![]() ![]() This contributes to additional variability in the predictive distribution and we must simulate T h from the state equation 71 in order to simulate the predictive distribution. The prior specification is completed with independent inverse Wishart priors for and Q, (73) iW, v Q iW Q, v Q. Note that the state equation implies that t 1 t, Q N t, Q and that this in a sense serves as prior distribution for t 1 and the prior for all the states (parameters) is simply a product of normal distributions that needs to be complemented with a prior for the first state, 1, which is then usefully also taken to be normal, (72) 1 N s 1 0, P 1 0. The basic TVP-VAR complements the observation equation (69) with the state equation 23 (71) t 1 t t. Koop and Korobilis (2009) provide a good introduction to TVP-VARs. The popularity of the Bayesian approach to TVP-VARs owes much to Cogley and Sargent (2002, 2005) and Primiceri (2005), who, although not primarily concerned with forecasting, provide the foundations for Bayesian inference in these models. This includes models accommodating structural breaks by including dummy variables that interact with some or all of the right-hand-side variables and Markov switching models with a fixed number of regimes ( Chib, 1998 ) or an evolving number of regimes ( Pesaran et al., 2006 and Koop and Potter, 2007 ). There are, of course, other ways to formulate a model where the parameters are allowed to change over time. These are all examples of the type of time-varying parameter VAR models (TVP-VAR) formulated as state-space models that we will focus on. Highfield (1987) relaxes the assumption of a known diagonal error variance-covariance matrix and uses the normal-Whishart conjugate prior in a state-space formulation of the model. (1984) show how the estimation can be conducted using the Kalman filter to update the state vector t and conduct a search over a subset of the hyperparameters to find the combinations that provide the best forecast accuracy in a 10-variable VAR. View Dw In Oxmetrics Update The Stateĭoan et al. (1984), Highfield (1987), and Sims (1993) were among the earliest to introduce parameter variation in VAR models. ![]()
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