Univariate and Multivariate Methods PEARSON. Addison Wesley
|
|
- Philippa Henderson
- 8 years ago
- Views:
Transcription
1 Time Series Analysis Univariate and Multivariate Methods SECOND EDITION William W. S. Wei Department of Statistics The Fox School of Business and Management Temple University PEARSON Addison Wesley Boston San Francisco New York London Toronto Sydney Tokyo Singapore Madrid Mexico City Munich Paris Cape Town Hong Kong Montreal
2 CHAPTER 1 CHAPTER 2 CHAPTER 3 Preface Overview 1.1 Introduction 1.2 Examples and Scope of This Book Fundamental Concepts 2.1 Stochastic Processes 2.2 The Autocovariance and Autocorrelation Functions 2.3 The Partial Autocorrelation Function 2.4 White Noise Processes 2.5 Estimation of the Mean, Autocovariances, and Autocorrelations Sample Mean Sample Autocovariance Function Sample Autocorrelation Function Sample Partial Autocorrelation Function 2.6 Moving Average and Autoregressive Representations of Time Series Processes 2.7 Linear Difference Equations Exercises Stationary Time Series Models 3.1 Autoregressive Processes The First-Order Auloregressive AR( 1) Process The Second-Order Autoregressive AR(2) Process The General pth-order Autoregressive AR(p) Process 3.2 Moving Average Processes The First-Order Moving Average MA( 1) Process The Second-Order Moving Average MA(2) Process The General gth-order Moving Average MA(<y) Process XIX IX
3 3.3 The Dual Relationship Between AR(p) and MA(ij) Processes 3.4 Autoregressive Moving Average ARMA(p, q) Processes The General Mixed ARMA(p, q) Process The ARMA( 1, 1) Process Exercises CHAPTER 4 Nonstationary Time Series Models Nonstationarity in the Mean Deterministic Trend Models Stochastic Trend Models and Differencing Autoregressive Integrated Moving Average (ARIMA) Models The General ARIMA Model The Random Walk Model The ARIMA(0, 1, 1) or IMA( 1,1) Model Nonstationarity in the Variance and the Autocovariance Variance and Autocovariance of the ARIMA Models Variance Stabilizing Transformations 83 Exercises 86 CHAPTER 5 Forecasting 5.1 Introduction 5.2 Minimum Mean Square Error Forecasts Minimum Mean Square Error Forecasts for ARMA Models Minimum Mean Square Error Forecasts for ARIMA Models 5.3 Computation of Forecasts 5.4 The ARIMA Forecast as a Weighted Average of Previous Observations 5.5 Updating Forecasts 5.6 Eventual Forecast Functions 5.7 A Numerical Example Exercises CHAPTER 6 Model Identification 6.1 Steps for Model Identification 6.2 Empirical Examples 6.3 The Inverse Autocorrelation Function (IACF)
4 XI 6.4 Extended Sample Autocorrelation Function and Other Identification Procedures The Extended Sample Autocorrelation Function (ESACF) Other Identification Procedures 133 Exercises 134 CHAPTER 7 Parameter Estimation, Diagnostic Checking, and Model Selection The Method of Moments Maximum Likelihood Method Conditional Maximum Likelihood Estimation Unconditional Maximum Likelihood Estimation and Backcasting Method Exact Likelihood Functions Nonlinear Estimation Ordinary Least Squares (OLS) Estimation in Time Series Analysis Diagnostic Checking Empirical Examples for Series W1-W Model Selection Criteria 156 Exercises 158 CHAPTER 8 Seasonal Time Series Models 8.1 General Concepts 8.2 Traditional Methods Regression Method Moving Average Method 8.3 Seasonal ARIMA Models 8.4 Empirical Examples Exercises CHAPTER 9 Testing for a Unit Root Introduction Some Useful Limiting Distributions Testing for a Unit Root in the AR( 1) Model Testing the AR(1) Model without a Constant Term Testing the AR( 1) Model with a Constant Term Testing the AR( 1) Model with a Linear Time Trend Testing for a Unit Root in a More General Model 196
5 xii Contents 9.5 Testing for a Unit Root in Seasonal Time Series Models Testing the Simple Zero Mean Seasonal Model Testing the General Multiplicative Zero Mean Seasonal Model 207 Exercises 211 CHAPTER 10 Intervention Analysis and Outlier Detection Intervention Models Examples of Intervention Analysis Time Series Outliers Additive and Innovational Outliers Estimation of the Outlier Effect When the Timing of the Outlier Is Known Detection of Outliers Using an Iterative Procedure Examples of Outlier Analysis Model Identification in the Presence of Outliers 230 Exercises 235 CHAPTER 11 Fourier Analysis General Concepts Orthogonal Functions Fourier Representation of Finite Sequences Fourier Representation of Periodic Sequences Fourier Representation of Nonperiodic Sequences: The Discrete-Time Fourier Transform Fourier Representation of Continuous-Time Functions Fourier Representation of Periodic Functions Fourier Representation of Nonperiodic Functions: The Continuous-Time Fourier Transform The Fast Fourier Transform 258 Exercises 261 CHAPTER 12 Spectral Theory of Stationary Processes The Spectrum The Spectrum and Its Properties The Spectral Representation of Autocovariance Functions: The Spectral Distribution Function Wold's Decomposition of a Stationary Process The Spectral Representation of Stationary Processes 272
