Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies
针对连续时间向量ARMAX模型，当数据以不同频率的存量和流量形式观测时，推导了离散时间状态空间表示，并利用卡尔曼滤波计算高斯似然函数，用于最大似然估计。
For purposes of maximum likelihood estimation, we show how to compute the Gaussian likelihood function when the data are generated by a higher-order continuous-time vector ARMAX model and are observed as stocks and flows at different frequencies. Continuous-time ARMAX models are analogous to discrete-time autoregressive moving-average models with distributed-lag exogenous variables. Stocks are variables observed at points in time and flows are variables observed as integrals over sampling intervals. We derive the implied state-space model of the discrete-time data and show how to use it to compute the Gaussian likelihood function with Kalman-filtering, prediction-error, decomposition of the data.