A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))

Abstract

A simple time series model for bivariate exponential variables having first-order autoregressive structure is presented, the BEAR(1) model. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR(2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross-correlations. The marginal processes are shown to have correlation structure of ARMA(2, 1) models.time series, bivariate exponential distribution, autoregressive models, NEAR(2), ARMA(2, 1) models, Gaussian AR(1) bivariate time series model, BEAR(1) model

A simple integer-valued bilinear time series model

“…Jacobs and Lewis in [16], [17], and [18] presented and applied the so-called discrete autoregressive moving average models. Some autoregressive moving average models for dependent sequences of Poisson counts were suggested in [8], [21], [23], and [24]. In [2], Alzaid and Al-Osh introduced integer-valued pth-order autoregressive (INAR(p)) models and, in [1], integer-valued qth-order moving average (INMA(q)) models.…”

A simple integer-valued bilinear time series model

“…Jacobs and Lewis in [16], [17], and [18] presented and applied the so-called discrete autoregressive moving average models. Some autoregressive moving average models for dependent sequences of Poisson counts were suggested in [8], [21], [23], and [24]. In [2], Alzaid and Al-Osh introduced integer-valued pth-order autoregressive (INAR(p)) models and, in [1], integer-valued qth-order moving average (INMA(q)) models.…”