6 xiii 12.2 The Spectrum of Some Common Processes The Spectrum and the Autocovariance Generating Function The Spectrum of ARMA Models The Spectrum of the Sum of Two Independent Processes The Spectrum of Seasonal Models The Spectrum of Linear Filters The Filter Function Effect of Moving Average Effect of Differencing Aliasing 285 Exercises 286 CHAPTER 13 Estimation of the Spectrum Periodogram Analysis The Periodogram Sampling Properties of the Periodogram Tests for Hidden Periodic Components The Sample Spectrum The Smoothed Spectrum Smoothing in the Frequency Domain: The Spectral Window Smoothing in the Time Domain: The Lag Window Some Commonly Used Windows Approximate Confidence Intervals for Spectral Ordinates ARMA Spectral Estimation 318 Exercises 321 CHAPTER 14 Transfer Function Models Single-Input Transfer Function Models General Concepts Some Typical Impulse Response Functions The Cross-Correlation Function and Transfer Function Models The Cross-Correlation Function (CCF) The Relationship between the Cross-Correlation Function and the Transfer Function Construction of Transfer Function Models Sample Cross-Correlation Function Identification of Transfer Function Models Estimation of Transfer Function Models 332
7 xiv Contents Diagnostic Checking of Transfer Function Models An Empirical Example Forecasting Using Transfer Function Models Minimum Mean Square Error Forecasts for Stationary Input and Output Scries Minimum Mean Square Error Forecasts for Nonstationary Input and Output Series An Example Bivariate Frequency-Domain Analysis Cross-Covariance Generating Functions and the Cross-Spectrum Interpretation of the Cross-Spectral Functions Examples Estimation of the Cross-Spectrum The Cross-Spectrum and Transfer Function Models Construction of Transfer Function Models through Cross-Spectrum Analysis Cross-Spectral Functions of Transfer Function Models Multiple-Input Transfer Function Models 361 Exercises 363 CHAPTER 15 Time Series Regression and GARCH Models Regression with Autocorrelated Errors ARCH and GARCH Models Estimation of GARCH Models Maximum Likelihood Estimation Iterative Estimation Computation of Forecast Error Variance Illustrative Examples 376 Exercises 380 CHAPTER 16 Vector Time Series Models Covariance and Correlation Matrix Functions Moving Average and Autoregressive Representations of Vector Processes The Vector Autoregressive Moving Average Process Covariance Matrix Function for the Vector AR(1) Model Vector AR(p) Models Vector MA(1) Models Vector MA(q) Models Vector ARMA( 1, 1) Models 398
8 xv 16.4 Nonstationary Vector Auloregressive Moving Average Models Identification of Vector Time Series Models Sample Correlation Matrix Function 401 [ Partial Autoregression Matrices Partial Lag Correlation Matrix Function 408 j 16.6 Model Fitting and Forecasting 414 i 16.7 An Empirical Example 416 [ Model Identification Parameter Estimation Diagnostic Checking Forecasting Further Remarks Spectral Properties of Vector Processes 421 Supplement 16.A Multivariate Linear Regression Models 423 Exercises 426 CHAPTER 17 More on Vector Time Series Unit Roots and Cointegration in Vector Processes Representations of Nonstationary Cointegrated Processes Decomposition of Z, Testing and Estimating Cointegration Partial Process and Partial Process Correlation Matrices Covariance Matrix Generating Function Partial Covariance Matrix Generating Function Partial Process Sample Correlation Matrix Functions An Empirical Example: The U.S. Hog Data Equivalent Representations of a Vector ARMA Model Finite-Order Representations of a Vector Time Series Process Some Implications 457 Exercises 460 CHAPTER 18 State Space Models and the Kalman Filter State Space Representation The Relationship between State Space and ARMA Models State Space Model Fitting and Canonical Correlation Analysis Empirical Examples The Kalman Filter and Its Applications 478 Supplement 18.A Canonical Correlations 483 Exercises 487
