Long Memory Time Series Analysis

Gnanadarsha Sanjaya Dissanayake, Hassan Doosti

• Publisher: Chapman and Hall/CRC
• Year: 2026
• eBook ISBN: 9781040712191
• Topic: Mathematics
• Index: Mathematics

Long Memory Time Series Analysis is a comprehensive text which covers long memory time series with the different long memory time series discussed. The authors cover modelling and forecasting using various time series, deploying traditional and machine learning methodologies. The reader also learns recent research trends, such as state space modelling of generalized long memory time series and the use of the tsfGRNN machine learning tool in R. The book starts from autoregressive (AR) and moving average (MA) processes to descriptions of the autoregressive integrated moving average (ARMA) time series, the ARIMA model, and the autoregressive fractionally integrated moving average (ARFIMA) process. The differences of short, intermediate, and long memory processes are highlighted. The reader will gain knowledge of elementary time series through this extensive coverage.

The book discusses generalized Gegenbauer autoregressive moving averages (GARMA) and seasonal GARMA long memory time series and state space modelling of generalized and seasonal GARMA. The extensions of the short and long memory models driven by generalised autoregressive conditionally heteroskedastic (GARCH) errors are also presented. The extensive range of problems linked with generalized Gegenbauer long memory time series are presented to reinforce the reader's conceptual learning. Coverage on the use of time series with high frequency data captured through the latest technological innovations is an invaluable resource to the reader. This learning is done through examples of time series application case studies in medicine, biology, and finance.

The core audience is students attending advanced studies in time series. The book can also be used by researchers and data scientists involved in utilizing time series analysis in a modern context.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• 1 Introduction to AR, MA Time Series, Autocorrelation, Partial Autocorrelation, Spectral Density
• 2 ARMA Process and Box–Jenkins Model
• 3 Integer Differencing and ARIMA Process with White Noise
• 4 Fractional Differencing and ARFIMA Process with White Noise
• 5 Short, Intermediate, and Long Memory Properties of Time Series
• 6 Standard Long Memory and State Space Modeling of ARFIMA Process with White Noise
• 7 State Space Modeling of GARMA Processes with Generalized Long Memory
• 8 Nonlinear and Nonstationary Time Series
• 9 An Introduction to Nonparametric Long Memory Time Series
• 10 ARMA, ARIMA, ARFIMA, and GARMA Models with GARCH Errors
• 11 Enhancing Time Series Analysis with Machine Learning, High-Frequency Data, and Applications in Medicine and Biology
• Bibliography
• R Software Codes with and/or without Machine Learning
• Answers to Selected Chapter Exercises
• Index