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Preface | |
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Introduction | |
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Examples of Time Series | |
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Objectives of Time Series Analysis | |
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Some Simple Time Series Models | |
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Some Zero-Mean Models | |
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Models with Trend and Seasonality | |
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A General Approach to Time Series Modeling | |
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Stationary Models and the Autocorrelation Function | |
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The Sample Autocorrelation Function | |
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A Model for the Lake Huron Data | |
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Estimation and Elimination of Trend and Seasonal Components | |
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Estimation and Elimination of Trend in the Absence of Seasonality | |
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Estimation and Elimination of Both Trend and Seasonality | |
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Testing the Estimated Noise Sequence | |
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Problems | |
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Stationary Processes | |
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Basic Properties | |
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Linear Processes | |
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Introduction to ARMA Processes | |
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Properties of the Sample Mean and Autocorrelation Function | |
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Estimation of [mu] | |
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Estimation of [gamma]([middle dot]) and [rho]([middle dot]) | |
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Forecasting Stationary Time Series | |
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The Durbin-Levinson Algorithm | |
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The Innovations Algorithm | |
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Prediction of a Stationary Process in Terms of Infinitely Many Past Values | |
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The Wold Decomposition | |
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Problems | |
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ARMA Models | |
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ARMA(p, q) Processes | |
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The ACF and PACF of an ARMA(p, q) Process | |
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Calculation of the ACVF | |
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The Autocorrelation Function | |
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The Partial Autocorrelation Function | |
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Examples | |
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Forecasting ARMA Processes | |
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Problems | |
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Spectral Analysis | |
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Spectral Densities | |
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The Periodogram | |
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Time-Invariant Linear Filters | |
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The Spectral Density of an ARMA Process | |
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Problems | |
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Modeling and Forecasting with ARMA Processes | |
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Preliminary Estimation | |
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Yule-Walker Estimation | |
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Burg's Algorithm | |
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The Innovations Algorithm | |
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The Hannan-Rissanen Algorithm | |
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Maximum Likelihood Estimation | |
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Diagnostic Checking | |
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The Graph of {R[subscript t], t = 1, ..., n{ | |
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The Sample ACF of the Residuals | |
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Tests for Randomness of the Residuals | |
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Forecasting | |
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Order Selection | |
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The FPE Criterion | |
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The AICC Criterion | |
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Problems | |
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Nonstationary and Seasonal Time Series Models | |
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ARIMA Models for Nonstationary Time Series | |
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Identification Techniques | |
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Unit Roots in Time Series Models | |
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Unit Roots in Autoregressions | |
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Unit Roots in Moving Averages | |
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Forecasting ARIMA Models | |
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The Forecast Function | |
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Seasonal ARIMA Models | |
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Forecasting SARIMA Processes | |
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Regression with ARMA Errors | |
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OLS and GLS Estimation | |
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ML Estimation | |
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Problems | |
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Multivariate Time Series | |
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Examples | |
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Second-Order Properties of Multivariate Time Series | |
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Estimation of the Mean and Covariance Function | |
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Estimation of [mu] | |
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Estimation of [Gamma](h) | |
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Testing for Independence of Two Stationary Time Series | |
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Bartlett's Formula | |
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Multivariate ARMA Processes | |
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The Covariance Matrix Function of a Causal ARMA Process | |
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Best Linear Predictors of Second-Order Random Vectors | |
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Modeling and Forecasting with Multivariate AR Processes | |
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Estimation for Autoregressive Processes Using Whittle's Algorithm | |
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Forecasting Multivariate Autoregressive Processes | |
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Cointegration | |
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Problems | |
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State-Space Models | |
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State-Space Representations | |
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The Basic Structural Model | |
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State-Space Representation of ARIMA Models | |
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The Kalman Recursions | |
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Estimation For State-Space Models | |
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State-Space Models with Missing Observations | |
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The EM Algorithm | |
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Generalized State-Space Models | |
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Parameter-Driven Models | |
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Observation-Driven Models | |
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Problems | |
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Forecasting Techniques | |
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The ARAR Algorithm | |
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Memory Shortening | |
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Fitting a Subset Autoregression | |
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Forecasting | |
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Application of the ARAR Algorithm | |
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The Holt-Winters Algorithm | |
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The Algorithm | |
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Holt-Winters and ARIMA Forecasting | |
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The Holt-Winters Seasonal Algorithm | |
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The Algorithm | |
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Holt-Winters Seasonal and ARIMA Forecasting | |
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Choosing a Forecasting Algorithm | |
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Problems | |
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Further Topics | |
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Transfer Function Models | |
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Prediction Based on a Transfer Function Model | |
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Intervention Analysis | |
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Nonlinear Models | |
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Deviations from Linearity | |
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Chaotic Deterministic Sequences | |
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Distinguishing Between White Noise and iid Sequences | |
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Three Useful Classes of Nonlinear Models | |
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Modeling Volatility | |
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Continuous-Time Models | |
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Long-Memory Models | |
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Problems | |
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Random Variables and Probability Distributions | |
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Distribution Functions and Expectation | |
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Random Vectors | |
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The Multivariate Normal Distribution | |
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Problems | |
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Statistical Complements | |
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Least Squares Estimation | |
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The Gauss-Markov Theorem | |
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Generalized Least Squares | |
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Maximum Likelihood Estimation | |
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Properties of Maximum Likelihood Estimators | |
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Confidence Intervals | |
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Large-Sample Confidence Regions | |
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Hypothesis Testing | |
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Error Probabilities | |
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Large-Sample Tests Based on Confidence Regions | |
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Mean Square Convergence | |
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The Cauchy Criterion | |
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An ITSM Tutorial | |
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Getting Started | |
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Running ITSM | |
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Preparing Your Data for Modeling | |
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Entering Data | |
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Information | |
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Filing Data | |
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Plotting Data | |
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Transforming Data | |
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Finding a Model for Your Data | |
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Autofit | |
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The Sample ACF and PACF | |
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Entering a Model | |
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Preliminary Estimation | |
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The AICC Statistic | |
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Changing Your Model | |
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Maximum Likelihood Estimation | |
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Optimization Results | |
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Testing Your Model | |
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Plotting the Residuals | |
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ACF/PACF of the Residuals | |
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Testing for Randomness of the Residuals | |
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Prediction | |
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Forecast Criteria | |
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Forecast Results | |
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Model Properties | |
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ARMA Models | |
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Model ACF, PACF | |
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Model Representations | |
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Generating Realizations of a Random Series | |
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Spectral Properties | |
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Multivariate Time Series | |
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References | |
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Index | |