Summary

Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested,

Applied Time Series Analysis with R, Second Editionincludes examples across a variety of fields, develops theory, and provides an R-based software package in CRAN (tswge) to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis.

Features

- Gives readers the ability to actually solve significant real-world problems
- Addresses many types of nonstationary time series and cutting-edge methodologies
- Promotes understanding of the data and associated models rather than viewing the series as the output of a "black box"
- Over 150 exercises and extensive support for instructors

New to the Second EditionThe second edition has several enhancements that make it an ideal text for a stand-alone one semester or a two semester course in applied time series analysis. New features include:

- An accompanying, easy to use R package that includes 50+ functions for analyzing time series data and producing associated graphical presentations
- Many additional real-world data sets, all of which are included in the accompanying R package. The package contains about 100 data sets (real and simulated).
- Discusses new advances in the analysis of long memory and data with time-varying frequencies (TVF).

Stationary Time Series

Time Series

Stationary Time Series

Autocovariance and Autocorrelation Functions for Stationary Time Series

Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series

Power Spectrum

Estimating the Power Spectrum and Spectral Density for Discrete Time Series

Time Series Examples

Linear Filters

Introduction to Linear Filters

Stationary General Linear Processes

Wold Decomposition Theorem

Filtering Applications

ARMA Time Series Models

Moving Average Processes

Autoregressive Processes

Autoregressive–Moving Average Processes

Visualizing Autoregressive Components

Seasonal ARMA(p,q) x (Ps,Qs)s Models

Generating Realizations from ARMA(p,q) Processes

Transformations

Other Stationary Time Series Models

Stationary Harmonic Models

ARCH and GARCH Models

Nonstationary Time Series Models

Deterministic Signal-Plus-Noise Models

ARIMA(p,d,q) and ARUMA(p,d,q) Models

Multiplicative Seasonal ARUMA(p,d,q) x (Ps,Ds,Qs)s Model

Random Walk Models

G-Stationary Models for Data with Time-Varying Frequencies

Forecasting

Mean Square Prediction Background

Box–Jenkins Forecasting for ARMA(p,q) Models

Properties of the Best Forecast

π-Weight Form of the Forecast Function

Forecasting Based on the Difference Equation

Eventual Forecast Function

Probability Limits for Forecasts

Forecasts Using ARUMA(p,d,q) Models

Forecasts Using Multiplicative Seasonal ARUMA Models

Forecasts Based on Signal-Plus-Noise Models

Parameter Estimation

Introduction

Preliminary Estimates

Maximum Likelihood Estimation of ARMA( p,q) Parameters

Backcasting and Estimating white noise variance

Asymptotic Properties of Estimators

Estimation Examples Using Data

ARMA Spectral Estimation

ARUMA Spectral Estimation

Model Identification

Preliminary Check for White Noise

Model Identification for Stationary ARMA Models

Model Identification for Nonstationary ARUMA(p,d,q) Models

Model Building

Residual Analysis

Stationarity versus Nonstationarity

Signal-plus-Noise versus Purely Autocorrelation-Driven Models

Checking Realization Characteristics

Comprehensive Analysis of Time Series Data

Vector-Valued (Multivariate) Time Series

Multivariate Time Series Basics

Stationary Multivariate Time Series

Multivariate (Vector) ARMA Processes

Nonstationary VARMA Processes

Testing for Association between Time Series

State-Space Models

Long-Memory Processes

Long Memory

Fractional Difference and FARMA Models

Gegenbauer and GARMA Processes

k-Factor Gegenbauer and GARMA Models

Parameter Estimation and Model Identification

Forecasting Based on the k-Factor GARMA Model

Testing for long memory

Modeling Atmospheric CO2 Data Using Long-Memory Models

Wavelets

Shortcomings of Traditional Spectral Analysis for TVF Data

Methods That Localize the ‘‘Spectrum’’ in Time

Wavelet Analysis

Wavelet Packets

Concluding Remarks on Wavelets

G-Stationary Processes

Generalized-Stationary Processes

M-Stationary Processes

G(λ)-Stationary Processes

Linear Chirp Processes

G-Filtering

Index