The STARMA - Poisson Model: a New Approach to Short Term Demand Forecasting
GARR/DO R, University of Texas at Austin, USA
The aim of this article is to present a novel modeling framework for the freight demand forecasting problem (FDFP) and also to show the effect of ignoring spatial interactions in model's specification. The FDFP is defined as follows. Several activity cent
The aim of this article is to present a novel modeling framework for the freight demand forecasting problem (FDFP) and also to show the effect of ignoring spatial interactions in model's specification. The FDFP is defined as follows. Several activity centers are spatially distributed over a bounded region where the inhabitants exchange goods and services. The actors that perform the exchange are consumers (final consignees), shippers (origin of the loads) and carriers (transportation companies). A shipper-carrier agreement consists in picking up a load during certain time interval at a given origin to be delivered at certain destination. Both shippers and consumers' locations are fixed and known by the carriers and referred to as sites. The time span is divided into T intervals of equal length. The carriers operate in a less-than-truck load (LTL) manner, that is, pickups and deliveries are separated operations; a load is picked up, sent to a breakbulk terminal, consolidated with other loads and then sent to its final destination. The problem consists in estimating the probability that a load has to be picked up (delivered) at a given origin (destination) at certain interval.
In this paper the freight transportation demand is considered a stochastic process with both time and space interactions. The underlying process is assumed to be compound Poisson. Each site at each time interval has an arrival rate that depends on its past as well as the history of arrival rates at other locations. The dynamic dependence among the arrival rates is assumed to be linear in a space-time autoregressive moving average model (STARMA).
The relevance of considering spatial interactions among the sites is analyzed through a comparison of the "true" freight demand probability distribution (assumed compound Poisson with STARMA arrival rate) with a pure dynamic model (ARMA) fitted to a simulated data set with explicit space-time autocorrelated arrival rates.
In this approach the assumption is that each spatial unit has a rate of requests for service which is both time and space dependent. Thus, there are interactions between the rate of requests at one site and the rates of requests at other sites in a cross-sectional way as well as interactions between the current value of such rates and the history of rates at that particular site. This is captured by a linear STARMA model (Pfeifer and Deutsch, 1980a and 1980b) which will be summarized below.
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