book

Linear Models and Time-Series Analysis

by Marc S. Paolella

December 2018

Intermediate to advanced

896 pages

33h 54m

English

Wiley

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1.1 Regression, Correlation, and Causality1.2 Ordinary and Generalized Least Squares1.3 The Geometric Approach to Least Squares1.4 Linear Parameter Restrictions1.5 Alternative Residual Calculation1.6 Further Topics1.7 Problems1.A Appendix: Derivation of the BLUS Residual Vector1.B Appendix: The Recursive Residuals1.C Appendix: Solutions
2.1 Introduction: Fixed, Random, and Mixed Effects Models2.2 Two Sample ‐Tests for Differences in Means2.3 The Two Sample ‐Test with Ignored Block Effects2.4 One‐Way ANOVA with Fixed Effects2.5 Two‐Way Balanced Fixed Effects ANOVA
3.1 One‐Factor Balanced Random Effects Model3.2 Crossed Random Effects Models3.3 Nested Random Effects Models3.4 Problems3.5 Appendix: Solutions
4.1 Moments and Stationarity4.2 Order of Integration and Long‐Run Variance4.3 Least Squares and ML Estimation4.4 Forecasting4.5 Small Sample Distribution of the OLS and ML Point Estimators4.6 Alternative Point Estimators of 4.7 Confidence Intervals for 4.8 Problems
5.1 The AR(1) Regression Model and the Likelihood5.2 OLS Point and Interval Estimation of 5.3 Testing in the ARX(1) Model5.4 Bias‐Adjusted Point Estimation5.5 Unit Root Testing in the ARX(1) Model5.6 Time‐Varying Parameter Regression
6.1 AR( ) Processes6.2 Moving Average Processes6.3 Problems6.4 Appendix: Solutions

7.1 Basics of ARMA Models7.2 Infinite AR and MA Representations7.3 Initial Parameter Estimation7.4 Likelihood‐Based Estimation7.5 Forecasting7.6 Bias‐Adjusted Point Estimation: Extension to the ARMAX model7.7 Some ARIMAX Model Extensions7.8 Problems7.9 Appendix: Generalized Least Squares for ARMA Estimation7.10 Appendix: Multivariate AR( ) Processes and Stationarity, and General Block Toeplitz Matrix Inversion
8.1 Theoretical and Sample Autocorrelation Function8.2 Theoretical and Sample Partial Autocorrelation Function8.3 Problems8.4 Appendix: Solutions
9.1 Introduction9.2 Visual Correlogram Analysis9.3 Significance Tests9.4 Penalty Criteria9.5 Use of the Conditional SACF for Sequential Testing9.6 Use of the Singular Value Decomposition9.7 Further Methods: Pattern Identification
10.1 Introduction10.2 Gaussian GARCH and Estimation10.3 Non‐Gaussian ARMA‐APARCH, QMLE, and Forecasting10.4 Near‐Instantaneous Estimation of NCT‐APARCH(1,1)10.5 ‐APARCH and Testing the IID Stable Hypothesis10.6 Mixed Normal GARCH
11.1 Value at Risk and Expected Shortfall Prediction11.2 MGARCH Constructs Via Univariate GARCH11.3 Introducing Portfolio Optimization
12.1 Multivariate Student's 12.2 Multivariate Noncentral Student's 12.3 Jones Multivariate Distribution12.4 Shaw and Lee Multivariate Distributions12.5 The Meta‐Elliptical Distribution12.6 MEST: Marginally Endowed Student's 12.7 Some Closing Remarks12.A ES of Convolution of AFaK Margins12.B Covariance Matrix for the FaK
13.1 Concept13.2 Determination of Optimal Weighting13.3 Density Forecasting and Backtest Overfitting13.4 Portfolio Optimization Using (A)FaK
14.1 The Distribution14.2 Model Diagnostics and Forecasting14.3 MCD for Robustness and Estimation14.4 Some Thoughts on Model Assumptions and Estimation14.5 The Multivariate Laplace and Distributions
A.1 Distribution and MomentsA.2 Basic Distributional ResultsA.3 Ratios of Quadratic Forms in Normal VariablesA.4 ProblemsA.A Appendix: Solutions
B.1 For and B.2 For B.3 For B.4 For B.5 Useful Matrix Algebra ResultsB.6 Saddlepoint Equivalence Result
C.1 Student's Characteristic FunctionC.2 Sphericity and Ellipticity
D.1 Introduction to SASD.2 Basic Data HandlingD.3 Advanced Data HandlingD.4 Generating Charts, Tables, and GraphsD.5 The SAS Macro ProcessorD.6 ProblemsD.7 Appendix: Solutions

Overview

A comprehensive and timely edition on an emerging new trend in time series

Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author's previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation.

The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedicated to it. With respect to the subject/technology, many chapters in Linear Models and Time-Series Analysis cover firmly entrenched topics (regression and ARMA). Several others are dedicated to very modern methods, as used in empirical finance, asset pricing, risk management, and portfolio optimization, in order to address the severe change in performance of many pension funds, and changes in how fund managers work.

Covers traditional time series analysis with new guidelines
Provides access to cutting edge topics that are at the forefront of financial econometrics and industry
Includes latest developments and topics such as financial returns data, notably also in a multivariate context
Written by a leading expert in time series analysis
Extensively classroom tested
Includes a tutorial on SAS
Supplemented with a companion website containing numerous Matlab programs
Solutions to most exercises are provided in the book

Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH is suitable for advanced masters students in statistics and quantitative finance, as well as doctoral students in economics and finance. It is also useful for quantitative financial practitioners in large financial institutions and smaller finance outlets.