DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES
推导了连续时间自回归移动平均(ARMA)系统生成数据的精确离散时间表示，涵盖混合存量和流量数据，并通过三个实例（包括太阳黑子数据、短期利率和美国非耐用品消费支出）展示了MA(1)分量消除序列相关性的显著效果。
This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.