9 xvi Contents CHAPTER 19 Long Memory and Nonlinear Processes Long Memory Processes and Fractional Differencing Fractionally Integrated ARMA Models and Their ACF Practical Implications of the ARFIMA Processes Estimation of the Fractional Difference Nonlinear Processes Cumulants, Polyspectrum, and Tests for Linearity and Normality Some Nonlinear Time Series Models Threshold Autoregressive Models Tests for TAR Models Modeling TAR Models 502 Exercises 506 CHAPTER 20 Aggregation and Systematic Sampling in Time Series Temporal Aggregation of the ARIMA Process The Relationship of Autocovariances between the Nonaggregate and Aggregate Series Temporal Aggregation of the IMA(J, q) Process Temporal Aggregation of the AR(p) Process Temporal Aggregation of the ARIMA(p, d, q) Process The Limiting Behavior of Time Series Aggregates The Effects of Aggregation on Forecasting and Parameter Estimation Hilbert Space The Application of Hilbert Space in Forecasting The Effect of Temporal Aggregation on Forecasting Information Loss Due to Aggregation in Parameter Estimation Systematic Sampling of the ARIMA Process The Effects of Systematic Sampling and Temporal Aggregation on Causality Decomposition of Linear Relationship between Two Time Series An Illustrative Underlying Model The Effects of Systematic Sampling and Temporal Aggregation on Causality The Effects of Aggregation on Testing for Linearity and Normality Testing for Linearity and Normality The Effects of Temporal Aggregation on Testing for Linearity and Normality 537
10 xvii 20.6 The Effects of Aggregation on Testing for a Unit Root The Model of Aggregate Scries The Effects of Aggregation on the Distribution of the Test Statistics The Effects of Aggregation on the Significance Level and the Power of the Test Examples General Cases and Concluding Remarks Further Comments 549 Exercises 550 References 553 Appendix 565 Time Series Data Used for Illustrations 565 Statistical Tables 565 Author Index 601 Subject Index 605
Software Review: ITSM 2000 Professional Version 6.0.
Lee, J. & Strazicich, M.C. (2002). Software Review: ITSM 2000 Professional Version 6.0. International Journal of Forecasting, 18(3): 455-459 (June 2002). Published by Elsevier (ISSN: 0169-2070). http://0-
More informationQUANTITATIVE METHODS. for Decision Makers. Mik Wisniewski. Fifth Edition. FT Prentice Hall
Fifth Edition QUANTITATIVE METHODS for Decision Makers Mik Wisniewski Senior Research Fellow, Department of Management Science, University of Strathclyde Business School FT Prentice Hall FINANCIAL TIMES
More informationSome useful concepts in univariate time series analysis
Some useful concepts in univariate time series analysis Autoregressive moving average models Autocorrelation functions Model Estimation Diagnostic measure Model selection Forecasting Assumptions: 1. Non-seasonal
More informationRob J Hyndman. Forecasting using. 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1
Rob J Hyndman Forecasting using 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1 Outline 1 Regression with ARIMA errors 2 Example: Japanese cars 3 Using Fourier terms for seasonality 4
More informationAdvanced Signal Processing and Digital Noise Reduction
Advanced Signal Processing and Digital Noise Reduction Saeed V. Vaseghi Queen's University of Belfast UK WILEY HTEUBNER A Partnership between John Wiley & Sons and B. G. Teubner Publishers Chichester New
More informationApplied Regression Analysis and Other Multivariable Methods
THIRD EDITION Applied Regression Analysis and Other Multivariable Methods David G. Kleinbaum Emory University Lawrence L. Kupper University of North Carolina, Chapel Hill Keith E. Muller University of
More informationITSM-R Reference Manual
ITSM-R Reference Manual George Weigt June 5, 2015 1 Contents 1 Introduction 3 1.1 Time series analysis in a nutshell............................... 3 1.2 White Noise Variance.....................................
More informationTime Series Analysis
JUNE 2012 Time Series Analysis CONTENT A time series is a chronological sequence of observations on a particular variable. Usually the observations are taken at regular intervals (days, months, years),
More informationLecture 2: ARMA(p,q) models (part 3)
Lecture 2: ARMA(p,q) models (part 3) Florian Pelgrin University of Lausanne, École des HEC Department of mathematics (IMEA-Nice) Sept. 2011 - Jan. 2012 Florian Pelgrin (HEC) Univariate time series Sept.
