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冲击矩阵两种表达式的等价性AI 解读

This note gives a proof of the equivalence between two expressions of the moving-average impact matrix; one is given by Johansen (1995, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models ) and Paruolo (1997, Econometric Theory 13, 79–118), and the other appears in Phillips (1998, Journal of Econometrics 83, 21–56) as the limit of the impulse response function. Because these expressions are shown to be parametrically equivalent, we can make the same…

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误设自回归时间序列模型中预测量的性质AI 解读

This article investigates major effects of misspecification in stationary linear time series models when we fit a pth-order autoregressive model. The true model can be an autoregressive moving average model. We derive the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain. Contrary to previous studies, the process in estimation is not necessarily independent of the process in prediction, and…

多元自回归移动平均模型的预测AI 解读

A simple formula for multiperiod perdietions of mulativariate autoregressive-moving average models is derived. The formula is explicitly given as a function of suitably defined parameter matrices and an observation vectors, and includes simple models as its special cases. The asymptotic prediction mean squared error is also derived for perdictions with estimated parameters.

多变量自回归移动平均模型的预测AI 解读

A simple formula for multiperiod perdietions of mulativariate autoregressive-moving average models is derived. The formula is explicitly given as a function of suitably defined parameter matrices and an observation vectors, and includes simple models as its special cases. The asymptotic prediction mean squared error is also derived for perdictions with estimated parameters.