This article considers the problem of estimating dynamic linear regression models when the data are generated from finite mixture probability density function where the mixture components are characterized by different dynamic regression model parameters. Specifically, conventional linear models assume that the data are generated by a single probability density function characterized by a single set of regression model parameters. However, when the true generating model is finite mixture density function, then estimation of conventional linear models under the assumption of a single density function may lead to erroneous conclusions. Instead, it may be desirable to estimate the regression model under the assumption that the data are derived from a finite mixture density function and to examine differences in the parameters of the model within each mixture component. Dynamic regression models and subsequent dynamic response analysis using dynamic multipliers are also likely to be affected by the existence of a finite mixture density because dynamic multipliers are functions of the regression model parameters. Utilizing finite mixture modeling applied to two real data examples, this article shows that dynamic responses to changes in exogenous variables can be quite different depending on the number and nature of underlying mixture components. Implications for substantive conclusions based on the use of dynamic multipliers is discussed.
Anℓ1-oracle inequality for the Lasso in multivariate finite mixture of multivariate Gaussian regression models
