We describe some fast algorithms for reconciling large collections of time series forecasts with aggregation constraints. The constraints arise due to the need for forecasts of collections of time series with hierarchical or grouped structures to add up in the same manner as the observed time...

In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these "hierarchical time series". They are commonly forecast using either a "bottom-up"...

Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be...

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The first reduces parameter space by imposing long-term...

The vector innovation structural time series framework is proposed as a way of modelling a set of related time series. Like all multi-series approaches, the aim is to exploit potential inter-series dependencies to improve the fit and forecasts. A key feature of the framework is that the series...

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a...

We compare the short- to medium-term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These...

The focus of this paper is on the relationship between the exponential smoothing methods of forecasting and the integrated autoregressive-moving average models underlying them. In this paper we derive, for the first time, the general linear relationship between their parameters. A method,...

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical...

We propose a new method for forecasting age-specific mortality and fertility rates observed over time. Our approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and...