# CHAPTER 9: SERIAL CORRELATION

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Serial correlation (or autocorrelation) is the violation of Assumption 4 (observations of the error term are uncorrelated with each other). Pure Serial Correlation This type of correlation tends to be seen in time series data. To denote a time series data set we will use a subscript. This type of serial correlation occurs when the error in one period is correlated with the errors in other periods. The model is assumed to be correctly specified. The most common form of serial correlation is called first-order serial correlation in which the error in time is related to the previous ( 1 period s error:, 1 1 The new parameter is called the first-order autocorrelation coefficient. The process for the error term is referred to as a first-order autoregressive process or AR(1). Page 1 of 19

2 The magnitude of tells us about the strength of the serial correlation and the sign indicates the nature of the serial correlation. 0 indicates no serial correlation 0 indicates positive serial correlation the error terms will tend to have the same sign from one period to the next Page 2 of 19

3 0 indicates negative serial correlation the error terms will tend to have a different sign from one period to the next Page 3 of 19

4 Impure Serial Correlation CHAPTER 9: SERIAL CORRELATION This type of serial correlation is caused by a specification error such as an omitted variable or ignoring nonlinearities. Suppose the true regression equation is given by but in our model we do not include. The error term will capture the effect of. Since many economic variables exhibit trends over time, is likely to depend on,,,,. This will translate into a seeming correlation between and,, and this serial correlation would violate Assumption 4. Page 4 of 19

5 Page 5 of 19

6 A specification error of the functional form can also cause this type of serial correlation. Suppose the true regression equation between Y and X is quadratic but we assume it s linear. The error term will depend on. Page 6 of 19

7 The Consequences of Serial Correlation CHAPTER 9: SERIAL CORRELATION 1. Pure serial correlation does not cause bias in the regression coefficient estimates. 2. Serial correlation causes OLS to no longer be a minimum variance estimator. 3. Serial correlation causes the estimated variances of the regression coefficients to be biased, leading to unreliable hypothesis testing. The t-statistics will actually appear to be more significant than they really are. Page 7 of 19

8 Testing for First-Order Serial Correlation Plotting the residuals is always a good first step. The most common formal test is the Durbin-Watson d test. The Durbin-Watson Test Consider the regression equation. We are interested in determining if there is first-order autocorrelation in the error term, where is not autocorrelated. Page 8 of 19

9 The test of the null hypothesis of no autocorrelation ( 0) is based on the Durbin- Watson statistic where the s are the residuals from the regression equation estimated by least squares. The value of this statistic is automatically reported in EViews regression output. Let s consider a few cases: Extreme positive correlation Extreme negative correlation No serial correlation Page 9 of 19

10 For an alternative of positive autocorrelation, : 0, look up the critical values in tables B-4, B-5 or B-6. The decision rule is as follows: Reject if. Do not reject if. Test inconclusive if. Page 10 of 19

11 Remedies for Serial Correlation 1. Cochrane-Orcutt Procedure Transform the equation with AR(1) error structure, into one that is not autocorrelated. Consider the same model in period 1: Multiply both sides of this equation by : Page 11 of 19

12 Subtract this equation from the original equation: If were known, we could use OLS to obtain estimates that are BLUE. Unfortunately is not known and therefore must be estimated. Page 12 of 19

13 Step 1: Compute the residuals from the OLS estimation of Step 2: Estimate the first-order serial correlation coefficient using. Call this estimate. Step 3: Transform the variables:,,, etc. Step 4: Regress on a constant,,,, and obtain the OLS estimates of the transformed equation. Step 5: Use these estimates to obtain a new set of estimates for the residual and then go back to Step 2. Step 6: This iterative procedure is stopped when the estimates of differ by no more than some pre-specified amount (eg ) in two successive iterations. Page 13 of 19

14 2. Newey-West Standard Errors CHAPTER 9: SERIAL CORRELATION Adjust the standard errors of the estimated regression coefficients but not the estimates themselves since they are still unbiased. Page 14 of 19

15 Example Let s examine the relationship between Microsoft s marketing and advertising expenditures and its revenues. revenues marketing REVENUES: Microsoft s revenues in millions of dollars MARKETING: Microsoft s expenditures on marketing and advertising in millions of dollars Data: real data from Microsoft s website for 1987 through to 1999 Dependent Variable: REVENUES Method: Least Squares Sample: 1 13 Included observations: 13 Variable Coefficient Std. Error t-statistic Prob. MARKETING C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Page 15 of 19

