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When one analyzes multiple time series, the natural extension to the autoregressive model is the vector autoregression, or VAR, in which a vector of variables is modeled as depending on their own lags and on the lags of every other variable in the vector. A two-variable VAR with one lag looks like \begin{align}

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Regime switching vector autoregression

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Jan 01, 2020 · Exploring Sleep Dynamic of Mother-Infant Dyads Using a Regime-Switching Vector Autoregressive Model Publication Date: January 1, 2020 Author(s): Linying Ji, Sy-Miin Chow, Brian Crosby, Douglas M. Teti (1989) model of the US Business Cycle, the Markov-switching vector autoregressive (VAR) model of the business cycle is presented. Then, x 3 considers the construction of turning point chronologies with Markov-switching models. We present the regime inference in Markov-switching VAR models and dis-threshold autoregressive models, which are recognized for their ability to repre-sent nonlinear features in time series, such as abrupt changes, time-irreversibility and regime-shifting behavior. Through the use of the proposed approach, one can determine and monitor the set of co-moving time series variables across the time dimension.

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A collection of special topics chapters study Threshold and Smooth Transition Autoregressive (TAR and STAR) models, Markov switching regime models, state space models and the Kalman filter, mixed frequency data models, nowcasting, forecasting using large datasets and, finally, volatility models.

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Consider a vector autoregressive process with state vector x t2Rn evolving as (1) where the noise vector w tis a zero-mean normally distributed variable. The transition matrix Aand covariance matrix Q ware unknown. It is assumed that kAk 2 = ˙ max <1 to ensure the spectral radius of Ais bounded by 1 and the VAR process is stable. Note that if ˙