Space Time Autoregressive Model Research Articles

Evaluating forecasting accuracy of the temporally aggregated space–time autoregressive model

This article aims at analysing the effect of temporal aggregation in space–time autoregressive models. By means of a simulation experiment, it is shown that, the greater the spatial dependence in time series, the lower the bias due to temporal aggregation. However, the ratio between the average mean squared forecasting errors for daily data and that for yearly data seems to decrease for high parameter values.

Aggregation of space-time processes

Abstract In this paper we compare the relative efficiency of different methods of forecasting the aggregate of spatially correlated variables. Small sample simulations confirm the asymptotic result that improved forecasting performance can be obtained by imposing a priori constraints on the amount of spatial correlation in the system. One way to do so is to aggregate forecasts from a space-time autoregressive model (Elements of Spatial Structure, Cambridge University Press, Cambridge, 1975), which offers a solution to the ‘curse of dimensionality’ that arises when forecasting with VARs. We also show that ignoring spatial correlation, even when it is weak, leads to highly inaccurate forecasts. Finally, if the system satisfies a ‘poolability’ condition, there is a benefit in forecasting the aggregate variable directly.

Aggregation of Space-Time Processes

In this paper we compare the relative efficiency of different methods of forecasting the aggregate of spatially correlated variables. Small sample simulations confirm the asymptotic result that improved forecasting performance can be obtained by imposing a priori constraints on the amount of spatial correlation in the system. One way to do so is to aggregate forecasts from a Space-Time Autoregressive model (Cliff et al., 1975), which offers a solution to the 'curse of dimensionality' that arises when forecasting with VARs. We also show that ignoring spatial correlation, even when it is weak, leads to highly inaccurate forecasts. Finally, if the system satisfies a 'poolability' condition, there is a benefit in forecasting the aggregate variable directly.

Space–time series modelling of beach and shoreline data

This paper focuses on utilizing Box–Jenkins modelling procedures to identify models which best describe a time series (1978–1994) of beach and shoreline data collected from the Northeast Beach, Point Pelee, Lake Erie, Canada. The results highlight the influence of localized stochastic processes on beach sediment flux levels and on shoreline change. A spatial autoregressive model best describes the variation for beach net sediment flux. The model reinforces the hypothesis that beach net sediment flux in adjacent sites are interdependent and represent the cumulative spatial effects of short-term sediment flow processes such as longshore drift and persistent localized sediment circulation cells. Additional findings also suggest that a space–time autoregressive model best fits the data on spatial–temporal variations of shoreline retreat. The implication of this model is that the shoreline will retreat quite rapidly, but readjusts to an aggradational state at a much slower rate.

Spatial and space-time correlations in systems of subpopulations with genetic drift and migration.

The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.