16 Plot of residuals against year. CHAPTER 9: SERIAL CORRELATION RESID Residual Actual Fitted YEAR Page 16 of 19

17 Page 17 of 19

18 Cochrane-Orcutt Procedure CHAPTER 9: SERIAL CORRELATION Dependent Variable: REVENUES Method: Least Squares Sample(adjusted): 2 13 Included observations: 12 after adjusting endpoints Convergence achieved after 52 iterations Variable Coefficient Std. Error t-statistic Prob. MARKETING C AR(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots.73 Page 18 of 19

19 Newey-West Standard Errors CHAPTER 9: SERIAL CORRELATION Dependent Variable: REVENUES Method: Least Squares Sample: 1 13 Included observations: 13 White Heteroskedasticity-Consistent Standard Errors & Covariance Variable Coefficient Std. Error t-statistic Prob. MARKETING C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Page 19 of 19

### 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.

### Chapter 12: Time Series Models

Chapter 12: Time Series Models In this chapter: 1. Estimating ad hoc distributed lag & Koyck distributed lag models (UE 12.1.3) 2. Testing for serial correlation in Koyck distributed lag models (UE 12.2.2)

### 2. Linear regression with multiple regressors

2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions

### 2. What are the theoretical and practical consequences of autocorrelation?

Lecture 10 Serial Correlation In this lecture, you will learn the following: 1. What is the nature of autocorrelation? 2. What are the theoretical and practical consequences of autocorrelation? 3. Since

### Eviews Tutorial. File New Workfile. Start observation End observation Annual

APS 425 Professor G. William Schwert Advanced Managerial Data Analysis CS3-110L, 585-275-2470 Fax: 585-461-5475 email: schwert@schwert.ssb.rochester.edu Eviews Tutorial 1. Creating a Workfile: First you

### 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

### CONSOLIDATED EDISON COMPANY OF NEW YORK, INC. VOLUME FORECASTING MODELS. Variable Coefficient Std. Error t-statistic Prob.

PAGE 1 OF 6 SC 1 (RESIDENTIAL AND RELIGIOUS) Dependent Variable: DLOG(GWH17/BDA0,0,4) Convergence achieved after 16 iterations MA Backcast: 1987Q2 C 0.011618 0.003667 3.168199 0.002100 DLOG(PRICE17S(-3),0,4)

### Chapter 5: Basic Statistics and Hypothesis Testing

Chapter 5: Basic Statistics and Hypothesis Testing In this chapter: 1. Viewing the t-value from an OLS regression (UE 5.2.1) 2. Calculating critical t-values and applying the decision rule (UE 5.2.2) 3.

### Air passenger departures forecast models A technical note

Ministry of Transport Air passenger departures forecast models A technical note By Haobo Wang Financial, Economic and Statistical Analysis Page 1 of 15 1. Introduction Sine 1999, the Ministry of Business,

### On the Degree of Openness of an Open Economy Carlos Alfredo Rodriguez, Universidad del CEMA Buenos Aires, Argentina

On the Degree of Openness of an Open Economy Carlos Alfredo Rodriguez, Universidad del CEMA Buenos Aires, Argentina car@cema.edu.ar www.cema.edu.ar\~car Version1-February 14,2000 All data can be consulted

### Competition as an Effective Tool in Developing Social Marketing Programs: Driving Behavior Change through Online Activities

Competition as an Effective Tool in Developing Social Marketing Programs: Driving Behavior Change through Online Activities Corina ŞERBAN 1 ABSTRACT Nowadays, social marketing practices represent an important

### The Impact of Privatization in Insurance Industry on Insurance Efficiency in Iran

The Impact of Privatization in Insurance Industry on Insurance Efficiency in Iran Shahram Gilaninia 1, Hosein Ganjinia, Azadeh Asadian 3 * 1. Department of Industrial Management, Islamic Azad University,

### Regression analysis in practice with GRETL

Regression analysis in practice with GRETL Prerequisites You will need the GNU econometrics software GRETL installed on your computer (http://gretl.sourceforge.net/), together with the sample files that

### IMPACT OF WORKING CAPITAL MANAGEMENT ON PROFITABILITY

IMPACT OF WORKING CAPITAL MANAGEMENT ON PROFITABILITY Hina Agha, Mba, Mphil Bahria University Karachi Campus, Pakistan Abstract The main purpose of this study is to empirically test the impact of working

