RT Generic
T1 More is not always better : back to the Kalman filter in dynamic factor models
A1 Poncela, Pilar
A1 Ruiz Ortega, Esther
A2 Universidad Carlos III de Madrid. Departamento de EstadÃstica,
AB In the context of dynamic factor models (DFM), it is known that, if the cross-sectionaland time dimensions tend to infinity, the Kalman filter yields consistent smoothedestimates of the underlying factors. When looking at asymptotic properties, the cross-sectional dimension needs to increase for the filter or stochastic error uncertainty todecrease while the time dimension needs to increase for the parameter uncertainty todecrease. ln this paper, assuming that the model specification is known, we separate thefinite sample contribution of each of both uncertainties to the total uncertaintyassociated with the estimation of the underlying factors. Assuming that the parametersare known, we show that, as far as the serial dependence of the idiosyncratic noises isnot very persistent and regardless of whether their contemporaneous correlations areweak or strong, the filter un-certainty is a non-increasing function of the cross-sectionaldimension. Furthermore, in situations of empirical interest, if the cross-sectionaldimension is beyond a relatively small number, the filter uncertainty only decreasesmarginally. Assuming weak contemporaneous correlations among the seriallyuncorrelated idiosyncratic noises, we prove the consistency not only of smooth but alsoof real time filtered estimates of the underlying factors in a simple case, extending theresults to non-stationary DFM. In practice, the model parameters are un-known andhave to be estimated, adding further uncertainty to the estimated factors. We usesimulations to measure this uncertainty in finite samples and show that, for the samplesizes usually encountered in practice when DFM are fitted to macroeconomic variables,the contribution of the parameter uncertainty can represent a large percentage of thetotal uncertainty involved in factor extraction. All results are illustrated estimatingcommon factors of simulated time series
YR 2012
FD 2012-10
LK https://hdl.handle.net/10016/15782
UL https://hdl.handle.net/10016/15782
LA eng
NO Financial support from the Spanish Government projects ECO2009-10287 and ECO2012-32854 is acknowledged bythe first author while the second author acknowledges support from projectsECO2009-08100 and ECO2012-32401.
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RD 28 may. 2024