## New directions in time series analysis, Volume 2Part of a two volume set based on a recent IMA program of the same name. The goal of the program and these books is to develop a community of statistical and other scientists kept up-to-date on developments in this quickly evolving and interdisciplinary field. Consequently, these books present recent material by distinguished researchers. Topics discussed in Part I include nonlinear and non- Gaussian models and processes (higher order moments and spectra, nonlinear systems, applications in astronomy, geophysics, engineering, and simulation) and the interaction of time series analysis and statistics (information model identification, categorical valued time series, nonparametric and semiparametric methods). Self-similar processes and long-range dependence (time series with long memory, fractals, 1/f noise, stable noise) and time series research common to engineers and economists (modeling of multivariate and possibly non-stationary time series, state space and adaptive methods) are discussed in Part II. |

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### Contents

Recent developments in location estimation and regression | 1 |

Autoregressive estimation of the prediction mean squared error | 9 |

Phasetransition in statistical physical models | 11 |

Copyright | |

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adaptive control algorithm applications approximation ARMA assume assumption asymptotic autoregressive Bayesian Bilinear model Cauchy index coefficients component compute conditional consider constant convergence corresponding covariance defined denotes differentiable Econometrics Economic equation equivalent ergodicity error exists finite Gaussian Gersch given Hankel matrix Hence Hilbert space hyperparameter identification IEEE Trans integral invariant probability measure kernel least squares Lemma limit theorems linear dynamical models long-range dependence Lyapunov function M-estimators Markov markovian Mathematics matrix maximum likelihood mc(E mean method minimal moving average multivariate nonlinear nonstationary observations obtained optimal polynomial posterior distribution prediction probability measure problem properties random variables regression model representation RKHS sample satisfies self-similar sequence smoothness priors solution space spectral density stable stationary stationary process Statistics stochastic complexity stochastic process stochastic stability submanifold Taqqu Tauchen tests theory trend unit root values variance vector zero