A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m, eigenvalue restrictions have been proposed as necessary and sufficient restrictions for existence of a unique mth moment of...

Production capital and technology, fundamental to understanding output and productivity growth, are unobserved except at disaggregated levels and must be estimated prior to being used in empirical analysis. We develop and apply a new estimation method, based on advances in economics, statistics,...

Consider the discrete-time state equation and feedback control rule (1) x(t) = Fx(t-1) + Gu(t) + e(t), (2) u(t) = Px(t-1), where x is an nx1 state vector, u is an mx1 control variable, and e is an nx1 disturbance distributed NIID(0,S), F and G are nxn and nxm parameter matrices, and P is an mxn...

The paper obtains two principal results. First, using a new definition of higher-order (2) matrix derivatives, the paper derives a recursion for computing any Gaussian multivariate moment. Second, the paper uses this result in a perturbation method to derive equations for computing the 4th-order...

Fourth-order multi-step perturbation (MSP) is described and applied as a general method for numerically solving nonlinear, differentiable, algebraic equations which are first-order conditions of economic optimization problems. MSP is first described at a general level and is, then, applied to...