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...

Multi-step forecasts can be produced recursively by iterating a one-step model, or directly using a specific model for each horizon. Choosing between these two strategies is not an easy task since it involves a trade-off between bias and estimation variance over the forecast horizon. Using a...

Theoretical results on the properties of forecasts obtained using singular spectrum analysis are presented in this paper. The mean squared forecast error is derived under broad regularity conditions, and it is shown that the forecasts obtained in practice will converge to their population...

One of the most widely used standard procedures for model evaluation in classification and regression is K-fold cross-validation (CV). However, when it comes to time series forecasting, because of the inherent serial correlation and potential non-stationarity of the data, its application is not...

This paper investigates the empirical properties of autoregressive approximations to two classes of process for which the usual regularity conditions do not apply; namely the non-invertible and fractionally integrated processes considered in Poskitt (2006). In that paper the theoretical...

We show how cubic smoothing splines fitted to univariate time series data can be used to obtain local linear forecasts. Our approach is based on a stochastic state space model which allows the use of a likelihood approach for estimating the smoothing parameter, and which enables easy...

In this paper we explore the hierarchical nature of tourism demand time series and produce short-term forecasts for Australian domestic tourism. The data and forecasts are organized in a hierarchy based on disaggregating the data for different geographical regions and for different purposes of...

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...