More informationTime Series Analysis in Economics. Klaus Neusser
Time Series Analysis in Economics Klaus Neusser May 26, 2015 Contents I Univariate Time Series Analysis 3 1 Introduction 1 1.1 Some examples.......................... 2 1.2 Formal definitions.........................
More informationChapter 10 Introduction to Time Series Analysis
Chapter 1 Introduction to Time Series Analysis A time series is a collection of observations made sequentially in time. Examples are daily mortality counts, particulate air pollution measurements, and
More informationTime Series - ARIMA Models. Instructor: G. William Schwert
APS 425 Fall 25 Time Series : ARIMA Models Instructor: G. William Schwert 585-275-247 schwert@schwert.ssb.rochester.edu Topics Typical time series plot Pattern recognition in auto and partial autocorrelations
More informationTime Series Analysis of Aviation Data
Time Series Analysis of Aviation Data Dr. Richard Xie February, 2012 What is a Time Series A time series is a sequence of observations in chorological order, such as Daily closing price of stock MSFT in
More informationState Space Time Series Analysis
State Space Time Series Analysis p. 1 State Space Time Series Analysis Siem Jan Koopman http://staff.feweb.vu.nl/koopman Department of Econometrics VU University Amsterdam Tinbergen Institute 2011 State
More informationNAG C Library Chapter Introduction. g13 Time Series Analysis
g13 Time Series Analysis Introduction g13 NAG C Library Chapter Introduction g13 Time Series Analysis Contents 1 Scope of the Chapter... 3 2 Background to the Problems... 3 2.1 Univariate Analysis... 3
More informationAnalysis of algorithms of time series analysis for forecasting sales
SAINT-PETERSBURG STATE UNIVERSITY Mathematics & Mechanics Faculty Chair of Analytical Information Systems Garipov Emil Analysis of algorithms of time series analysis for forecasting sales Course Work Scientific
More informationUnivariate Time Series Analysis; ARIMA Models
Econometrics 2 Spring 25 Univariate Time Series Analysis; ARIMA Models Heino Bohn Nielsen of4 Outline of the Lecture () Introduction to univariate time series analysis. (2) Stationarity. (3) Characterizing
More informationSales forecasting # 2
Sales forecasting # 2 Arthur Charpentier arthur.charpentier@univ-rennes1.fr 1 Agenda Qualitative and quantitative methods, a very general introduction Series decomposition Short versus long term forecasting
More informationTime Series Analysis
Time Series 1 April 9, 2013 Time Series Analysis This chapter presents an introduction to the branch of statistics known as time series analysis. Often the data we collect in environmental studies is collected
More informationIntroduction to Time Series Analysis and Forecasting. 2nd Edition. Wiley Series in Probability and Statistics
Brochure More information from http://www.researchandmarkets.com/reports/3024948/ Introduction to Time Series Analysis and Forecasting. 2nd Edition. Wiley Series in Probability and Statistics Description:
More information1 Short Introduction to Time Series
ECONOMICS 7344, Spring 202 Bent E. Sørensen January 24, 202 Short Introduction to Time Series A time series is a collection of stochastic variables x,.., x t,.., x T indexed by an integer value t. The
More informationAnalysis of Financial Time Series
Analysis of Financial Time Series Analysis of Financial Time Series Financial Econometrics RUEY S. TSAY University of Chicago A Wiley-Interscience Publication JOHN WILEY & SONS, INC. This book is printed
More informationFinancial Statement Analysis
Financial Statement Analysis Valuation Credit analysis Executive compensation Christian V. Petersen and Thomas Plenborg Financial Times Prentice Hall is an imprint of Harlow, England London New York Boston
More informationTime Series Analysis
Time Series Analysis Identifying possible ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos
More informationTIME SERIES ANALYSIS
TIME SERIES ANALYSIS L.M. BHAR AND V.K.SHARMA Indian Agricultural Statistics Research Institute Library Avenue, New Delhi-0 02 lmb@iasri.res.in. Introduction Time series (TS) data refers to observations
More informationInternational Investments
2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. International Investments Bruno Solnik H.E.C. SCHOOL of MANAGEMENT
More informationTime Series Analysis
Time Series Analysis Forecasting with ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos (UC3M-UPM)
More informationHow To Model A Series With Sas
Chapter 7 Chapter Table of Contents OVERVIEW...193 GETTING STARTED...194 TheThreeStagesofARIMAModeling...194 IdentificationStage...194 Estimation and Diagnostic Checking Stage...... 200 Forecasting Stage...205
More informationTime Series Analysis 1. Lecture 8: Time Series Analysis. Time Series Analysis MIT 18.S096. Dr. Kempthorne. Fall 2013 MIT 18.S096
Lecture 8: Time Series Analysis MIT 18.S096 Dr. Kempthorne Fall 2013 MIT 18.S096 Time Series Analysis 1 Outline Time Series Analysis 1 Time Series Analysis MIT 18.S096 Time Series Analysis 2 A stochastic
More informationForecasting model of electricity demand in the Nordic countries. Tone Pedersen
Forecasting model of electricity demand in the Nordic countries Tone Pedersen 3/19/2014 Abstract A model implemented in order to describe the electricity demand on hourly basis for the Nordic countries.
