1 Elements of Exploratory Time Series Analysis 1
1.1 The Additive Model for a Time Series . . . . . . . . . . . . . . . . 2
1.2 Linear Filtering of Time Series . . . . . . . . . . . . . . . . . . . . 16
1.3 Autocovariances and Autocorrelations . . . . . . . . . . . . . . . . 30
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Models of Time Series 41
2.1 Linear Filters and Stochastic Processes . . . . . . . . . . . . . . . . 41
2.2 Moving Averages and Autoregressive Processes . . . . . . . . . . . 52
2.3 Specification of ARMA-Models: The Box–Jenkins Program . . . . 85
2.4 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3 The Frequency Domain Approach of a Time Series 113
3.1 Least Squares Approach with Known Frequencies . . . . . . . . . . 114
3.2 The Periodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4 The Spectrum of a Stationary Process 135
4.1 Characterizations of Autocovariance Functions . . . . . . . . . . . 136
4.2 Linear Filters and Frequencies . . . . . . . . . . . . . . . . . . . . . 141
4.3 Spectral Densities of ARMA-Processes . . . . . . . . . . . . . . . . 149
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5 Statistical Analysis in the Frequency Domain 159
5.1 Testing for a White Noise . . . . . . . . . . . . . . . . . . . . . . . 159
5.2 Estimating Spectral Densities . . . . . . . . . . . . . . . . . . . . . 167
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
References 189
Index 193
SAS-Index 197
A GNU Free Documentation License 199