The paper estimates an index of coincident economic indicators for the US economy by using time series with different frequencies of observation (monthly and quarterly, possibly with missing values). The model that is considered is the dynamic factor model that was proposed by Stock and Watson, specified in the logarithms of the original variables and at the monthly frequency, which poses a problem of temporal aggregation with a non-linear observational constraint when quarterly time series are included. Our main methodological contribution is to provide an exact solution to this problem that hinges on conditional mode estimation by iteration of the extended Kalman filtering and smoothing equations. On the empirical side the contribution of the paper is to provide monthly estimates of quarterly indicators, among which is the gross domestic product, that are consistent with the quarterly totals. Two applications are considered: the first dealing with the construction of a coincident index for the US economy, whereas the second does the same with reference to the euro area. Copyright 2006 Royal Statistical Society.

In this paper we provide a multivariate framework for temporal disaggregation of time series observed at a certain frequency into higher frequency data. The suggested method uses the seemingly unrelated time series equations model and is estimated by the Kalman filter. The methodology is flexible enough to allow for almost any kind of temporal disaggregation problem of both raw and seasonally adjusted time series. Comparisons with other temporal disaggregation methods proposed by the literature are presented using a wide OECD data set.

The paper presents a comparative real-time analysis of alternative indirect estimates relative to monthly euro area employment. In the experiment quarterly employment is temporally disaggregated using monthly unemployment as related series. The strategies under comparison make use of the contribution of sectoral data of the euro area and its six larger member states. The comparison is carried out among univariate temporal disaggregations of the Chow and Lin type and multivariate structural time series models of small and medium size. Specifications in logarithms are also systematically assessed. All multivariate set-ups, up to 49 series modelled simultaneously, are estimated via the EM algorithm. Main conclusions are that mean revision errors of disaggregated estimates are overall small, a gain is obtained when the model strategy takes into account the information by both sector and member state and that larger multivariate set-ups perform very well, with several advantages with respect to simpler models.

In this paper, we discuss the most recent developments in temporal disaggregation techniques carried out at the Istituto Nazionale di Statistica (ISTAT). They concern the extension from static to dynamic autoregressive distributed lag regressions and the adoption of the state-space framework for the statistical treatment of temporal disaggregation. Beyond the development of a unified procedure for both static and dynamic methods from one side and the treatment of the logarithmic transformation from the other, we provide short guidelines for model selection. The inclusion of stochastic trends in the regressions is also discussed. We evaluate the new dynamic methods by implementing a large-scale exercise using the ISTAT annual value added data jointly with quarterly industrial production over the 1995-2013 period. The main finding is that autoregressive distributed lag disaggregations reduce forecast errors in comparison to static variants, at a price of lower correlations with related high-frequency indicators. Moreover, problematic outcomes are limited to few cases.

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