SAS时间序列分析的第一门课程(Michael Falk等)A First Course on Time Series Analysis with SAS (Michael Falk, et al)

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本书的独特之处在于它与统计软件包SAS(统计分析系统)计算环境的集成。 通过多元回归假设基本的应用统计数据。
Preface The analysis of real data by neans of statistical inethods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work The practical need for an investigation of time series data is exempli fied by the following plot, which displays the yearly sunspot numbers betwcen 1749 and 1924. Thesc data arc also known as thc wolf or Wolfer(a student of Wolf)Data. For a discussion of these data and further literature we refer to Wei and Reilly(1989), Example 6.2.5 5P9七 1600 1400 1300 120 1100 600 7:00 600 1U0 1740175017501770178017901800810132018:018401E5018518701880189c1900191019201930 Plot 1: Sunspot data The prescnt book links up clements from timc scrics analysis with a sc- lection of statistical procedures used in general practice including the statistical software package SAS (Statistical Analysis System). Conse quently this book addresses students of statistics as well as students of othcr branches such as economics, demography and cnginccring, wherc lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems il- lustrate the applicability of the presented statistical procedures, where sas gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAs nor in a spccial computcr systcm so that a short training pcriod is guaranteed This book is meant for a, two semester course(lecture, seminar or practical training) where the first three chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters四回and囵 deal with its analvsis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background soine terms are useful such as convergence in distribution stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7(case study) deals with a practical case and demonstrates the presented mcthods. It is possible to usc this chapter independent in a seminar or practical training course, if the concepts of tiine series analysis are already well understood Due to the vast field a selection of the subjects was necessary. Chap- terI contains elements of an exploratory time series analysis, in- cluding the fit of models (logistic, Mitscherlich, Gompertz curve to a series of data, linear filters for seasonal and trend adjustments (difference filters, Census X 11 Program)and exponential filters for Monitoring a, systeIn. Autocovariances and autocorrelations as well as variance stabilizing techniques(Box-Cox transformations) are in troduced. Chapter 2 provides an account of mathematical models of stationary sequences of random variables (white noise, moving averages, autoregressive processes. ARIMA models, cointegrated se quences, ARCH- and GARCH-processes) together with their math- cmatical background (cXistcncc of stationary processes, covariance generating function, inverse and causal filters, stationarity condition Yule Walker equations, partial autocorrelation). The Box-Jenkins program for thc spccification of ARMA-modcls is discussed in dctail (AIC, BIC and HQ in fornation criterion). Gaussian processes and maximum likelihod estimation in gaussian models are introduced as well as least squares estimators as a nonparametric alternative. The diagnostic check includes the Box-Ljung test. Many models of time series can be embedded in state-space models which are introduced in Chapter B The Kalman filter as a unified prediction technique closes the analysis of a timc scrics in the time domain. The analysis of a series of data. in the frequency donain starts in Chapter 4(ha arnold waves, Fourier frequencies, periodogram, Fourier transform and its inverse). The proof of the fact that the periodogram is the e fourier transform of the empirical autocovariance function is given. This links the analysis in the time domain with the analysis in the frequency do main. Chapter 5 gives an account of the analysis of the spectrum of the stationary process(spectral distributiOn function, spectral den sity, Herglotz's theorem). The effects of a linear filter are studied (transfer and power transfer function, low pass and high pass filters filter design) and the spectral densities of ARMA-processes are com puted. Some basic elements of a statistical analysis of a series of data in the frequency domain are provided in Chapter 6 The problem of testing for a white noise is dealt with(Fisher's K-statistic, Bartlett Kolmogorov-Smirnov test) togcthcr with the estimation of the spec tral densit,y (periodogralll, discrete spectral average estimator, kernel estimator, confidence intervals). Chapter 7 deals with the practical application of the box-Jenkins Program to a real dataset consisting of 7300 discharge measurements from the Donau river at Donauwoerth For the purpose of studying, the data have been kindly made avail- able to the University of wurzburg. A special thank is dedicated to Rudolf neusiedl. additionally, the asymptotic normality of the partial and general autocorrelation estimators is proven in this chapter and some topics discussed earlier are further elaborated (order selection, diagnostic check, forecasting This book is consecutively subdivided in a statistical part and a sas specific part. For better clearness the SAs-specific part, includin the diagrams gencratcd with SAs, is betwccn two horizontal bars separating it from the rest of the text / Thi sample comment 2/* The first comment