Abstract: We propose a new copula-based Markov model to analyze count time series data. One challenge in using copula to analyze count data is due to the identifiability issue that arises from the discrepancy of using a continuous copula function to characterize the discrete distribution. We find that identifiability can be ensured in the regression setup under one sufficient condition. Resolving the identifiability issue allows us to develop a method to select the appropriate copula to capture different types of temporal dependence, leading to more flexibility in modeling. We propose an estimation procedure and establish the asymptotic properties of the proposed estimators. For capturing temporal dependence, the proposed method is data-adaptive and computationally efficient. It also provides a convenient way to construct both point and interval predictions at a future time. Through a simulation study and the analysis of COVID-19 daily death data, we show that our method produces more stable point and interval predictions than existing methods based on Gaussian copula and autoregression.

Key words and phrases: Conditional quantile, copula, identifiability, Markov, temporal dependence.