Implementation of the statistical model as a Dynamic Linear Model Sample Clauses

Implementation of the statistical model as a Dynamic Linear Model. The formulation of the statistical model in section 1.2 allows for a straightforward implementation within the dynamic linear model (DLM) framework. DLMs are based on a state-space approach, i.e., unobservable state variables are used that allow direct modeling of the process (Y) generating the observed data (Z). DLMs have the general form: Z(t) = F Y(t) + v(t) (1.10) Y(t) = G Y(t-1) + w(t) (1.11) where t is the discrete time variable, which in a typical case represents monthly values, Z(t) is a vector of p observations at time t, Y(t) is the underlying state vector of dimension m, G is the mxm system matrix, and F is the mxp observation matrix. We suppose that v(t)~N(0,V) and w(t)~N(0,W) are the observation and model Gaussian errors, respectively, that are serially and mutually uncorrelated. In this formulation, the matrices V and W contain the model parameters Ɵ. If we suppose that the unknown parameters are random the DLM formulation is a BHM where (10) and