Abstract
Abstract In this chapter, we review some basic properties of stationary stochastic processes. Results on martingale limit theorems and laws of large numbers for mixing sequences, as well as central limit theorems for sums of dependent random variables have been discussed. We then discuss weak convergence of empirical processes obtained from stationary observations. These results have been applied to generate consistent and asymptotically normal estimators of parameters of a stationary stochastic process.KeywordsWeak ConvergenceErgodic TheoremEmpirical ProcessEmpirical Distribution FunctionGeneral Random SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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