Abstract-A time-series model for Laplace (double-exponential) variables having second-order autoregressive structure (NLAR(2)) is presented. The model is Markovian and extends the second-order process in exponential variables, NEAR(2), to the case where the marginal distribution is Laplace. The properties of the Laplace distribution make it useful for modeling in some cases where the normal distribution is not appropriate. The time-series model has four parameters and is easily simulated. The autocorrelation function for the process is derived as well as third-order moments to further explore dependency in the process. The model can exhibit a broad range of positive and negative correlations and is partially time reversible. Joint distributions and the distrfbution of differences are presented for the first-order case NLAR(l).

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

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2. THE LAP:LACE LAR(1) MODEL. In many practical cases in time series analysis, marginal distributions in stationary situations are not Gaussian.It is therefore necessary to be able to generate and analyze nonGaussian time series. Several non-Gaussian time series models are discussed in this paper. The marginal distributions are Laplace or l-Laplace distributions, and the correlation structure of the processes mimics that of the standard additive, linear, constant coefficient ARMA(p,q) models.

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