Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

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John Wiley & Sons, Dec 12, 2019 - Mathematics - 308 pages

Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences.

Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.

 

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Contents

Stationary Increments of Discrete Time Stochastic
1
Extrapolation Problem for Stochastic Sequences with
9
with Stationary nth Increments Based on Observations with
53
class Pu v
86
Filtering Problem of Stochastic Sequences with
107
class Duv
135
Filtering Problem for Stochastic Sequences with
155
Stationary Increments of Continuous Time Stochastic
181
Extrapolation Problem for Stochastic Processes with
187
Interpolation Problem for Stochastic Processes with
217
Filtering Problem for Stochastic Processes with
239
Problems to Solve
253
Appendix
259
References
267
Index
281
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About the author (2019)

Maksym Luz is Deputy Local Chief Actuary and Risk Officer at BNP Paribas Cardif, Ukraine.

Mikhail Moklyachuk is Full Professor at the Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.

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