### 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)

### 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

### MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

### UK GDP is the best predictor of UK GDP, literally.

UK GDP IS THE BEST PREDICTOR OF UK GDP, LITERALLY ERIK BRITTON AND DANNY GABAY 6 NOVEMBER 2009 UK GDP is the best predictor of UK GDP, literally. The ONS s preliminary estimate of UK GDP for the third

### Source engine marketing: A preliminary empirical analysis of web search data

Source engine marketing: A preliminary empirical analysis of web search data ABSTRACT Bruce Q. Budd Alfaisal University The purpose of this paper is to empirically investigate a website performance and

### Determinants of Stock Market Performance in Pakistan

Determinants of Stock Market Performance in Pakistan Mehwish Zafar Sr. Lecturer Bahria University, Karachi campus Abstract Stock market performance, economic and political condition of a country is interrelated

### Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?

Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing

### RELATIONSHIP BETWEEN STOCK MARKET VOLATILITY AND EXCHANGE RATE: A STUDY OF KSE

RELATIONSHIP BETWEEN STOCK MARKET VOLATILITY AND EXCHANGE RATE: A STUDY OF KSE Waseem ASLAM Department of Finance and Economics, Foundation University Rawalpindi, Pakistan seem_aslam@yahoo.com Abstract:

### The relationship between stock market parameters and interbank lending market: an empirical evidence

Magomet Yandiev Associate Professor, Department of Economics, Lomonosov Moscow State University mag2097@mail.ru Alexander Pakhalov, PG student, Department of Economics, Lomonosov Moscow State University

### Monitoring web traffic source effectiveness with Google Analytics An experiment with time series

The current issue and full text archive of this journal is available at wwwemeraldinsightcom/0001-253xhtm AP 474 Received 9 July 2008 Revised 21 January 2009 Accepted 6 February 2009 Monitoring web traffic

### MACRO ECONOMIC PATTERNS AND STORIES. Is Your Job Cyclical?

Is Your Job at Risk? Page 1 of 8 Is Your Job Cyclical? Accessing the website of the Bureau of Labor Statistics Finding out about the ups and downs of your job Total Nonfarm Employment is illustrated in

### Price volatility in the silver spot market: An empirical study using Garch applications

Price volatility in the silver spot market: An empirical study using Garch applications ABSTRACT Alan Harper, South University Zhenhu Jin Valparaiso University Raufu Sokunle UBS Investment Bank Manish

### THE CORRELATION BETWEEN UNEMPLOYMENT AND REAL GDP GROWTH. A STUDY CASE ON ROMANIA

THE CORRELATION BETWEEN UNEMPLOYMENT AND REAL GDP GROWTH. A STUDY CASE ON ROMANIA Dumitrescu Bogdan Andrei The Academy of Economic Studies Faculty of Finance, Insurance, Banking and Stock Exchange 6, Romana

### Chapter 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

### The Relationship between Life Insurance and Economic Growth: Evidence from India

Global Journal of Management and Business Studies. ISSN 2248-9878 Volume 3, Number 4 (2013), pp. 413-422 Research India Publications http://www.ripublication.com/gjmbs.htm The Relationship between Life

### 5. Multiple regression

5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful

### Chapter 9: Serial Correlation

Chapter 9: Serial Correlation In this chapter: 1. Creating a residual series from a regression model 2. Plotting the error term to detect serial correlation (UE, pp. 313-315) 3. Using regression to estimate

### 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

### 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

### MISSING DATA TECHNIQUES WITH SAS. IDRE Statistical Consulting Group

MISSING DATA TECHNIQUES WITH SAS IDRE Statistical Consulting Group ROAD MAP FOR TODAY To discuss: 1. Commonly used techniques for handling missing data, focusing on multiple imputation 2. Issues that could

### Multiple Linear Regression in Data Mining

Multiple Linear Regression in Data Mining Contents 2.1. A Review of Multiple Linear Regression 2.2. Illustration of the Regression Process 2.3. Subset Selection in Linear Regression 1 2 Chap. 2 Multiple

### Please follow the directions once you locate the Stata software in your computer. Room 114 (Business Lab) has computers with Stata software

STATA Tutorial Professor Erdinç Please follow the directions once you locate the Stata software in your computer. Room 114 (Business Lab) has computers with Stata software 1.Wald Test Wald Test is used

### The Effect of Seasonality in the CPI on Indexed Bond Pricing and Inflation Expectations

The Effect of Seasonality in the CPI on Indexed Bond Pricing and Inflation Expectations Roy Stein* *Research Department, Roy Stein roy.stein@boi.org.il, tel: 02-6552559 This research was partially supported

