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Estimation, Prediction, and Interpolation for Nonstationary Series with the Kalman Filter
Stochastic linear trends
Revisions in ARIMA Signal Extraction
ARIMA 信号提取中的修订
The problem of decomposing an observed series, assumed to follow an ARIMA process, into signal plus noise is considered. It is well known that the preliminary estimates of the signal will be subject to revisions as more data become available. For a general ARIMA process, the revision in the concurrent estimate of the signal is seen to follow a stationary ARMA process, easily derived from the overall series model. The results are extended to non-concurrent preliminary…
Revisions in ARIMA Signal Extraction
ARIMA 信号提取中的修订
The problem of decomposing an observed series, assumed to follow an ARIMA process, into signal plus noise is considered. It is well known that the preliminary estimates of the signal will be subject to revisions as more data become available. For a general ARIMA process, the revision in the concurrent estimate of the signal is seen to follow a stationary ARMA process, easily derived from the overall series model. The results are extended to non-concurrent preliminary…
On Structural Time Series Models and the Characterization of Components
结构时间序列模型与成分的刻画
This article analyzes certain properties of a class of recently proposed structural time series models in which particular structures are imposed upon the unobserved components of an observed time series. It is shown how the overall model can be expected to fit series, such as those for which the X-11 or Airline models are appropriate. As for the components, identification of the model is achieved by assigning a certain amount of white noise variation to the trend and…
Comment
[Issues Involved with the Seasonal Adjustment of Economic Time Series]: Comment
Identification and Informative Sample Size.
An Application of Nonlinear Time Series Forecasting
非线性时间序列预测的一项应用
By means of a real application, it is seen how ARIMA forecasts can be improved when nonlinearities are present. The autocorrelation function (ACF) of the squared residuals provides a convenient tool to check the linearity assumption. Once nonlinearity has been detected, parsimonious bilinear processes seem rather adequate to model it. The detection of nonlinearity and the forecast improvement appear to be rather robust with respect to changes in the linear and bilinear…