Some useful concepts in univariate time series analysis

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Some useful concepts in univariate time series analysis"

Transcription

1 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 2. Linear 3. Non-trending 4. Constant variance 1

2 White Noise: Lag operator: Autoregressive (AR) model AR(p) Model: 2

3 Example: Example: AR(1) Model 3

4 1. If the parameters converges to zero and 2. If, the time series is explosives. 3. If, random walk. Artificial Data in Figure 3.1: numbers are generated from independent standard normal distributions 2. Replace the 100 th observation by 3. y 1 is set to zero 4. The other 199 observations are generated by where t=2,,200 and. 4

5 In this chapter, we consider the shocks have only transitory effects, i.e. <1 in the above case. 2. When a series display permanent effects of shocks, the series is usually transformed to a series with transitory effects by taking first differences of the series. 5

6 Moving average (MA) model MA(q) Model: or with Remark: Since the explanatory variables are Unobserved, it may cause estimation problem if q is big. Empirically, we usually set q=1 or 2. Roots of If at least one root is on or inside the unit circle, the MA(q) model is not invertible. If all roots are outside the unit circle, the MA(q) model is invertible. 6

7 Example: MA(1) Model 1.The impact of the values of the MA parameter is less clear-cut as in case of AR models. 2. Large shocks do not tend to change the direction of the time series. Non-invertible Invertible 7

8 Autoregressive moving average (ARMA) model ARMA(p,q) where How to choose the order p and q in ARMA model? Two tools that are useful to characterize ARMA model: Autocorrelations (ACF) Partical autocorrelations (PACF) 8

9 Autocorrelation function The autocorrelation function (ACF) of a time series y t is defined by where AR(1): AR(2): See Figure 3.3, 3.4, 3.5, and 3.6 9

10 10

11 11

12 ACF is not useful to identify the lag of AR model But, it is useful in MA(q) model MA(2): ARMA(p,q): the pattern of the ACF is a mixture of the ACF pattern for pure AR and MA models. ARMA(1,1) 12

13 Partical autocorrelation function The PACF value at lag 1, is given by The second PACF value regression results from the The third PACF value AR(1): = =0 AR(2): are not equal to zero, but AR(p): 13

14 Estimation of ACF and PACF ACF PACF (ACF) 14

15 Model estimation Start with an inspection of the ACF and EPACF, and decide the order or structure of ARMA models Investigate whether the residuals are approximately white noise 15

16 Estimation of AR models The choice of p is based on PACF values that are significant Estimate AR(p) by OLS AR(1) 16

17 Estimation of ARMA models Consider an ARMA(1,1) model z t = z t-1 then Given a value for, we can construct z t and estimate by OLS Diagnostic testing for residual autocorrelation The estimated residual time series is approximately white noise. If not, we may have missed some dynamic structure in y t. H 0 : All of the first m residual autocorrelation are significant ~ 2 (m-p-q) 17

18 LM test for residual autocorrelation H 0 : AR(p) H a : AR(p+r) or ARMA(p,r) (i) Estimate the model in H 0 (ii) Estimate the model where are the estimated residuals of model H 0 (iii) nr 2 ~ 2 (r) The F-version of the test, denoted F AC,1-r Diagnostic testing for normality of residuals H 0 : The residuals are normal distributed Where The Bera-Jarque test 18

19 Model selection min k is the number of parameter RSS is the residual sum of squares min 19

20 Forecasting Consider a MA(2) model Forecast error (Since ) Two step ahead forecast error Three step ahead forecast error 20

21 Consider an AR(2) model: 21

22 Comparing forecasts Check whether 95 percent of the forecasts indeed lie within the 95 percent interval (If not, the variance may be underestimate) The forecast error is about randomly positive or negative. (If not, the models underestimate or overestimate the conditional mean of the time series) Evaluation Mean square prediction error Mean absolute percentage error 22

23 Ho: the MSPEs of models A and B are the same Let d i =1 if MSPE Ai >MSPE Bi ; d i =0 otherwise The mean may not be well estimated 23

TIME SERIES ANALYSIS

TIME 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 information

Time Series Analysis

Time 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 information

Univariate Time Series Analysis; ARIMA Models

Univariate 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 information

Sales forecasting # 2

Sales 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 information

Univariate Time Series Analysis; ARIMA Models

Univariate 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 information

Time Series - ARIMA Models. Instructor: G. William Schwert

Time 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 information

Univariate and Multivariate Methods PEARSON. Addison Wesley

Univariate and Multivariate Methods PEARSON. Addison Wesley 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

