The STATE statement option TYPE=CYCLE specifies a (2*dim)-dimensional , needed for defining a dim-dimensional cycle. As in the LL case, the first dim elements of correspond to the needed dim-dimensional cycle, and the remaining dim elements contain some auxiliary quantities. The cycle model defined in this subsection requires a regular data typeâ€”that is, the CT option is not included. Let denote the damping factor, and let period be the frequency associated with the cycle. The admissible parameter ranges are and period , which implies that . Let , a matrix, and let , a matrix. With this notation, the transition equation associated with is
where is a sequence of zero mean, independent, -dimensional Gaussian vectors with covariance . If , the initial condition is fully diffuse ( and ). Otherwise, it is nondiffuse: and .
The multivariate cycle is useful for capturing periodic behavior for multivariate time series data. The cycle term for the
ith response variable is defined by a component that simply picks the ith element of . For example, the component cycle_i
defined as follows can be used as a cycle term in the MODEL statement of the ith response variable:
state cycleState(dim) type=cycle ...; component cycle_2 = cycleState[2];