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TESTING FOR EMBEDDABILITY BY STATIONARY REVERSIBLE CONTINUOUS-TIME MARKOV PROCESSES
平稳可逆连续时间马尔可夫过程的可嵌入性检验
Given an observation of a discrete-time process { Y i , i = 0... n } assumed to be Markov, stationary, and time reversible, we develop a (conservative) test procedure of embeddability by a continuous-time reversible Markov process. The test statistic is derived from a set of moment inequality restrictions implied by the spectral properties of such continuous-time processes. Most interesting is that the embeddability condition of interest is a direct extension of the…
Short Run and Long Run Causality in Time Series: Theory
时间序列中的短期与长期因果性：理论
Causality in Granger's sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1 <= h <= inifinity, providing a rigorous formalization of indirect causal effects and causality chains in (possibly) nonstationary time series. The authors derive necessary and sufficient conditions for noncausality between vectors up to any given horizon. They observe that coefficients of lagged variables…