More information

Analysis of algorithms of time series analysis for forecasting sales

Analysis 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 information

Luciano 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) 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 information

Time Series Laboratory

Time Series Laboratory Time Series Laboratory Computing in Weber Classrooms 205-206: To log in, make sure that the DOMAIN NAME is set to MATHSTAT. Use the workshop username: primesw The password will be distributed during the

More information

Time Series Analysis

Time 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 information

1 Short Introduction to Time Series

1 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 information

Lecture 2: ARMA(p,q) models (part 3)

Lecture 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 information

Forecasting model of electricity demand in the Nordic countries. Tone Pedersen

Forecasting 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 information

Time Series Analysis

Time 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 information

TIME SERIES ANALYSIS

TIME 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 information

Rob 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 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 information

Chapter 7 The ARIMA Procedure. Chapter Table of Contents

Chapter 7 The ARIMA Procedure. Chapter Table of Contents 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 information

Graphical Tools for Exploring and Analyzing Data From ARIMA Time Series Models

Graphical 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 information

Non-Stationary Time Series andunitroottests

Non-Stationary Time Series andunitroottests Econometrics 2 Fall 2005 Non-Stationary Time Series andunitroottests Heino Bohn Nielsen 1of25 Introduction Many economic time series are trending. Important to distinguish between two important cases:

More information

9th Russian Summer School in Information Retrieval Big Data Analytics with R

9th 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 information

Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model

Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model Tropical Agricultural Research Vol. 24 (): 2-3 (22) Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model V. Sivapathasundaram * and C. Bogahawatte Postgraduate Institute

More information

Analysis and Computation for Finance Time Series - An Introduction

Analysis 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 information

Time Series Analysis of Aviation Data

Time 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 information

Energy Load Mining Using Univariate Time Series Analysis

Energy 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 information

Readers will be provided a link to download the software and Excel files that are used in the book after payment. Please visit http://www.xlpert.

Readers will be provided a link to download the software and Excel files that are used in the book after payment. Please visit http://www.xlpert. Readers will be provided a link to download the software and Excel files that are used in the book after payment. Please visit http://www.xlpert.com for more information on the book. The Excel files are

More information

Lecture Notes on Univariate Time Series Analysis and Box Jenkins Forecasting John Frain Economic Analysis, Research and Publications April 1992 (reprinted with revisions) January 1999 Abstract These are

More information

USE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY

USE 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 information

Advanced Forecasting Techniques and Models: ARIMA

Advanced 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 information

MGT 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 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 information

COMP6053 lecture: Time series analysis, autocorrelation. jn2@ecs.soton.ac.uk

COMP6053 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 information

Booth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay. Solutions to Midterm

Booth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay. Solutions to Midterm Booth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (30 pts) Answer briefly the following questions. Each question has

More information

Time Series Analysis and Forecasting

Time Series Analysis and Forecasting Time Series Analysis and Forecasting Math 667 Al Nosedal Department of Mathematics Indiana University of Pennsylvania Time Series Analysis and Forecasting p. 1/11 Introduction Many decision-making applications

More information

ADVANCED FORECASTING MODELS USING SAS SOFTWARE

ADVANCED 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 information

Studying Achievement

Studying 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 information

Vector Time Series Model Representations and Analysis with XploRe

Vector 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 information

Discrete Time Series Analysis with ARMA Models

Discrete 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 information

Do Electricity Prices Reflect Economic Fundamentals?: Evidence from the California ISO

Do Electricity Prices Reflect Economic Fundamentals?: Evidence from the California ISO Do Electricity Prices Reflect Economic Fundamentals?: Evidence from the California ISO Kevin F. Forbes and Ernest M. Zampelli Department of Business and Economics The Center for the Study of Energy and

More information

ARMA, GARCH and Related Option Pricing Method

ARMA, 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 information

ITSM-R Reference Manual

ITSM-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 information

Time Series Analysis: Basic Forecasting.

