A simple first-order autoregressive model for the generation of non-Gaussian time series is described. It is defined by X/sub n/= rho X/sub n-1/+W/sub n/ and has a hyperbolic secant marginal distribution. This hyperbolic secant model can be used to generate random non-Gaussian sequences which are free of the degeneracy that afflicts the sequences generated using the Laplace model. The generation formula and the bivariate distributions of this model are derived. It is shown that the mean-square (MS) backward prediction error is strictly less than the MS forward prediction error for all first-order autoregressive non-Gaussian models.
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机译：描述了用于生成非高斯时间序列的简单一阶自回归模型。它由X / sub n / = rho X / sub n-1 / + W / sub n /定义，并且具有双曲正割边际分布。该双曲正割模型可用于生成随机的非高斯序列，该序列不存在折衷问题，该简并性折衷于使用Laplace模型生成的序列。推导了该模型的生成公式和二元分布。结果表明，对于所有一阶自回归非高斯模型，均方根（MS）后向预测误差严格小于MS前向预测误差。
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