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.
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Rajarshi, M.B. (2013). CAN Estimators from Dependent Observations. In: Statistical Inference for Discrete Time Stochastic Processes. SpringerBriefs in Statistics. Springer, India. https://doi.org/10.1007/978-81-322-0763-4_1
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DOI: https://doi.org/10.1007/978-81-322-0763-4_1
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