SAS时间序列分析的第一门课程（MichaelFalk等）AFirstCourseonTimeSeriesAnalysiswithSAS(MichaelFalk,etal)资源-CSDN文库

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A First Course on

Time Series Analysis

Examples with SAS

Chair of Statistics, University of W

¨

urzburg

March 20, 2011

iv

statistical software package SAS (Statistical Analysis System). Conse-

quently this book addresses students of statistics as well as students of

other branches such as economics, demography and engineering, where

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

special computer system so that a short training period 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 4, 5 and 6

deal with its analysis in the frequency domain and can be worked

through in the second term. In order to understand the mathematical

background some 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

methods. It is possible to use this chapter independent in a seminar

or practical training course, if the concepts of time series analysis are

already well understood.

Due to the vast ﬁeld a selection of the subjects was necessary. Chap-

ter 1 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 system. 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-

ematical background (existence of stationary processes, covariance

v

generating function, inverse and causal ﬁlters, stationarity condition,

Yule–Walker equations, partial autocorrelation). The Box–Jenkins

program for the speciﬁcation of ARMA-models is discussed in detail

(AIC, BIC and HQ information 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 3. The Kalman ﬁlter as a uniﬁed prediction technique closes

the analysis of a time series in the time domain. The analysis of a

series of data in the frequency domain starts in Chapter 4 (harmonic

waves, Fourier frequencies, periodogram, Fourier transform and its

inverse). The proof of the fact that the periodogram is the 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 κ-statistic, Bartlett–

Kolmogorov–Smirnov test) together with the estimation of the spec-

tral density (periodogram, 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 W¨urzburg. 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, including

the diagrams generated with SAS, is between two horizontal bars,

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