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