Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series
提出一种自回归条件比例模型，用于处理取值在0到1之间的时间序列数据，通过乘法误差结构建模，并采用指数拟极大似然估计方法，在一般条件下证明了估计量的一致性和渐近正态性。
We propose a multiplicative autoregressive conditional proportion (ARCP) model for (0,1)‐valued time series, in the spirit of GARCH (generalized autoregressive conditional heteroscedastic) and ACD (autoregressive conditional duration) models. In particular, our underlying process is defined as the product of a (0,1)‐valued independent and identically distributed (i.i.d.) sequence and the inverted conditional mean, which, in turn, depends on past reciprocal observations in such a way that is larger than unity. The probability structure of the model is studied in the context of the stochastic recurrence equation theory, while estimation of the model parameters is performed with the exponential quasi‐maximum likelihood estimator (EQMLE). The consistency and asymptotic normality of the EQMLE are both established under general regularity assumptions. Finally, the usefulness of our proposed model is illustrated with two real datasets.