Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series

Abstract

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.