Regression Models for Time Series Analysis
A thorough review of the most current regression methods in time series analysis
Regression methods have been an integral part of time series analysis for over a century. Recently, new developments have made major strides in such areas as non-continuous data where a linear model is not appropriate. This book introduces the reader to newer developments and more diverse regression models and methods for time series analysis.
Accessible to anyone who is familiar with the basic modern concepts of statistical inference, Regression Models for Time Series Analysis provides a much-needed examination of recent statistical developments. Primary among them is the important class of models known as generalized linear models (GLM) which provides, under some conditions, a unified regression theory suitable for continuous, categorical, and count data.
The authors extend GLM methodology systematically to time series where the primary and covariate data are both random and stochastically dependent. They introduce readers to various regression models developed during the last thirty years or so and summarize classical and more recent results concerning state space models. To conclude, they present a Bayesian approach to prediction and interpolation in spatial data adapted to time series that may be short and/or observed irregularly. Real data applications and further results are presented throughout by means of chapter problems and complements.
Notably, the book covers:
* Important recent developments in Kalman filtering, dynamic GLMs, and state-space modeling
* Associated computational issues such as Markov chain, Monte Carlo, and the EM-algorithm
* Prediction and interpolation
* Stationary processes
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2 Regression Models for Binary Time Series
3 Regression Models for Categorical Time Series
4 Regression Models for Count Time Series
5 Other Models and Alternative Approaches
6 State Space Models
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algorithm American Statistical Association Applications assume assumption asymptotic normality autocorrelation function autocovariance autoregressive process Bayesian binary time series Biometrika canonical link categorical time series component conditional consider converges correlation corresponding covariance matrix deﬁned deﬁnite denotes equation example exponential family ﬁltering ﬁrst ﬁt ﬁxed Gaussian Gibbs sampling given hidden Markov models independent inference information matrix inverse Journal Kalman Kedem kriging least squares linear models link function logistic regression Markov chain martingale maximum likelihood estimator maximum partial likelihood mean method Monte Carlo MTDg multinomial multivariate nonlinear observed obtained ofthe p-value parameters partial likelihood estimator partial score Pearson residuals Poisson distribution Poisson regression posterior prediction intervals probability probit problem random ﬁeld random variables recursions regression models response Sample autocorrelation satisﬁes sequence Series Analysis signiﬁcant simulated space models spatial speciﬁc stationary stationary process Stochastic Processes sufﬁcient Table Theorem Theory variance Yt_1 Zt_1