A Space‐Time Bilinear Model and its Identification

Abstract

In this paper we propose a class of space±time bilinear (STBL) models which can be used to model space±time series which exhibit bilinear behavior. The STBL model is shown to be an extension of a space±time autoregressive movingaverage model and a special form of the multiple bilinear model. We focus on the identi®cation procedure of the models. Some results about stationarity and the covariance structure of these models are also discussed. An identi®cation procedure based on the squared observations is established for the simplest pure bilinear model and some illustrative examples are provided.

Evaluating restricted common factor models for non-stationary data

“…Two statically loaded independent I(1) common factors (F j , j = 1, 2), the first with a drift δ = 0.01, shape long-term growth over time (with T = 50, 100, 150) and pervasive dependence across N spatial units, hereafter regions (with N = 50, 100, 150). Short-term and local fluctuations of the error at time t for unit i, ε t,i , are governed by a STARMA(1,1,1) process (that is, an ARMA(1,1) augmented with a spatial lag term at time (t−1); see, e.g, Dai and Billard, 1998). Thus, the value of the variable Y at time t for region i is generated as follows:…”

Bayesian Inferences and Forecasting in Spatial Time Series Models

“…A class of STBL models designed to model spatial time series data which exhibit bilinear behavior has been presented in Dai and Billard (1998). The spatial time series bilinear model can be defined as in Definition 1.…”

“…Hence, the eight provinces in Mumps study and the 1 st order weighting matrix(here, (8 × 8)) is that as shown in Figure 2. The full model STBL (1 1 , 1 1 , 1 1 , 1 1 ) were identified with method proposed by Dai and Billard(1998) and we employ the residuals of ST AR(5 1 ) regression of z(t) as ini- The results in Table 2 and Figure 3 indicate that the Bayesian analysis with Gibbs sampler provides reasonable inference for the complex STBL model, since the estimated posterior means of parameters are all within interquartile ranges and the sequential plots of the Gibbs sequences are stable and fluctuate in the neighborhood of the estimated posterior means.…”

β -Spline Estimation in a Semiparametric Regression Model with Nonlinear Time Series Errors

“…[17] applied model (1.2) to study the well-known Wolfer sunspot numbers for the years from 1700 to 1955 and a seismic record obtained from an underground nuclear explosion that was carried out in the USA on October 29th, 1966. Recently, model (1.2) has been extended to the case of space time [18,19] . More references about the theoretical results, applications and the extensions of the model (1.2) can be found in the monograph of [9] .…”