are interpreted as the level, slope and curvature of the term structure. The factors are modelled by a vector autoregressive process. We propose to extend this framework in two directions. First, the factor loadings are made time-varying through a simple single step function and we show that the model fit increases significantly as a result. The step function can be replaced by a spline function to allow for more smoothness and flexibility. Second, we investigate empirically whether the volatility in interest rates across different time periods is constant. For this purpose, we introduce a common volatility component that is specified as a spline function of time and scaled appropriately for each series.Based on a data-set that is analysed by others, we present empirical evidence where time-varying loadings and volatilities in the dynamic Nelson-Siegel framework lead to significant increases in model fit. Improvements in the forecasting of the term structure are also reported. Finally, we provide an illustration where the model is applied to an unbalanced dataset. It shows that missing data entries can be estimated accurately.

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The multivariate analysis of a panel of economic and financial time series with mixed frequencies is a challenging problem. The standard solution is to analyze the mix of monthly and quarterly time series jointly by means of a multivariate dynamic model with a monthly time index: artificial missing values are inserted for the intermediate months of the quarterly time series. In this paper we explore an alternative solution for a class of dynamic factor models that is specified by means of a low frequency quarterly time index. We show that there is no need to introduce artificial missing values while the high frequency (monthly) information is preserved and can still be analyzed. We also provide evidence that the analysis based on a low frequency specification can be carried out in a computationally more efficient way. A comparison study with existing mixed frequency procedures is presented and discussed. Furthermore, we modify the method of maximum likelihood in the context of a dynamic factor model. We introduce variable-specific weights in the likelihood function to let some variable equations be of more importance during the estimation process. We derive the asymptotic properties of the weighted maximum likelihood estimator and we show that the estimator is consistent and asymptotically normal. We also verify the weighted estimation method in a Monte Carlo study to investigate the effect of different choices for the weights in different scenarios. Finally, we empirically illustrate the new developments for the extraction of a coincident economic indicator from a small panel of mixed frequency economic time series.