A - Mathematica - (Ebook-Pdf) - Mathematics - Time Series

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1、TIMESERIESContentsSyllabus..................................iiiBooks...................................iiiKeywords.................................iv1Modelsfortimeseries11.1Timeseriesdata..............................11.2Trend,seasonality,cyclesandresi

2、duals.................11.3Stationaryprocesses...........................11.4Autoregressiveprocesses.........................21.5Movingaverageprocesses.........................31.6Whitenoise................................41.7Theturningpointtest........

3、..................42Modelsofstationaryprocesses52.1Purelyindeterministicprocesses.....................52.2ARMAprocesses.............................52.3ARIMAprocesses.............................62.4Estimationoftheautocovariancefunction...............6

4、2.5IdentifyingaMA(q)process.......................72.6IdentifyinganAR(p)process.......................72.7DistributionsoftheACFandPACF..................83Spectralmethods93.1ThediscreteFouriertransform......................93.2Thespectraldensity........

5、...................93.3Analysingtheeectsofsmoothing....................124Estimationofthespectrum134.1Theperiodogram.............................134.2Distributionofspectralestimates....................154.3ThefastFouriertransform......................

6、..165Linearlters175.1TheFilterTheorem............................175.2Applicationtoautoregressiveprocesses.................175.3Applicationtomovingaverageprocesses................185.4Thegenerallinearprocess........................19i5.5FiltersandARMA

7、processes.......................205.6CalculatingautocovariancesinARMAmodels.............206Estimationoftrendandseasonality216.1Movingaverages..............................216.2Centredmovingaverages.........................226.3TheSlutzky-Yuleeect.....

8、.....................226.4Exponentialsmoothing..........................236.5Calculationofseasonalindices......................247FittingARIMAmodels257.1TheBox-Jenkinsprocedure.......................257.2Identication...................