Monitoring Structural Changes in Econometric Models

The problem of sequential detection and diagnosis of structural changes in stochastic multivariate systems on the basis of sequential observations has many applications, including detection of changes in parameters of regression equations, testing adequacy of econometric models, fault detection and isolation in complex dynamical systems. There is an extensive statistical and econometric literature dealing with methods of solving these problems. Page (1954) considered the cumulative sums (CUSUM) test for detection of possible changes in the distribution function (d.f.) of a sequence of independent observations. Girshick and Rubin (1952) proposed a quasi-Bayesian test for solving the same problem. In 1959 Kolmogorov and Shiryaev proposed the formal statement of the problem of "quickiest detection of spontaneous effects" which was later called the "disorder problem". Shiryaev in 1959-1965 found the optimal solution of this problem for the situation of full a priori information on the distribution function (d.f.) of observations and a change-point. This test coincides with the Girshick-Rubin test is therefore called the GRSh (Girshick-Rubin-Shiryaev) test. In the situation when there is no a priori information on a change-point, Lorden (1971), Pollack (1985), and Moustakides (1986) proved that CUSUM and GRSh tests are asymptotically optimal in the problem of sequential detection of an abrupt change in the one-dimensional d.f. of independent observations. Willsky (1976), Willsky and Jones (1976) pioneered research into sequential detection of abrupt changes in stochastic dynamical systems. Stochastic "noises" in such systems were assumed to be Gaussian and structural changes were interpreted as spontaneously emerging additive terms in equations of considered systems. For detection of these structural changes, the innovation process of the Kalman filter was used. Different methods generalising these ideas for sequential change-point detection in stochastic dynamical systems