The rôle of past and future in estimation and the reversibility of stochastic processes
نویسندگان
چکیده
The purpose of this paper is to elucidate a dichotomy between past and future in prediction of multivariate time-series. More specifically, vector-valued gaussian stochastic processes may be deterministic in one time-direction and not the other. This fact, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discuss are based on the work of Douglas, Shapiro and Shields on cyclic vectors of the backward shift and relate to classical ideas going back to Wiener and Komogoroff. The paper builds on examples and the goal is to provide insight to a control engineering audience.
منابع مشابه
Confidence Interval Estimation of the Mean of Stationary Stochastic Processes: a Comparison of Batch Means and Weighted Batch Means Approach (TECHNICAL NOTE)
Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...
متن کاملA Stochastic Model for Water Resources Management
Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. Over the past decades, controversial and conflictladen water-allocation issues among competing municipal, industrial and agricultural interests have raised increasing concerns. Particularly, growing population, varying natural conditions and shrinking wa...
متن کاملMedium Term Hydroelectric Production Planning - A Multistage Stochastic Optimization Model
Multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. One of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices) that can be described by stochastic proc...
متن کاملEstimation of groundwater level using a hybrid genetic algorithm-neural network
In this paper, we present an application of evolved neural networks using a real coded genetic algorithm for simulations of monthly groundwater levels in a coastal aquifer located in the Shabestar Plain, Iran. After initializing the model with groundwater elevations observed at a given time, the developed hybrid genetic algorithm-back propagation (GA-BP) should be able to reproduce groundwater ...
متن کاملEstimation of groundwater level using a hybrid genetic algorithm-neural network
In this paper, we present an application of evolved neural networks using a real coded genetic algorithm for simulations of monthly groundwater levels in a coastal aquifer located in the Shabestar Plain, Iran. After initializing the model with groundwater elevations observed at a given time, the developed hybrid genetic algorithm-back propagation (GA-BP) should be able to reproduce groundwater ...
متن کامل