Robustness in statistical forecasting Yuriy Kharin

Format:

Book

Author/Creator:

Kharin, I︠U︡. S., author.

Language:

English

Subjects (All):

Time-series analysis.

Robust statistics.

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2013

System Details:

PDF

text file

Summary:

Traditional procedures in the statistical forecasting of time series, which are proved to be optimal under the hypothetical model, are often not robust under relatively small distortions (misspecification, outliers, missing values, etc.), leading to actual forecast risks (mean square errors of prediction) that are much higher than the theoretical values. This monograph fills a gap in the literature on robustness in statistical forecasting, offering solutions to the following topical problems: - developing mathematical models and descriptions of typical distortions in applied forecasting problems; - evaluating the robustness for traditional forecasting procedures under distortions; - obtaining the maximal distortion levels that allow the 'safe' use of the traditional forecasting algorithms; -creating new robust forecasting procedures to arrive at risks that are less sensitive to definite distortion types

Contents:

Introduction A Decision-Theoretic Approach to Forecasting Time Series Models of Statistical Forecasting Performance and Robustness Characteristics in Statistical Forecasting Forecasting Under Regression Models of Time Series Robustness of Time Series Forecasting Based on Regression Models Optimality and Robustness of ARIMA Forecasting Optimality and Robustness of Vector Autoregression Forecasting Under Missing Values Robustness of Multivariate Time Series Forecasting Based on Systems of Simultaneous Equations Forecasting of Discrete Time Series

