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.
Mục lục
1. Stationary Increments of Discrete Time Stochastic Processes: Spectral Representation.
2. Extrapolation Problem for Stochastic Sequences with Stationary nth Increments.
3. Interpolation Problem for Stochastic Sequences with Stationary nth Increments.
4. Extrapolation Problem for Stochastic Sequences?with Stationary nth Increments Based on Observations with Stationary Noise.
5. Interpolation Problem for Stochastic Sequences?with Stationary nth Increments Based on Observations with Stationary Noise.
6. Filtering Problem of Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise.
7. Interpolation Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise.
8. Filtering Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise.
9. Stationary Increments of Continuous Time Stochastic Processes: Spectral Representation.
10. Extrapolation Problem for Stochastic Processes with Stationary nth Increments.
11. Interpolation Problem for Stochastic Processes with Stationary nth Increments.
12. Filtering Problem for Stochastic Processes with Stationary nth Increments.
Giới thiệu về tác giả
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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