SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.

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Testing for a Unit Root in Time Series Regression

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

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Information Theory, Inference and Learning Algorithms

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems.

Probability: Theory and Examples

* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

Martingale Limit Theory and Its Application

Martingale Limit Theory and its Application

Quasi-likelihood and its application , Quasi-likelihood and its application , کتابخانه دیجیتال جندی شاپور اهواز

https://www.springer.com/productFlyer_978-0-387-98225-0.pdf?SGWID=0-0-1297-1542171-0

Quasi-likelihood and its application

Within the framework of estimating function theory, this paper provides a very general definition of quasi-likelihood estimating equations. Applications to stochastic processes are discussed. This work extends the previous results of Godambe (1985) and Hutton & Nelson (1986).

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Quasi-likelihood and Optimal Estimation

The General Framework.- An Alternative Approach: E-Sufficiency.- Asymptotic Confidence Zones of Minimum Size.- Asymptotic Quasi-Likelihood.- Combining Estimating Functions.- Projected Quasi-Likelihood.- Bypassing the Likelihood.- Hypothesis Testing.- Infinite Dimensional Problems.- Miscellaneous Applications.- Consistency and Asymptotic Normality for Estimating Functions.- Complements and Strategies for Application.

C. C. Heyde

Papers

Martingale Limit Theory and Its Application

Martingale Limit Theory and its Application

Quasi-likelihood and its application

Quasi-likelihood and Optimal Estimation

Quasi-likelihood and its application : a general approach to optimal parameter estimation