in each program will be its name. * 4 Program code will be set in typewriter font. SAs keywords like DATA or 5 PRoc will be set in bold 7 Also all SAs keywords are written in capital letters. This is nct 8 necessary as SAs code is not case sensitive, but it makes it easier to 9 read the code 11 Extra-long lines will be broken intc smaller lines with continuation c marked by an arrow and indentation 12(Al, the line-number is missing in his case. In this area, you will find a step-by-step expla- that SAS cannot be explained as a whole this nation of the above program. The keywords way. Only the actually used commands will be will be set in typewriter-font. Please note mentioned Contents 1 Elements of Exploratory Time Series Analysis 1.1 The Additive Model for a Time Series 2 .2 Linear Filtering of Time Series 16 1.3 Autocovariances and Autocorrelations 35 xercises 41 2 Models of Time Series 47 2. 1 Linear Filters and Stochastic Processes 47 2.2 Moving Averages and Autoregressive Processes 61 2.3 The Box-Jenkins Program 99 Exercises 111 3 State-Space Models 121 3.1 The State-Space Representation 121 3.2 The Kalman-Filter 125 正 xercises.... 132 4 The Frequency Domain Approach of a Time Series 135 4. 1 Least Squares Approach with Known Frequencies. 136 4.2 The Periodogram ,142 Exercises 155 Contents 5 The Spectrum of a Stationary Process 159 5.1 Characterizations of Autocovariance Functions 160 5.2 Linear Filters and Frequencies ..166 15. 3 Spectral Density of an ARMA-Processl 175 Exercises 181 6 Statistical Analysis in the Frequency Domain 187 16.1 Testing for a White Noise 187 6.2 Estimating Spectral Densities 196 巴 es xercise 216 7 The Box-Jenkins Program: A Case Study 223 7.1 Partial Correlation and Levinson-Durbin Recursion. 224 7.2 Asymptotic Normality of Partial Autocorrelation Esti- mator 234 7.3 Asymptotic Normality of Autocorrelation Estimator. 259 7.4 First Examinations 272 7.5 Order Selection 284 7.6 Diagnostic Check 311 7.7 Forecasting 324 Exercises 335 Bibliography 337 ndex 341 SAS-Index 348 GNU Free Documentation Licence 351 Chapter Elements of Exploratory Time Series Analysis 1 a time series is a sequence of observations that are arranged according to the timc of their outcome. The annual crop yicld of sugar-bccts and their price per ton for exanple is recorded in agriculture. The llewspa pers business sections report daily stock prices, weekly interest rates monthly rates of unemployment and annual turnovers. Meteorology records hourly wind speeds, daily maximum and minimum tempera- tures and annual rainfall. Geophysics is continuously observing the shaking or trembling of the earth in order to predict possibly impend ing earthquakes. An electroencephalogram traces brain waves made by an electroencephalograph in order to detect a cerebral disease, an electrocardiogram traces heart waves. The social sciences survey an nual death and birth rates. the number of accidents in the home and various forms of criminal activities. Parameters in a manufacturing process are permanently monitored in order to carry out an on-line inspection in quality assurance There arc. obviously, numcrous rcasons to rccord and to analyze the data, of a time series. Among these is the wish to gain a better under standing of the data generating mechanism, the prediction of future values or the optimal control of a system. The characteristic property of a time series is the fact that the data are not generated indepen- dently. their dispersion varies in time, they are often governed by a trend and they have cyclic components. Statistical procedures that supposc independent and identically distributed data arc, thcrcforc, excluded from the analysis of time series. This requires proper meth- ods that are summarized under time series analysis Elements of Exploratory Time Series Analysis 1.1 The additive model for a time series The additive model for a given time series 1, .., n is the assump- tion that these data are realizations of random variables yt that al themselves sums of four components Y+=T+Zt+st+R wherc It is a(monotone)function of t, called trend, and Zt roflccts sOIne nonrandom long tern cyclic influence. Think of the fanous business cycle usually consisting of recession, recovery, growth, and decline. St describes some nonrandom short term cyclic influence like a seasonal component whereas Rt is a random variable grasping all the deviations from the ideal non-stochastic model yt=Tt+ Zt t St The variables Tt and Zt are often summarized as describing the long torm behavior of the timc scrics. Wc supposc in the following that the expectation E(Rt) of the error variable exists and equals zero. reflecting the assumption that the random deviations above or below the nonrandom model balance each other on the av erage. Note that E(Rt)=0 can always be achieved by appropriately modifying one or more of the nonrandom components Example 1.1.1.(Unemployed1 Data). The following data yt, t 1,., 51. arc the monthly numbers of unemploycd workers in the building trade in Germany from July 1975 to September 1979 MONTH UNEMELYD Ju⊥y 6C572 August 52461 September 4735 October 48320 November 6C219 December 84418 January T123456789 119916 February 12435 March 87309

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试读 127P SAS时间序列分析的第一门课程(Michael Falk等)A First Course on Time Series Analysis with SAS (Michael Falk, et al)
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