Autoregressive models for time series of random sums of positive variables: application to tree growth as a function of climate and insect outbreaks
正变量随机和时间序列的自回归模型:气候与虫害下的树木生长应用
We present a broad class of semi-parametric models for time series of random sums of positive variables. Our methodology allows the number of terms inside the sum to be time-varying and is therefore well suited to many examples encountered in the natural sciences. We study the stability properties of the models and provide a valid statistical inference procedure to estimate the model parameters. It is shown that the proposed quasi-maximum likelihood estimator is consistent…