Modelling and forecasting time series sampled at different frequencies

Abstract

This paper discusses how to specify an observable high-frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both, the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high-frequency model, standard state-space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. Our method has three main uses. First, it is useful to disaggregate a vector of lowfrequency time series into high-frequency estimates coherent with both, the sample information and its statistical properties. Second, it may improve forecasting of the low-frequency variables, as the forecasts conditional to high-frequency indicators have in general smaller error variances than those derived from the corresponding low-frequency values. Third, the resulting forecasts can be updated as new high-frequency values become available, thus providing an effective tool to assess the effect of new information over medium term expectations. An example using national accounting data illustrates the practical application of this method.

Short‐term forecasts of economic activity: Are fortnightly factors useful?

“…These results are in line with the findings of Casals, Jerez, and Sotoca (2009), who show theoretically how temporal aggregation affects the predictive accuracy of the models estimated with low-frequency data (see also Marcellino, 1999). These results are in line with the findings of Casals, Jerez, and Sotoca (2009), who show theoretically how temporal aggregation affects the predictive accuracy of the models estimated with low-frequency data (see also Marcellino, 1999).…”

“…We find that the use of high-frequency indicators significantly contributes to improving the estimates and the forecasts of Italian GDP. These results are in line with the findings of Casals, Jerez, and Sotoca (2009), who show theoretically how temporal aggregation affects the predictive accuracy of the models estimated with low-frequency data (see also Marcellino, 1999). To assess the performance and forecasting ability of our model in real time, we conduct an out-of-sample exercise and compare our results with other alternative models that do not include the ortnightly frequency.…”

“…In particular, it seems that high-frequency indicators are particularly useful for nowcasting (i.e., the forecast of the current value of GDP, not yet released by statistical agencies), since in Q T − 1 and Q T we observe the highest difference between the RMSFEs of the fortnightly model compared to the other three competitive It is worth noting that the forecasts of the two alternative monthly factor models are very similar: The inclusion of high-frequency indicators aggregated at a lower frequency may not improve forecasting ability, as asserted by the theoretical finding of Casals et al (2009). In particular, it seems that high-frequency indicators are particularly useful for nowcasting (i.e., the forecast of the current value of GDP, not yet released by statistical agencies), since in Q T − 1 and Q T we observe the highest difference between the RMSFEs of the fortnightly model compared to the other three competitive It is worth noting that the forecasts of the two alternative monthly factor models are very similar: The inclusion of high-frequency indicators aggregated at a lower frequency may not improve forecasting ability, as asserted by the theoretical finding of Casals et al (2009).…”

“…The analysis is conducted over two different sample periods. It is worth noting that the forecasts of the two alternative monthly factor models are very similar: The inclusion of high-frequency indicators aggregated at a lower frequency may not improve forecasting ability, as asserted by the theoretical finding of Casals et al (2009). To predict the values of a low-frequency indicator (e.g., GDP, as in our case), then a model which efficiently combines lowand high-frequency data may provide better forecasts than a model that uses only low-frequency data.…”

Sovereign bond yield spreads and market sentiment and expectations: Empirical evidence from Euro area countries

“…Firstly, we re-estimate all the models using quarterly instead of monthly data since the presence of some explanatory variables with lower frequency may affect the specification of the dynamics of the models and thus it may influence our main empirical results (Casals, Jerez, & Sotoca, 2009). As discussed in Section 3.2, most of the fiscal and macroeconomic variables considered are taken from the Eurostat quarterly database and monthly series are then obtained by keeping the value constant in each month of the quarter.…”