Time 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 information

Integrated Resource Plan

Integrated Resource Plan Integrated Resource Plan March 19, 2004 PREPARED FOR KAUA I ISLAND UTILITY COOPERATIVE LCG Consulting 4962 El Camino Real, Suite 112 Los Altos, CA 94022 650-962-9670 1 IRP 1 ELECTRIC LOAD FORECASTING 1.1

More information

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4 4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

More information

The SAS Time Series Forecasting System

The SAS Time Series Forecasting System The SAS Time Series Forecasting System An Overview for Public Health Researchers Charles DiMaggio, PhD College of Physicians and Surgeons Departments of Anesthesiology and Epidemiology Columbia University

More information

Big Data Techniques Applied to Very Short-term Wind Power Forecasting

Big Data Techniques Applied to Very Short-term Wind Power Forecasting Big Data Techniques Applied to Very Short-term Wind Power Forecasting Ricardo Bessa Senior Researcher (ricardo.j.bessa@inesctec.pt) Center for Power and Energy Systems, INESC TEC, Portugal Joint work with

More information

Using 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 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 information

Time Series Analysis 1. Lecture 8: Time Series Analysis. Time Series Analysis MIT 18.S096. Dr. Kempthorne. Fall 2013 MIT 18.S096

Time 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 information

2.2 Elimination of Trend and Seasonality

2.2 Elimination of Trend and Seasonality 26 CHAPTER 2. TREND AND SEASONAL COMPONENTS 2.2 Elimination of Trend and Seasonality Here we assume that the TS model is additive and there exist both trend and seasonal components, that is X t = m t +

More information

I. Introduction. II. Background. KEY WORDS: Time series forecasting, Structural Models, CPS

I. 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 information

3.1 Stationary Processes and Mean Reversion

3.1 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 information

Time Series Analysis

Time 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 information

Time Series Analysis

Time 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 information

AR(p) + MA(q) = ARMA(p, q)

AR(p) + MA(q) = ARMA(p, q) AR(p) + MA(q) = ARMA(p, q) Outline 1 3.4: ARMA(p, q) Model 2 Homework 3a Arthur Berg AR(p) + MA(q) = ARMA(p, q) 2/ 12 ARMA(p, q) Model Definition (ARMA(p, q) Model) A time series is ARMA(p, q) if it is

More information

Univariate Regression

Univariate Regression Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

More information

APPLICATION 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 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 information

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More information

Lecture 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 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 information

Time Series Analysis in Economics. Klaus Neusser

Time 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 information

Agenda. Managing Uncertainty in the Supply Chain. The Economic Order Quantity. Classic inventory theory

Agenda. Managing Uncertainty in the Supply Chain. The Economic Order Quantity. Classic inventory theory Agenda Managing Uncertainty in the Supply Chain TIØ485 Produkjons- og nettverksøkonomi Lecture 3 Classic Inventory models Economic Order Quantity (aka Economic Lot Size) The (s,s) Inventory Policy Managing

More information

IBM SPSS Forecasting 22

IBM 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 information

Forecasting Using Eviews 2.0: An Overview

Forecasting Using Eviews 2.0: An Overview Forecasting Using Eviews 2.0: An Overview Some Preliminaries In what follows it will be useful to distinguish between ex post and ex ante forecasting. In terms of time series modeling, both predict values

More information

Predicting Indian GDP. And its relation with FMCG Sales

Predicting Indian GDP. And its relation with FMCG Sales Predicting Indian GDP And its relation with FMCG Sales GDP A Broad Measure of Economic Activity Definition The monetary value of all the finished goods and services produced within a country's borders

More information

Is the Basis of the Stock Index Futures Markets Nonlinear?

Is the Basis of the Stock Index Futures Markets Nonlinear? University of Wollongong Research Online Applied Statistics Education and Research Collaboration (ASEARC) - Conference Papers Faculty of Engineering and Information Sciences 2011 Is the Basis of the Stock

More information

Time Series Analysis

Time 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 information

Time Series Analysis and Forecasting Methods for Temporal Mining of Interlinked Documents

Time Series Analysis and Forecasting Methods for Temporal Mining of Interlinked Documents Time Series Analysis and Forecasting Methods for Temporal Mining of Interlinked Documents Prasanna Desikan and Jaideep Srivastava Department of Computer Science University of Minnesota. @cs.umn.edu

More information

Chapter 9: Univariate Time Series Analysis

Chapter 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 information

Forecasting of Economic Quantities using Fuzzy Autoregressive Model and Fuzzy Neural Network

Forecasting of Economic Quantities using Fuzzy Autoregressive Model and Fuzzy Neural Network Forecasting of Economic Quantities using Fuzzy Autoregressive Model and Fuzzy Neural Network Dušan Marček 1 Abstract Most models for the time series of stock prices have centered on autoregressive (AR)

More information

Software Review: ITSM 2000 Professional Version 6.0.