More informationTIME SERIES ANALYSIS
TIME SERIES ANALYSIS Ramasubramanian V. I.A.S.R.I., Library Avenue, New Delhi- 110 012 ram_stat@yahoo.co.in 1. Introduction A Time Series (TS) is a sequence of observations ordered in time. Mostly these
More informationStudying Achievement
Journal of Business and Economics, ISSN 2155-7950, USA November 2014, Volume 5, No. 11, pp. 2052-2056 DOI: 10.15341/jbe(2155-7950)/11.05.2014/009 Academic Star Publishing Company, 2014 http://www.academicstar.us
More informationTime Series Analysis
Time Series Analysis Autoregressive, MA and ARMA processes Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 212 Alonso and García-Martos
More informationIntroduction to Time Series Analysis. Lecture 1.
Introduction to Time Series Analysis. Lecture 1. Peter Bartlett 1. Organizational issues. 2. Objectives of time series analysis. Examples. 3. Overview of the course. 4. Time series models. 5. Time series
More informationPromotional Forecast Demonstration
Exhibit 2: Promotional Forecast Demonstration Consider the problem of forecasting for a proposed promotion that will start in December 1997 and continues beyond the forecast horizon. Assume that the promotion
More informationGraphical Tools for Exploring and Analyzing Data From ARIMA Time Series Models
Graphical Tools for Exploring and Analyzing Data From ARIMA Time Series Models William Q. Meeker Department of Statistics Iowa State University Ames, IA 50011 January 13, 2001 Abstract S-plus is a highly
More informationADVANCED FORECASTING MODELS USING SAS SOFTWARE
ADVANCED FORECASTING MODELS USING SAS SOFTWARE Girish Kumar Jha IARI, Pusa, New Delhi 110 012 gjha_eco@iari.res.in 1. Transfer Function Model Univariate ARIMA models are useful for analysis and forecasting
More informationMATHEMATICAL METHODS OF STATISTICS
MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS
More informationIntroduction to Financial Models for Management and Planning
CHAPMAN &HALL/CRC FINANCE SERIES Introduction to Financial Models for Management and Planning James R. Morris University of Colorado, Denver U. S. A. John P. Daley University of Colorado, Denver U. S.
More informationApplied Multiple Regression/Correlation Analysis for the Behavioral Sciences
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences Third Edition Jacob Cohen (deceased) New York University Patricia Cohen New York State Psychiatric Institute and Columbia University
More informationLuciano Rispoli Department of Economics, Mathematics and Statistics Birkbeck College (University of London)
Luciano Rispoli Department of Economics, Mathematics and Statistics Birkbeck College (University of London) 1 Forecasting: definition Forecasting is the process of making statements about events whose
More informationAdvanced Forecasting Techniques and Models: ARIMA
Advanced Forecasting Techniques and Models: ARIMA Short Examples Series using Risk Simulator For more information please visit: www.realoptionsvaluation.com or contact us at: admin@realoptionsvaluation.com
More informationEnergy Load Mining Using Univariate Time Series Analysis
Energy Load Mining Using Univariate Time Series Analysis By: Taghreed Alghamdi & Ali Almadan 03/02/2015 Caruth Hall 0184 Energy Forecasting Energy Saving Energy consumption Introduction: Energy consumption.
