Applied Time Series Analysis
Purchasing Options
Features
- Gives readers with limited time the ability to 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 it as the output of a "black box"
- Includes a Windows-based time series software package that is both tutorial and data analytic in nature
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 includes examples across a variety of fields, develops theory, and provides software to address time series problems in a broad spectrum of fields. The authors organize the information in such a format that graduate students in applied science, statistics, and economics can satisfactorily navigate their way through the book while maintaining mathematical rigor.
One of the unique features of Applied Time Series Analysis is the associated software, GW-WINKS, designed to help students easily generate realizations from models and explore the associated model and data characteristics. The text explores many important new methodologies that have developed in time series, such as ARCH and GARCH processes, time varying frequencies (TVF), wavelets, and more. Other programs (some written in R and some requiring S-plus) are available on an associated website for performing computations related to the material in the final four chapters.
Table of Contents
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 Xto(l)
pi-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 σ2a
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 Identification Based on Pattern Recognition
Model Building
Residual Analysis
Stationarity versus Nonstationarity
Signal-plus-Noise versus Purely Autocorrelation-Driven Models
Checking Realization Characteristics
Comprehensive Analysis of Time Series Data: A Summary
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
Proof of Kalman Recursion for Prediction and Filtering
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
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
Appendix: Mathematical Preliminaries for This Chapter
G-Stationary Processes
Generalized-Stationary Processes
M-Stationary Processes
G(λ)-Stationary Processes
Linear Chirp Processes
Concluding Remarks
Index