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 information

Wooldridge, Introductory Econometrics, 3d ed. Chapter 12: Serial correlation and heteroskedasticity in time series regressions

Wooldridge, Introductory Econometrics, 3d ed. Chapter 12: Serial correlation and heteroskedasticity in time series regressions Wooldridge, Introductory Econometrics, 3d ed. Chapter 12: Serial correlation and heteroskedasticity in time series regressions What will happen if we violate the assumption that the errors are not serially

More information

Chapter 4: Vector Autoregressive Models

Chapter 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 information

Threshold Autoregressive Models in Finance: A Comparative Approach

Threshold 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 information

Forecasting the US Dollar / Euro Exchange rate Using ARMA Models

Forecasting the US Dollar / Euro Exchange rate Using ARMA Models Forecasting the US Dollar / Euro Exchange rate Using ARMA Models LIUWEI (9906360) - 1 - ABSTRACT...3 1. INTRODUCTION...4 2. DATA ANALYSIS...5 2.1 Stationary estimation...5 2.2 Dickey-Fuller Test...6 3.

More information

IBM SPSS Forecasting 21

IBM 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 information

Time-Series Regression and Generalized Least Squares in R

Time-Series Regression and Generalized Least Squares in R Time-Series Regression and Generalized Least Squares in R An Appendix to An R Companion to Applied Regression, Second Edition John Fox & Sanford Weisberg last revision: 11 November 2010 Abstract Generalized

More information

State Space Time Series Analysis

State 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 information

Time Series in Mathematical Finance

Time Series in Mathematical Finance Instituto Superior Técnico (IST, Portugal) and CEMAT cnunes@math.ist.utl.pt European Summer School in Industrial Mathematics Universidad Carlos III de Madrid July 2013 Outline The objective of this short

More information

Causes of Inflation in the Iranian Economy

Causes of Inflation in the Iranian Economy Causes of Inflation in the Iranian Economy Hamed Armesh* and Abas Alavi Rad** It is clear that in the nearly last four decades inflation is one of the important problems of Iranian economy. In this study,

More information

Session 9 Case 3: Utilizing Available Software Statistical Analysis

Session 9 Case 3: Utilizing Available Software Statistical Analysis Session 9 Case 3: Utilizing Available Software Statistical Analysis Michelle Phillips Economist, PURC michelle.phillips@warrington.ufl.edu With material from Ted Kury Session Overview With Data from Cases

More information

Analysis of the Volatility of the Electricity Price in Kenya Using Autoregressive Integrated Moving Average Model

Analysis of the Volatility of the Electricity Price in Kenya Using Autoregressive Integrated Moving Average Model Science Journal of Applied Mathematics and Statistics 2015; 3(2): 47-57 Published online March 28, 2015 (http://www.sciencepublishinggroup.com/j/sjams) doi: 10.11648/j.sjams.20150302.14 ISSN: 2376-9491

More information

Introduction to Time Series Analysis. Lecture 6.

Introduction to Time Series Analysis. Lecture 6. Introduction to Time Series Analysis. Lecture 6. Peter Bartlett www.stat.berkeley.edu/ bartlett/courses/153-fall2010 Last lecture: 1. Causality 2. Invertibility 3. AR(p) models 4. ARMA(p,q) models 1 Introduction

More information

Traffic 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. 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 information

ECONOMETRIC MODELING VS ARTIFICIAL NEURAL

ECONOMETRIC MODELING VS ARTIFICIAL NEURAL ECONOMETRIC MODELING VS ARTIFICIAL NEURAL NETWORKS A SALES FORECASTING COMPARISON Master s (one year) thesis in Informatics (15 credits) Dinesh Bajracharya Autumn 2010:MI17 Title: Econometric Modeling

More information

Modeling and forecasting regional GDP in Sweden. using autoregressive models

Modeling and forecasting regional GDP in Sweden. using autoregressive models MASTER THESIS IN MICRODATA ANALYSIS Modeling and forecasting regional GDP in Sweden using autoregressive models Author: Haonan Zhang Supervisor: Niklas Rudholm 2013 Business Intelligence Program School

More information

Promotional Forecast Demonstration

Promotional 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 information

Time Series Analysis

Time Series Analysis Time Series Analysis Lecture Notes for 475.726 Ross Ihaka Statistics Department University of Auckland April 14, 2005 ii Contents 1 Introduction 1 1.1 Time Series.............................. 1 1.2 Stationarity

