Occasional large errors in data can have drastic effects on estimates for such quantities as correlation coefficients. regression coefficients, and spectral density estimates. In this article we investigate the effect of outliers on time series data by considering the influence function for the autocorrelations p ( k ) of a stationary time series. This influence function matrix is applied to simulated data, to power plant data, and to inventory data on nuclear materials.

This paper describes the use of the Kalman Filter in a certain ciass of forecasting problems. The time series is assumed to be modeled as a time varying mean with additive noise. The mean of the time series is assumed to be a linear combination of known functions. The coefficients appearing in the linear combination are unknown. Under such assumptions, the time series can be described as a linear system with the state vector of the system being the unknown parameters and present value of the mean of the process. The Kalman Filter can be used under these circumstances to obtain an "optimal" estimate of the state vector. One of the distinct advantages of the Kalman Filter is that time varying coefficients can be permitted in the model. Examples using the Kalman Filter in forecasting are presented.

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In recent years, many researchers have demonstrated the desirability of applying optimal control techniques to chemical processes. However, most of the experimental results were obtained by using computer simulations of the controlled system. The research reported herein is an attempt to "bridge the gap" between theory and practice by applying optimal control techniques to the actual system rather than a computer simulation of the system. A linear discrete time model of the process was used to obtain the optimal control law. The optimal control law was obtained by a dynamic programming solution procedure. The control is an explicit function of the state of the system and of future upsets to the system. Statistical models were developed which allow nonstationary stochastic upsets to be considered.