More informationAnalysis and Computation for Finance Time Series - An Introduction
ECMM703 Analysis and Computation for Finance Time Series - An Introduction Alejandra González Harrison 161 Email: mag208@exeter.ac.uk Time Series - An Introduction A time series is a sequence of observations
More informationChapter 6: Multivariate Cointegration Analysis
Chapter 6: Multivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie VI. Multivariate Cointegration
More informationARMA, GARCH and Related Option Pricing Method
ARMA, GARCH and Related Option Pricing Method Author: Yiyang Yang Advisor: Pr. Xiaolin Li, Pr. Zari Rachev Department of Applied Mathematics and Statistics State University of New York at Stony Brook September
More informationTime Series Analysis
Time Series Analysis hm@imm.dtu.dk Informatics and Mathematical Modelling Technical University of Denmark DK-2800 Kgs. Lyngby 1 Outline of the lecture Identification of univariate time series models, cont.:
More informationChapter 9: Univariate Time Series Analysis
Chapter 9: Univariate Time Series Analysis In the last chapter we discussed models with only lags of explanatory variables. These can be misleading if: 1. The dependent variable Y t depends on lags of
More informationFORECASTING AND TIME SERIES ANALYSIS USING THE SCA STATISTICAL SYSTEM
FORECASTING AND TIME SERIES ANALYSIS USING THE SCA STATISTICAL SYSTEM VOLUME 2 Expert System Capabilities for Time Series Modeling Simultaneous Transfer Function Modeling Vector Modeling by Lon-Mu Liu
More informationA FULLY INTEGRATED ENVIRONMENT FOR TIME-DEPENDENT DATA ANALYSIS
A FULLY INTEGRATED ENVIRONMENT FOR TIME-DEPENDENT DATA ANALYSIS Version 1.4 July 2007 First edition Intended for use with Mathematica 6 or higher Software and manual: Yu He, John Novak, Darren Glosemeyer
More informationThreshold Autoregressive Models in Finance: A Comparative Approach
University of Wollongong Research Online Applied Statistics Education and Research Collaboration (ASEARC) - Conference Papers Faculty of Informatics 2011 Threshold Autoregressive Models in Finance: A Comparative
More informationChapter 4: Vector Autoregressive Models
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
More informationHow To Understand The Theory Of Probability
Graduate Programs in Statistics Course Titles STAT 100 CALCULUS AND MATR IX ALGEBRA FOR STATISTICS. Differential and integral calculus; infinite series; matrix algebra STAT 195 INTRODUCTION TO MATHEMATICAL
More informationDiscrete Time Series Analysis with ARMA Models
Discrete Time Series Analysis with ARMA Models Veronica Sitsofe Ahiati (veronica@aims.ac.za) African Institute for Mathematical Sciences (AIMS) Supervised by Tina Marquardt Munich University of Technology,
More informationIntroduction to Time Series and Forecasting, Second Edition
Introduction to Time Series and Forecasting, Second Edition Peter J. Brockwell Richard A. Davis Springer Springer Texts in Statistics Advisors: George Casella Stephen Fienberg Ingram Olkin Springer New
More information9th Russian Summer School in Information Retrieval Big Data Analytics with R
9th Russian Summer School in Information Retrieval Big Data Analytics with R Introduction to Time Series with R A. Karakitsiou A. Migdalas Industrial Logistics, ETS Institute Luleå University of Technology
More informationTime Series Analysis: Basic Forecasting.
Time Series Analysis: Basic Forecasting. As published in Benchmarks RSS Matters, April 2015 http://web3.unt.edu/benchmarks/issues/2015/04/rss-matters Jon Starkweather, PhD 1 Jon Starkweather, PhD jonathan.starkweather@unt.edu
More informationProbability and Random Variables. Generation of random variables (r.v.)
