Mills T. Applied Time Series Analysis
Title
Copyright
Introduction
Endnotes
1 Time Series and Their Features
Autocorrelation and Periodic Movements
Seasonality
Stationarity and Nonstationarity
Trends
Volatility
Common Features
Time Series Having Natural Constraints
Endnotes
2 Transforming Time Series
Distributional Transformations
Stationarity Inducing Transformations
Decomposing a Time Series and Smoothing Transformations
Endnotes
3 ARMA Models for Stationary Time Series
Stochastic Processes and Stationarity
Woldโs Decomposition and Autocorrelation
First-Order Autoregressive Processes
First-Order Moving Average Processes
General AR and MA Processes
Autoregressive-Moving Average Models
ARMA Model Building and Estimation
Endnotes
4 ARIMA Models for Nonstationary Time Series
Nonstationarity
ARIMA Processes
ARIMA Modeling
Endnotes
5 Unit Roots, Difference and Trend Stationarity, and Fractional Differencing
Determining the Order of Integration of a Time Series
Testing for a Unit Root
Trend Versus Difference Stationarity
Testing for More Than One Unit Root
Other Approaches to Testing for a Unit Root
Estimating Trends Robustly
Fractional Differencing and Long Memory
Testing for Fractional Differencing
Estimating the Fractional Differencing Parameter
Endnotes
6 Breaking and Nonlinear Trends
Breaking Trend Models
Breaking Trends and Unit Root Tests
Unit Roots Tests When the Break Date Is Unknown
Robust Tests for a Breaking Trend
Confidence Intervals for the Break Date and Multiple Breaks
Nonlinear Trends
Endnotes
7 An Introduction to Forecasting With Univariate Models
Forecasting With Autoregressive-Integrated-Moving Average (ARIMA) Models
Forecasting a Trend Stationary Process
Endnotes
8 Unobserved Component Models, Signal Extraction, and Filters
Unobserved Component Models
Signal Extraction
Filters
Endnotes
9 Seasonality and Exponential Smoothing
Seasonal Patterns in Time Series
Modeling Deterministic Seasonality
Modeling Stochastic Seasonality
Mixed Seasonal Models
Seasonal Adjustment
Exponential Smoothing
Endnotes
10 Volatility and Generalized Autoregressive Conditional Heteroskedastic Processes
Volatility
Autoregressive Conditional Heteroskedastic Processes
Testing for the Presence of ARCH Errors
Forecasting From an ARMA-GARCH Model
Endnotes
11 Nonlinear Stochastic Processes
Martingales, Random Walks, and Nonlinearity
Nonlinear Stochastic Models
Bilinear Models
Threshold and Smooth Transition Autoregressions
Markov-Switching Models
Neural Networks
Nonlinear Dynamics and Chaos
Testing for Nonlinearity
Forecasting With Nonlinear Models
Endnotes
12 Transfer Functions and Autoregressive Distributed Lag Modeling
Transfer Function-Noise Models
Autoregressive Distributed Lag Models
Endnotes
13 Vector Autoregressions and Granger Causality
Multivariate Dynamic Regression Models
Vector Autoregressions
Granger Causality
Determining the Lag Order of a Vector Autoregression
Variance Decompositions and Innovation Accounting
Structural Vector Autoregressions
Endnotes
14 Error Correction, Spurious Regressions, and Cointegration
The Error Correction Form of an Autoregressive Distributed Lag Model
Spurious Regressions
Error Correction and Cointegration
Testing for Cointegration
Estimating Cointegrating Regressions
Endnotes
15 Vector Autoregressions With Integrated Variables, Vector Error Correction Models, and Common Trends
Vector Autoregressions With Integrated Variables
Vector autoregressions With Cointegrated Variables
Estimation of Vector Error Correction Models and Tests of Cointegrating Rank
Identification of Vector Error Correction Models
Structural Vector Error Correction Models
Causality Testing in Vector Error Correction Models
Impulse Response Asymptotics in Nonstationary VARs
Vector Error Correction Model-X Models
Common Trends and Cycles
Endnotes
16 Compositional and Count Time Series
Constrained Time Series
Modeling Compositional Data
Forecasting Compositional Time Series
Time Series Models for Counts: The IN-AR(1) Benchmark Model
Other Integer-Valued ARMA Processes
Estimation of Integer-Valued ARMA Models
Testing for Serial Dependence in Count Time Series
Forecasting Counts
Intermittent and Nonnegative Time Series
Endnotes
17 State Space Models
Formulating State Space Models
The Kalman Filter
ML Estimation and the Prediction Error Decomposition
Prediction and Smoothing
Multivariate State Space Models
Endnotes
18 Some Concluding Remarks
Endnotes
References
Index
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