Regression Models for Time Series Analysis
A thorough review of the most current regression methods in timeseries analysis
Regression methods have been an integral part of time seriesanalysis for over a century. Recently, new developments have mademajor strides in such areas as non-continuous data where a linearmodel is not appropriate. This book introduces the reader to newerdevelopments and more diverse regression models and methods fortime series analysis.
Accessible to anyone who is familiar with the basic modern conceptsof statistical inference, Regression Models for Time SeriesAnalysis provides a much-needed examination of recent statisticaldevelopments. Primary among them is the important class of modelsknown as generalized linear models (GLM) which provides, under someconditions, a unified regression theory suitable for continuous,categorical, and count data.
The authors extend GLM methodology systematically to time serieswhere the primary and covariate data are both random andstochastically dependent. They introduce readers to variousregression models developed during the last thirty years or so andsummarize classical and more recent results concerning state spacemodels. To conclude, they present a Bayesian approach to predictionand interpolation in spatial data adapted to time series that maybe short and/or observed irregularly. Real data applications andfurther results are presented throughout by means of chapterproblems 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, MonteCarlo, 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