Probability and Random Variables Method for generating random variables with a specified probability distribution function. Gaussian And Markov Processes Characterization of Stationary Random Process Linearly
More informationVector Time Series Model Representations and Analysis with XploRe
0-1 Vector Time Series Model Representations and Analysis with plore Julius Mungo CASE - Center for Applied Statistics and Economics Humboldt-Universität zu Berlin mungo@wiwi.hu-berlin.de plore MulTi Motivation
More informationChapter 5. Analysis of Multiple Time Series. 5.1 Vector Autoregressions
Chapter 5 Analysis of Multiple Time Series Note: The primary references for these notes are chapters 5 and 6 in Enders (2004). An alternative, but more technical treatment can be found in chapters 10-11
More informationTraffic Safety Facts. Research Note. Time Series Analysis and Forecast of Crash Fatalities during Six Holiday Periods Cejun Liu* and Chou-Lin Chen
Traffic Safety Facts Research Note March 2004 DOT HS 809 718 Time Series Analysis and Forecast of Crash Fatalities during Six Holiday Periods Cejun Liu* and Chou-Lin Chen Summary This research note uses
More informationUnivariate Time Series Analysis; ARIMA Models
Econometrics 2 Fall 25 Univariate Time Series Analysis; ARIMA Models Heino Bohn Nielsen of4 Univariate Time Series Analysis We consider a single time series, y,y 2,..., y T. We want to construct simple
More informationForecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA
Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA Abstract Virtually all businesses collect and use data that are associated with geographic locations, whether
More informationUsing JMP Version 4 for Time Series Analysis Bill Gjertsen, SAS, Cary, NC
Using JMP Version 4 for Time Series Analysis Bill Gjertsen, SAS, Cary, NC Abstract Three examples of time series will be illustrated. One is the classical airline passenger demand data with definite seasonal
More informationEMPIRICAL INVESTIGATION AND MODELING OF THE RELATIONSHIP BETWEEN GAS PRICE AND CRUDE OIL AND ELECTRICITY PRICES
Page 119 EMPIRICAL INVESTIGATION AND MODELING OF THE RELATIONSHIP BETWEEN GAS PRICE AND CRUDE OIL AND ELECTRICITY PRICES Morsheda Hassan, Wiley College Raja Nassar, Louisiana Tech University ABSTRACT Crude
More informationCOMP6053 lecture: Time series analysis, autocorrelation. jn2@ecs.soton.ac.uk
COMP6053 lecture: Time series analysis, autocorrelation jn2@ecs.soton.ac.uk Time series analysis The basic idea of time series analysis is simple: given an observed sequence, how can we build a model that
More informationHow To Understand Multivariate Models
Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction 1 1.1 Overview 1 1.2 Multivariate Models
More informationImpulse Response Functions
Impulse Response Functions Wouter J. Den Haan University of Amsterdam April 28, 2011 General definition IRFs The IRF gives the j th -period response when the system is shocked by a one-standard-deviation
More informationPITFALLS IN TIME SERIES ANALYSIS. Cliff Hurvich Stern School, NYU
PITFALLS IN TIME SERIES ANALYSIS Cliff Hurvich Stern School, NYU The t -Test If x 1,..., x n are independent and identically distributed with mean 0, and n is not too small, then t = x 0 s n has a standard
More informationAPPLICATION OF THE VARMA MODEL FOR SALES FORECAST: CASE OF URMIA GRAY CEMENT FACTORY
APPLICATION OF THE VARMA MODEL FOR SALES FORECAST: CASE OF URMIA GRAY CEMENT FACTORY DOI: 10.2478/tjeb-2014-0005 Ramin Bashir KHODAPARASTI 1 Samad MOSLEHI 2 To forecast sales as reliably as possible is
More informationIBM SPSS Forecasting 22
IBM SPSS Forecasting 22 Note Before using this information and the product it supports, read the information in Notices on page 33. Product Information This edition applies to version 22, release 0, modification
More informationLecture 4: Seasonal Time Series, Trend Analysis & Component Model Bus 41910, Time Series Analysis, Mr. R. Tsay
Lecture 4: Seasonal Time Series, Trend Analysis & Component Model Bus 41910, Time Series Analysis, Mr. R. Tsay Business cycle plays an important role in economics. In time series analysis, business cycle
More informationIBM SPSS Forecasting 21
IBM SPSS Forecasting 21 Note: Before using this information and the product it supports, read the general information under Notices on p. 107. This edition applies to IBM SPSS Statistics 21 and to all
More information11. Time series and dynamic linear models
11. Time series and dynamic linear models Objective To introduce the Bayesian approach to the modeling and forecasting of time series. Recommended reading West, M. and Harrison, J. (1997). models, (2 nd
More informationI. Introduction. II. Background. KEY WORDS: Time series forecasting, Structural Models, CPS
Predicting the National Unemployment Rate that the "Old" CPS Would Have Produced Richard Tiller and Michael Welch, Bureau of Labor Statistics Richard Tiller, Bureau of Labor Statistics, Room 4985, 2 Mass.
