| 简介： | Dynamic discrete valued time series data exist in many economic applications, such as market price moving direction, credit scoring and others, but its research is still relatively rare compared with the rich research of continuous-valued time series in semiparametric modelling. In this paper, we propose to explore how to utilise the useful high-dimensional dynamic lagged information for forecasting of time series data with discrete-valued response. Our approach will generalise the existing flexible semiparametric marginal regression model averaging (MARMA) forecasting of Li, Linton and Lu (2015), which has been shown a useful data-driven method, but was designed for nonlinear forecasting of continuous valued time series by a least square averaging. We have hence suggested a generalised MARMA (GMARMA) procedure under a general time series conditional exponential family of distributions, which flexibly accommodates nonlinear forecasting of discrete-valued response, and further allowing the lagged effects including discrete-valued information for forecasting. A conditional likelihood model averaging method, instead of the least squares, is thus developed for the averaging weights estimation in the GMARMA, under beta-mixing time series data generating process with asymptotic normality established. Furthermore, an adaptively penalised GMARMA (PGMARMA) is suggested to select the important variables for an improved forecasting. The oracle properties of the PGMARMA weights are established as if the true non-zero weights were known. These procedures are further supported by Monte Carlo simulations and empirical applications to forecasting of the FTSE 100 index market moving direction and causal analysis of the UK road casualty data, which are shown to outperform many popular machine learning tools, including the random forest method, etc.. |