另一本研究稳定数据流的书。研读的目的是如何对待不稳定数据流。
Chapter I
Stationary Processes

Table of Contents

9

1. General Discussion ................................... . . . . . . . . 12
2. Positive Definite Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3. Fourier Representation of a Weakly Stationary Process. . . . . . . . . . . 15
Problems ................................................... 22
Notes ...................................................... 24


Chapter II
Prediction and Moments
1. Prediction .................................................. 30
2. Moments and Cumulants ..................................... 33
3. Autoregressive and Moving Average Processes. . . . . . . . . . . . . . . . . . . 37
4. Non-Gaussian Linear Processes ................................ 46
5. The Kalman-Eucy Filter ..................................... 48
Problerlls ................................................... 50
Notes ...................................................... 51


Chapter III
Quadratic Forms, Limit Theorems and Mixing Conditions
1. Introduction ................................................ 54
2. Quadratic Forms ............................................ 54
3. A Limit Theorem ............................................ 62
4. Summability of Cumulants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5. Long-range Dependence....... .... .... ....... ..... ... ..... ... 71
6. Strong Mixing and Random Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Problems ................................................... 78
Notes ...................................................... 79


Chapter IV
Estimation of Parameters of Finite Parameter Models
1. Maximum Likelihood Estimates ............................... 84
2. The Newton-Raphson Procedure and Gaussian ARMA Schemes. . .. 92
3. Asymptotic Properties of Some Finite Parameter Estimates ....... 101
4. Sample Computations Using Monte Carlo Simulation ............. 111
5. Estimating the Order of a Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6. Finite Parameter Stationary Random Fields .................... 115
Problems ................................................... 120


Chapter V
Spectral Density Estimates
1. The Periodogram ............................................ 126
2. Bias and Variance of Spectral Density Estimates ................ 132
3. Asymptotic Distribution of Spectral Density Estimates ........... 138
4. Prewhitening and Tapering ................................... 143
5. Spectral Density Estimates Using Blocks ....................... 144
6. A Lower Bound for the Precision of Spectral Density Estimates ... 146
7. Turbulence and the Kolmogorov Spectrum . . . . . . . . . . . . . . . . . . . . .. 152
8. Spectral Density Estimates for Random Fields .................. 155
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157
Notes.... ... ...... ...... .................. ......... .. ...... 159


Chapter VI
Cumulant Spectral Estimates
1. Introduction ................................................ 164
2. The Discrete Fourier Transform and Fast Fourier Transform. .. . .. 164
3. Vector-Valued Processes ...................................... 166
4. Smoothed Periodograms ...................................... 175
5. Aliasing and Discretely Sampled Time Series .................... 182
Notes ...................................................... 190


Chapter VII
Density and Regression Estimates
1. Introduction. The Case of Independent Observations ............. 192
2. Density and Regression Estimates for Stationary Sequences.. . . . .. 196
Notes ...................................................... 203

Chapter VIII
Non-Gaussian Linear Processes
1. Estimates of Phase, Coefficients, and Deconvolution for Non-Gaussian
Linear Processes ............................................. 206
2. Random Fields .............................................. 221
3. Non-Gaussian Linear Random Fields. . . . . . . . . . . . . . . . . . . . . . . . . .. 234
Notes ...................................................... 237
Appendix
1. Monotone Functions and Measures ............................. 240
2. Hilbert Space ............................................... 242
3. Banach Space ............................................... 244
4. Banach Algebras and Homomorphisms ......................... 245