A Schmidt filter is proposed to compute an optimal orthonormal basis for a set of noisy filter input functions. Procedures for determining the transfer function and inverse transfer function of the filter are given. The Schmidt filter is applied to the problem of determining mathematical models of discrete, stationary, linear, dynamic systems for the case where measurements may be corrupted by noise of unknown statistics. The identification problem is reconsidered for the case where noise and signal moments are specified. Procedures are given which insure unbiased, adaptive estimates of system order and parameters for this case. These theoretical propositions are applied to the modeling of speculative prices. The stock market is formulated as a discrete, linear, dynamic system and the results of several simulation studies are presented. Evidence indicates that certain segments of the market can be approximated by high-order linear systems computed from small samples and tends to refute the random walk hypothesis. Computer programs (written in PL/1) are presented which allow for efficient digital realization of the theoretical procedures discussed in the body of this work --Abstract, page iii
