Discussion on "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Problems" by Søren Johansen and Bent Nielsen

2016 ◽  
Vol 43 (2) ◽  
pp. 366-367
Author(s):  
Hannu Oja
Keyword(s):  
Time Series ◽  
Outlier Detection ◽  
Asymptotic Theory ◽  
Linear Time ◽  
Time Series Regression ◽  
Detection Algorithms ◽  
Regression Problems

The asymptotic theory of linear time-series models

1973 ◽  
Vol 10 (01) ◽  
pp. 130-145 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Theory ◽  
Linear Time ◽  
Stationary Time Series ◽  
Linear Predictor ◽  
The Central Limit Theorem ◽  
Best Linear Predictor

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.

scholarly journals Forecasting Migration Flows for New Zealand: Arrivals of New and Returning New Zealanders & Departing by Destinations

1970 ◽  
Author(s):  
Xintao Zhao ◽  
Ram SriRamaratnam ◽  
Dirk Van Seventer
Keyword(s):  
Time Series ◽  
New Zealand ◽  
Linear Time ◽  
Exponential Smoothing ◽  
Smoothing Method ◽  
Time Series Regression ◽  
Quarterly Data ◽  
Migration Flows ◽  
Exponential Smoothing Method ◽  
New Zealanders

The purpose of this paper was to outline the methods and to report results of an econometric attempt to forecast New Zealand migration flows. Flows were decomposed into eight components: two relating to arrivals and six components relating to departures by several destinations. Linear time series regression and the Holt­Winters exponential smoothing method were applied to quarterly data from June 1978 to June 2008 or from March 1990 to June 2008. Within­sample mean absolute percentage errors were presented and full­sample estimates from June 1978 to September 2010 or from March 1990 to September 2010 were used to forecast migration flows for each component for the next two years.

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