More informationPublic Relations in Schools
Public Relations in Schools Fifth Edition Theodore J. Kowalski University of Dayton Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan
More informationMultivariate Statistical Inference and Applications
Multivariate Statistical Inference and Applications ALVIN C. RENCHER Department of Statistics Brigham Young University A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim
More informationContents. List of Figures. List of Tables. List of Examples. Preface to Volume IV
Contents List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.1 Value at Risk and Other Risk Metrics 1 IV.1.1 Introduction 1 IV.1.2 An Overview of Market
More informationPractical. I conometrics. data collection, analysis, and application. Christiana E. Hilmer. Michael J. Hilmer San Diego State University
Practical I conometrics data collection, analysis, and application Christiana E. Hilmer Michael J. Hilmer San Diego State University Mi Table of Contents PART ONE THE BASICS 1 Chapter 1 An Introduction
More informationRelationship marketing
Relationship marketing WBIbliothek Exploring relational strategies in marketing FOURTH EDITION JOHN EGAN London South Bank University Financial Times Prentice Hall is an imprint of Harlow, England London
More informationUSE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY
Paper PO10 USE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY Beatrice Ugiliweneza, University of Louisville, Louisville, KY ABSTRACT Objectives: To forecast the sales made by
More information3.1 Stationary Processes and Mean Reversion
3. Univariate Time Series Models 3.1 Stationary Processes and Mean Reversion Definition 3.1: A time series y t, t = 1,..., T is called (covariance) stationary if (1) E[y t ] = µ, for all t Cov[y t, y t
More informationTHE SVM APPROACH FOR BOX JENKINS MODELS
REVSTAT Statistical Journal Volume 7, Number 1, April 2009, 23 36 THE SVM APPROACH FOR BOX JENKINS MODELS Authors: Saeid Amiri Dep. of Energy and Technology, Swedish Univ. of Agriculture Sciences, P.O.Box
More informationForecasting methods applied to engineering management
Forecasting methods applied to engineering management Áron Szász-Gábor Abstract. This paper presents arguments for the usefulness of a simple forecasting application package for sustaining operational
More informationPromotional Analysis and Forecasting for Demand Planning: A Practical Time Series Approach Michael Leonard, SAS Institute Inc.
Promotional Analysis and Forecasting for Demand Planning: A Practical Time Series Approach Michael Leonard, SAS Institute Inc. Cary, NC, USA Abstract Many businesses use sales promotions to increase the
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationMIKE COHN. Software Development Using Scrum. VAddison-Wesley. Upper Saddle River, NJ Boston Indianapolis San Francisco
Software Development Using Scrum MIKE COHN VAddison-Wesley Upper Saddle River, NJ Boston Indianapolis San Francisco New York Toronto Montreal London Munich Paris Madrid Cape Town Sydney Tokyo Singapore
More informationFinancial TIme Series Analysis: Part II
Department of Mathematics and Statistics, University of Vaasa, Finland January 29 February 13, 2015 Feb 14, 2015 1 Univariate linear stochastic models: further topics Unobserved component model Signal
More informationSilvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com
SPSS-SA Silvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com SPSS-SA Training Brochure 2009 TABLE OF CONTENTS 1 SPSS TRAINING COURSES FOCUSING
More informationEmpirical Model-Building and Response Surfaces
Empirical Model-Building and Response Surfaces GEORGE E. P. BOX NORMAN R. DRAPER Technische Universitat Darmstadt FACHBEREICH INFORMATIK BIBLIOTHEK Invortar-Nf.-. Sachgsbiete: Standort: New York John Wiley
More informationEstimating an ARMA Process
Statistics 910, #12 1 Overview Estimating an ARMA Process 1. Main ideas 2. Fitting autoregressions 3. Fitting with moving average components 4. Standard errors 5. Examples 6. Appendix: Simple estimators
More informationNumerical Methods for Engineers
Steven C. Chapra Berger Chair in Computing and Engineering Tufts University RaymondP. Canale Professor Emeritus of Civil Engineering University of Michigan Numerical Methods for Engineers With Software
More informationMGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal
MGT 267 PROJECT Forecasting the United States Retail Sales of the Pharmacies and Drug Stores Done by: Shunwei Wang & Mohammad Zainal Dec. 2002 The retail sale (Million) ABSTRACT The present study aims
More informationWinning the Hardware-Software Game
Winning the Hardware-Software Game Using Game Theory to Optimize the Pace of New Technology Adoption Ruth D. Fisher PRENTICE Upper Saddle River, NJ Boston Indianapolis San Francisco New York Toronto Montreal
More informationLectures in Modern Economic Time Series Analysis. 2 ed. c. Linköping, Sweden email:bo.sjo@liu.se
Lectures in Modern Economic Time Series Analysis. 2 ed. c Bo Sjö Linköping, Sweden email:bo.sjo@liu.se October 30, 2011 2 CONTENTS 1 Introduction 7 1.1 Outline of this Book/Text/Course/Workshop............
More information