Tanaka K. Time Series Analysis. Nonstationary and Noninvertible Distribution Theory

Hoboken: Wiley, 2017. — 886 p.Nonstationary and noninvertible time series are unconventional subareas of time series analysis that provide extremely accurate information on certain types of data. In recent years, researchers working in a variety of disciplines--especially in the economic and financial arenas--have developed numerous groundbreaking applications for nonstationary and noninvertible methods. Interest in these areas continues to grow. However, the mathematics of nonstationary time series analysis differs significantly from that used in traditional time series analysis. Relying heavily upon probability and differential and integral equations, nonstationary time series mathematics is often inaccessible to statistics-oriented time series analysts.
Time Series Analysis is written for the traditional statistician who lacks the rigorous mathematical background required to use nonstationary time series methods. This practical, accessible volume:
Offers statisticians the first comprehensive guide to nonstationary and noninvertible time series analysis
Interprets and explains nonstationary time series from an exclusively statistical point of view
Features over 90 illustrations and 50 tables that help clarify each technical point covered
Provides helpful problems and solutions at the end of each section
Offering in-depth coverage of a mathematically rigorous topic in terms that statisticians can understand, Time Series Analysis is an indispensable reference for researchers and graduate students in econometrics, statistics, probability, actuarial science, and engineering.
Motivating Examples.
Stochastic Calculus in Mean Square.
Functional Central Limit Theorems.
The Stochastic Process Approach.
The Fredholm Approach.
Numerical Integration.
Estimation Problems in Nonstationary Autoregressive Models.
Estimation Problems in Noninvertible Moving Average Models.
Unit Root Tests in Autoregressive Models.
Unit Root Tests in Moving Average Models.
Statistical Analysis of Cointegration.
Solutions to Problems.Indexes.