Machine generated contents note: References

2.1. Mathematical Model of Decision Making

2.2. Minimax, Admissible, and Bayesian Families of Decision Rules

2.3. Bayesian Forecast Density

2.4. Forecasting Discrete States by Discriminant Analysis

2.4.1. Mathematical Model

2.4.2. Complete Prior Knowledge of {πi, pi[ð]([•])}

2.4.3. Prior Uncertainty References

3.1. Regression Models of Time Series

3.2. Stationary Time Series Models

3.3. ARIMA(p, d, q) Time Series Model

3.4. Nonlinear Time Series

3.4.1. General Nonlinear Model

3.4.2. Bilinear Model BL(p, q, P, Q)

3.4.3. Functional-Coefficient Autoregression Model FAR(p, d)

3.4.4. Generalized Exponential Autoregression Model EXPAR(p, d)

3.4.5. Threshold Autoregression Model TAR(k)

3.4.6. ARCH(p) Model

3.4.7. GARCH(p, q) Model

3.5. Multivariate Time Series Models

3.5.1. Multivariate Stationary Time Series

3.5.2. Vector Autoregression Model VAR(p)

3.5.3. Vector Moving Average Model VMA(q)

3.5.4. VARMA(p, 9) Model

3.5.5. System of Simultaneous Equations (SSE) Model

3.6. Discrete Time Series

3.6.1. Markov Chains

3.6.2. Markov Chains of Order s

3.6.3. DAR(s) Model of Jacobs and Lewis

3.6.4. DMA(q) Model

3.6.5. INAR(m) Model References

4.1. General Formulation of the Statistical Forecasting Problem

4.2. Risk Functional and Optimality of Forecasting Statistics

4.3. Classification of Model Distortions

4.4. Robustness Characteristics References

5.1. Optimal Forecasting Under Complete Prior Information

5.2. Regression Forecasting Under Parametric Prior Uncertainty

5.2.1. Bayesian Approach in the PU-P getting

5.2.2. Joint Estimation Using the Maximum Likelihood (ML) Principle

5.2.3. Using the Plug-In Principle

5.3. Logistic Regression Forecasting

5.4. Nonparametric Kernel Regression Forecasting

5.5. Nonparametric k-NN-Regression Forecasting

5.6. Some Other Nonparametric Regression Forecasting Methods

5.6.1. Functional Series Expansions of Regression Functions

5.6.2. Spline Smoothing

5.6.3. Regressograms and Median Smoothing References

6.1. Robustness of Least Squares Forecasting Under Functional Distortions of Multiple Linear Regression Models

6.1.1. Formulation of the Problem

6.1.2. Hypothetical Regression Model and Its Functional Distortions

6.1.3. Robustness Characteristics of Forecasting Algorithms

6.1.4. Robustness Analysis of Least Squares Forecasting

6.2. Robustness of Least Squares Forecasting Under Functional Distortions of Multivariate Linear Regression Models

6.2.1. Mathematical Description of Model Distortions

6.2.2. Robustness Evaluation of Least Squares Forecasting

6.3. Robustness of Least Squares Forecasting Under Outliers

6.4. Impact of Correlation Between Observation Errors on Forecast Risk

6.5. Robust Forecasting Based on M-Estimators Under Functional Distortion

6.5.1. Construction of a Robust Forecasting Algorithm

6.5.2. Evaluation of the Constructed Robust Forecasting Algorithm

6.5.3. Numerical Examples

6.6. Robust Regression Forecasting Under Outliers Based on the Huber Estimator

6.7. Local-Median (LM) Forecasting and Its Properties

6.7.1. Description of the Method

6.7.2. Breakdown Point

6.7.3. Probability Distribution of the LM Forecast

6.7.4. Risk of the LM Forecast

6.7.5. Robustness of LM Forecasting Compared to the Traditional Least Squares Method

6.7.6. Generalization of the LM Method for Multivariate Regression

6.7.7. Numerical Results References

7.1. Kolmogorov's Method

7.2. Optimal Forecasting Under ARIMA Time Series Models

7.2.1. General Method for Stationary Time Series

7.2.2. Forecasting Under the AR(p) Model

7.2.3. Forecasting Under the MA(q) Model

7.2.4. Forecasting Under the ARMA(p, q) Model

7.2.5. Forecasting Under the ARIMA(p, d, q) Model

7.3. Plug-In Forecasting Algorithms

7.3.1. Plug-In Forecasting Algorithms Based on Covariance Function Estimators

7.3.2. Plug-In Forecasting Algorithms Based on AR(p) Parameter Estimators

7.3.3. Plug-In Forecasting Algorithms Based on Parameter Estimation of MA(q) Models

7.3.4. Plug-In Forecasting Algorithms Based on ARMA(p, q) Parameter Estimators

7.3.5. Plug-In Forecasting Algorithms Based on ARIMA(p, d, q) Parameter Estimators

7.4. Robustness Under Parametric Model Specification Errors

7.4.1. General Case

7.4.2. Stationary Time Series Forecasting Under Misspecification of Covariance Functions

7.4.3. Forecasting of AR(p) Time Series Under Misspecification of Autoregression Coefficients

7.5. Robustness Under Functional Innovation Process Distortions in the Mean Value

7.6. Robustness of Autoregression Forecasting Under Heteroscedasticity of the Innovation Process

7.6.1. Mathematical Model

7.6.2. Presence of a Specification Error

7.6.3. Least Squares Estimation of θ[ð]

7.7. Robustness of Autoregression Time Series Forecasting Under IO-Outliers

7.8. Robustness of Autoregression Time Series Forecasting Under AO Outliers

7.9. Robustness of Autoregression Forecasting Under Bilinear Distortion

7.9.1. Introduction

7.9.2. Bilinear Model and Its Stationarity Conditions

7.9.3. First and Second Order Moments in Stationary Bilinear Time Series Models

7.9.4. Robustness of Autoregression Forecasting Under Bilinear Distortion

7.9.5. Robustness Analysis of Autoregression Forecasting

7.9.6. Numerical Results References

8.1. VAR Time Series Models Under Missing Values

8.2. Optimal Forecasting Statistic and Its Risk

8.3. Robustness of the Optimal Forecasting Statistic Under Specification Errors

8.4. Modified Least Squares Estimators Under Missing Values

8.5. Least Squares Forecasting and Its Risk Under Missing Values

8.6. Results of Computer Experiments

8.6.1. Performance of the Estimator B

8.6.2. Experimental Evaluation of the Forecast Risk

8.7. Robust Plug-In Forecasting Under Simultaneous Influence of Outliers and Missing Values

8.7.1. Mathematical Model of Simultaneous Distortion by Outliers and Missing Values

8.7.2. Family of Robust Estimators for Correlations Based on the Cauchy Probability Distribution

8.7.3. Minimizing Asymptotic Variance of ψ-Estimators

8.7.4. Robust Estimators of Autoregression Coefficients

8.7.5. Estimation of the Contamination Level epsilon

8.7.6. Simulation-Based Performance Evaluation of the Constructed Estimators and Forecasting Algorithms References

9.1. Systems of Simultaneous Equations

9.1.1. SSE Model

9.1.2. Example of an SSE: Klein's Model I

9.1.3. Optimal Forecasting Statistic Under the SSE Model

9.2. Robustness of SSE-Based Forecasting Under Specification Errors

9.3. Plug-In Forecasting Statistics in the SSE Model

9.4. Asymptotic Properties of the Least Squares Estimator Under Drifting Coefficients

9.4.1. Drifting Coefficient Models for SSEs

9.4.2. LS Parameter Estimators Under Parameter Drift

9.5. Sensitivity of Forecast Risk to Parameter Drift

9.6. Numerical Results for the Ludeke Econometric Model References

10.1. Forecasting by Discriminant Analysis of Markov Chains

10.1.1. Time Series Model

10.1.2. Bayesian Decision Rule and Its Properties

10.1.3. Plug-In Decision Rule and Its Risk

10.1.4. Asymptotic Expansion of the PBDR Risk

10.2. HMC Forecasting Under Missing Values

10.2.1. Likelihood Functions for HMCs with Missing Values

10.2.2. Decision Rule for Known {π(l), P(l}

10.2.3. Case of Unknown Parameters

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Kharin, I︠U︡. S. Robustness in statistical forecasting

ISBN:

9783319008400

3319008404

OCLC:

858275398

Access Restriction:

Restricted for use by site license