S. K. Pandit and Wu, S.-M. Time Series and System Analysis with Applications. Krieger Publishing Company, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....networks and genetic algorithms, and spectral decomposition. 3.2. 2 Statistical Analysis Statistical time series analysis comes from the theory for analyzing linear, stationary time series, and includes such methods as the Box Jenkins or Autoregressive Integrated Moving Average (ARIMA) method [64]. The ARIMA method assumes that a series can be reduced to a stationary time series by di#erencing or detrending. ARIMA is limited by the requirement of stationarity of the time series and normality and independence of the residuals. The statistical characteristics of a stationary time series ....

....is a methodology for studying the sequential progression of events. Predictions for future values of a variable are expressed based on the dependence or regression on the variable s own past values. A model that is derived from data that are autocorrelated is referred to as an autoregression[64]. For a more detailed discussion on the ARIMA method, see [64, 50] Structured time series models are linear models which are formulated directly in terms of the components of interest in the time series[32] Observed series = trend seasonal irregular, where the irregular component ....

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Pandit, S.M., Time Series and System Analysis with Applications , John Wiley and Sons, New York, 1983.

....= 53) Also, A n n p A n n p ( f f f f f f f f 1 0 1 0 = 54) Thus, A n ( f f f f 1 , and therefore OI ME, decreases as the order increases until n p . 4. 3 PE ME: Assume the least square algorithm [14] is used to estimate the parameters. In order to decouple PE ME from OI ME, let n p = The parameter estimate is ( f f f f 1 1 p T T T Y = F F F (55) where F = 56) y y y y y y p p N N p , 1 1 2 1 [ ....

....by using a standard non linear least squares subroutine. The order increase D D n m = 0 0 ( or D D m n = 0 0 ( can be selected between 1 and M step where M step is the maximum allowable order increase step which is selected to be 2 because of the possible conjugate roots. The F test [14] has been widely used in selecting ARMA orders. However, the results depend on the confidence factor. For the purpose of comparison, an objective criterion may be more appropriate. AIC is a well known objective criterion [8] Although studies have been performed to investigate its inconsistency, ....

Pandit, S.M. and Wu S.M., 1983, "Time series and system analysis with applications," John Wiley and Sons.

....a treatment without the calculus are referred to the book by Montgomery, Johnson, and Gardiner [47] This book explains the models discussed in this proposal in greater detail, including the background of the statistical theory involved. Another reference at the same level is by Pandit and Wu [52]. Alder and Roessler [1] or Bethea, Duran, and Boullion [4] provide introductory discussions of statistical methods for those with little or no background in statistics. The book by Alder and Roessler includes a discussion of seasonal models. APPENDIX B SPA COMMAND SYNTAX Command Description ....

Pandit, S. M., and Wu, S.-M. Time Series and System Analysis With Applications. John Wiley & Sons, New York, 1983.

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S. K. Pandit and Wu, S.-M. Time Series and System Analysis with Applications. Krieger Publishing Company, 1993.

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Wu, S. M. and S. M. Pandit, Time Series and System Analysis with Applications, John Wiley and Sons, 1983.

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Wu, S. M. and S. M. Pandit, Time Series and System Analysis with Applications, John Wiley and Sons, 1983.

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Wu, S. M. and S. M. Pandit, Time Series and System Analysis with Applications, John Wiley and Sons, 1983.

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