More information

PITFALLS IN TIME SERIES ANALYSIS. Cliff Hurvich Stern School, NYU

PITFALLS 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 information

Forecasting areas and production of rice in India using ARIMA model

Forecasting areas and production of rice in India using ARIMA model International Journal of Farm Sciences 4(1) :99-106, 2014 Forecasting areas and production of rice in India using ARIMA model K PRABAKARAN and C SIVAPRAGASAM* Agricultural College and Research Institute,

More information

Prediction of Stock Price usingautoregressiveintegrated Moving AverageFilter Arima P,D,Q

Prediction of Stock Price usingautoregressiveintegrated Moving AverageFilter Arima P,D,Q Global Journal of Science Frontier Research Mathematics and Decision Sciences Volume 13 Issue 8 Version 1.0 Year Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals

More information

Predictability of Non-Linear Trading Rules in the US Stock Market Chong & Lam 2010

Predictability of Non-Linear Trading Rules in the US Stock Market Chong & Lam 2010 Department of Mathematics QF505 Topics in quantitative finance Group Project Report Predictability of on-linear Trading Rules in the US Stock Market Chong & Lam 010 ame: Liu Min Qi Yichen Zhang Fengtian

More information

Application of ARIMA models in soybean series of prices in the north of Paraná

Application of ARIMA models in soybean series of prices in the north of Paraná 78 Application of ARIMA models in soybean series of prices in the north of Paraná Reception of originals: 09/24/2012 Release for publication: 10/26/2012 Israel José dos Santos Felipe Mestrando em Administração

More information

Financial Risk Management Exam Sample Questions/Answers

Financial Risk Management Exam Sample Questions/Answers Financial Risk Management Exam Sample Questions/Answers Prepared by Daniel HERLEMONT 1 2 3 4 5 6 Chapter 3 Fundamentals of Statistics FRM-99, Question 4 Random walk assumes that returns from one time period

More information

Multiple Linear Regression

Multiple Linear Regression Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is

More information

16 : Demand Forecasting

16 : Demand Forecasting 16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical

More information

Chapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem

Chapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become

More information

Promotional 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. 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 information

JOHANNES TSHEPISO TSOKU NONOFO PHOKONTSI DANIEL METSILENG FORECASTING SOUTH AFRICAN GOLD SALES: THE BOX-JENKINS METHODOLOGY

JOHANNES TSHEPISO TSOKU NONOFO PHOKONTSI DANIEL METSILENG FORECASTING SOUTH AFRICAN GOLD SALES: THE BOX-JENKINS METHODOLOGY DOI: 0.20472/IAC.205.08.3 JOHANNES TSHEPISO TSOKU North West University, South Africa NONOFO PHOKONTSI North West University, South Africa DANIEL METSILENG Department of Health, South Africa FORECASTING

More information

Forecasting Tourism Demand: Methods and Strategies. By D. C. Frechtling Oxford, UK: Butterworth Heinemann 2001

Forecasting Tourism Demand: Methods and Strategies. By D. C. Frechtling Oxford, UK: Butterworth Heinemann 2001 Forecasting Tourism Demand: Methods and Strategies By D. C. Frechtling Oxford, UK: Butterworth Heinemann 2001 Table of Contents List of Tables List of Figures Preface Acknowledgments i 1 Introduction 1

More information

Econometric Modelling for Revenue Projections

Econometric Modelling for Revenue Projections Econometric Modelling for Revenue Projections Annex E 1. An econometric modelling exercise has been undertaken to calibrate the quantitative relationship between the five major items of government revenue

More information

Turkey s Energy Demand

Turkey s Energy Demand Current Research Journal of Social Sciences 1(3): 123-128, 2009 ISSN: 2041-3246 Maxwell Scientific Organization, 2009 Submitted Date: September 28, 2009 Accepted Date: October 12, 2009 Published Date:

More information

In this paper we study how the time-series structure of the demand process affects the value of information

In this paper we study how the time-series structure of the demand process affects the value of information MANAGEMENT SCIENCE Vol. 51, No. 6, June 25, pp. 961 969 issn 25-199 eissn 1526-551 5 516 961 informs doi 1.1287/mnsc.15.385 25 INFORMS Information Sharing in a Supply Chain Under ARMA Demand Vishal Gaur

More information