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,
