## Time Series: Theory and MethodsThis edition contains a large number of additions and corrections scattered throughout the text, including the incorporation of a new chapter on state-space models. The companion diskette for the IBM PC has expanded into the software package ITSM: An Interactive Time Series Modelling Package for the PC, which includes a manual and can be ordered from Springer-Verlag. * We are indebted to many readers who have used the book and programs and made suggestions for improvements. Unfortunately there is not enough space to acknowledge all who have contributed in this way; however, special mention must be made of our prize-winning fault-finders, Sid Resnick and F. Pukelsheim. Special mention should also be made of Anthony Brockwell, whose advice and support on computing matters was invaluable in the preparation of the new diskettes. We have been fortunate to work on the new edition in the excellent environments provided by the University of Melbourne and Colorado State University. We thank Duane Boes particularly for his support and encouragement throughout, and the Australian Research Council and National Science Foundation for their support of research related to the new material. We are also indebted to Springer-Verlag for their constant support and assistance in preparing the second edition. Fort Collins, Colorado P. J. BROCKWELL November, 1990 R. A. DAVIS * /TSM: An Interactive Time Series Modelling Package for the PC by P. J. Brockwell and R. A. Davis. ISBN: 0-387-97482-2; 1991. |

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### Contents

III | 1 |

IV | 8 |

V | 11 |

VI | 14 |

VII | 25 |

VIII | 32 |

IX | 37 |

X | 39 |

LX | 238 |

LXI | 239 |

LXII | 241 |

LXIII | 245 |

LXIV | 250 |

LXV | 253 |

LXVI | 254 |

LXVII | 256 |

XI | 42 |

XII | 46 |

XIII | 48 |

XIV | 54 |

XV | 58 |

XVI | 60 |

XVII | 62 |

XVIII | 65 |

XIX | 67 |

XX | 68 |

XXI | 69 |

XXII | 73 |

XXIII | 77 |

XXIV | 89 |

XXV | 91 |

XXVI | 98 |

XXVII | 103 |

XXVIII | 105 |

XXIX | 110 |

XXX | 114 |

XXXI | 116 |

XXXII | 117 |

XXXIII | 122 |

XXXIV | 133 |

XXXV | 138 |

XXXVI | 140 |

XXXVII | 143 |

XXXVIII | 150 |

XXXIX | 152 |

XL | 157 |

XLI | 159 |

XLII | 166 |

XLIII | 169 |

XLIV | 175 |

XLV | 182 |

XLVII | 185 |

XLVIII | 187 |

XLIX | 191 |

L | 192 |

LI | 198 |

LII | 202 |

LIII | 204 |

LIV | 209 |

LV | 215 |

LVI | 218 |

LVII | 220 |

LVIII | 225 |

LIX | 236 |

LXVIII | 258 |

LXIX | 260 |

LXX | 262 |

LXXI | 265 |

LXXII | 269 |

LXXIII | 273 |

LXXIV | 274 |

LXXV | 284 |

LXXVI | 301 |

LXXVII | 306 |

LXXVIII | 314 |

LXXIX | 320 |

LXXX | 326 |

LXXXI | 330 |

LXXXII | 331 |

LXXXIII | 334 |

LXXXIV | 342 |

LXXXV | 350 |

LXXXVI | 362 |

LXXXVII | 365 |

LXXXVIII | 373 |

LXXXIX | 375 |

XC | 396 |

XCI | 401 |

XCII | 402 |

XCIII | 405 |

XCIV | 417 |

XCV | 421 |

XCVI | 430 |

XCVII | 434 |

XCVIII | 443 |

XCIX | 454 |

C | 459 |

CI | 463 |

CII | 474 |

CIII | 482 |

CIV | 489 |

CV | 498 |

CVI | 501 |

CVII | 506 |

CVIII | 520 |

CIX | 535 |

CX | 545 |

CXI | 552 |

CXII | 554 |

561 | |

567 | |

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### Common terms and phrases

absolutely summable algorithm applying approximation AR(p ARIMA ARMA process ARMA(p assumption asymptotic distribution autocorrelation function autocovariance function best linear predictor bounds Cauchy causal invertible coefficients complex-valued compute consider converges Corollary corresponding covariance matrix denote difference equations differenced Example finite fitted model follows given hence Hilbert space independent inner product inner-product space integer lags maximum likelihood estimators mean squared error mean zero minimize moving average non-negative definite non-zero observations obtain one-step predictors op(l orthogonal increment process parameters partial autocorrelation periodogram polynomial Problem process defined program PEST properties Proposition random variables random vector recursions Remark residuals sample autocorrelation function satisfies Section spectral density spectral distribution function spectral representation state-space model state-space representation stationary process stationary time series subspace Suppose transfer function uncorrelated unique stationary solution univariate white noise white noise variance Xn+1 Xn+h