### Measuring Risk for Venture Capital and Private Equity Portfolios

Measuring Risk for Venture Capital and Private Equity Portfolios Susan E. Woodward Sand Hill Econometrics August, 2009 For alternative assets such as venture capital, buyouts (private equity), real estate,

### Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

### European Journal of Business and Management ISSN 2222-1905 (Paper) ISSN 2222-2839 (Online) Vol.5, No.30, 2013

The Impact of Stock Market Liquidity on Economic Growth in Jordan Shatha Abdul-Khaliq Assistant Professor,AlBlqa Applied University, Jordan * E-mail of the corresponding author: yshatha@gmail.com Abstract

### What drove Irish Government bond yields during the crisis?

What drove Irish Government bond yields during the crisis? David Purdue and Rossa White, September 2014 1. Introduction The Irish Government bond market has been exceptionally volatile in the seven years

### Instrumental Variables & 2SLS

Instrumental Variables & 2SLS y 1 = β 0 + β 1 y 2 + β 2 z 1 +... β k z k + u y 2 = π 0 + π 1 z k+1 + π 2 z 1 +... π k z k + v Economics 20 - Prof. Schuetze 1 Why Use Instrumental Variables? Instrumental

### Predicting The Outcome Of NASCAR Races: The Role Of Driver Experience Mary Allender, University of Portland

Predicting The Outcome Of NASCAR Races: The Role Of Driver Experience Mary Allender, University of Portland ABSTRACT As national interest in NASCAR grows, the field of sports economics is increasingly

### Exploring Changes in the Labor Market of Health Care Service Workers in Texas and the Rio Grande Valley I. Introduction

Ina Ganguli ENG-SCI 103 Final Project May 16, 2007 Exploring Changes in the Labor Market of Health Care Service Workers in Texas and the Rio Grande Valley I. Introduction The shortage of healthcare workers

### Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model

Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written

### STAFF WORKING PAPER. The Relationship between Sustainable Growth and the Riskfree Rate: Evidence from UK Government Gilts. Staff Working Paper 2012.

STAFF WORKING PAPER The Relationship between Sustainable Growth and the Riskfree Rate: Evidence from UK Government Gilts Staff Working Paper 2012.1 Andrew Lilico & Stefano Ficco January 2012 FOREWORD Europe

### Project Finance: Determinants of the Bank Loan Spread

International Journal of Business and Social Science Vol. 5, No. 5; April 2014 Project Finance: Determinants of the Bank Loan Spread Neila BOUZGUENDA PhD in Finance Ecole Supérieure de Commerce (ESC) La

### Chapter 2 Regression Analysis and Forecasting Models

Chapter 2 Regression Analysis and Forecasting Models A forecast is merely a prediction about the future values of data. However, most extrapolative model forecasts assume that the past is a proxy for the

### The Time Series Performance Of UK Real Estate Indices

The Time Series Performance Of UK Real Estate Indices A report funded by the Real Estate Research Institute as part of an enquiry into property performance measures in the United States for the US Pensions

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### ECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2

University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages

### REGRESSION LINES IN STATA

REGRESSION LINES IN STATA THOMAS ELLIOTT 1. Introduction to Regression Regression analysis is about eploring linear relationships between a dependent variable and one or more independent variables. Regression

### MARKETING COMMUNICATION IN ONLINE SOCIAL PROGRAMS: OHANIAN MODEL OF SOURCE CREDIBILITY

MARKETING COMMUNICATION IN ONLINE SOCIAL PROGRAMS: OHANIAN MODEL OF SOURCE CREDIBILITY Serban Corina The Bucharest Academy of Economic Studies The Faculty of Marketing The development of the Internet as

### Intertemporal Effects of Online Advertising Channels on Customers

International Journal of Business and Social Science Vol. 5, No. 9; August 2014 Intertemporal Effects of Online Advertising Channels on Customers Mohammad Almotairi Department of Marketing College of Business

### PARTNERSHIP IN SOCIAL MARKETING PROGRAMS. SOCIALLY RESPONSIBLE COMPANIES AND NON-PROFIT ORGANIZATIONS ENGAGEMENT IN SOLVING SOCIETY S PROBLEMS

PARTNERSHIP IN SOCIAL MARKETING PROGRAMS. SOCIALLY RESPONSIBLE COMPANIES AND NON-PROFIT ORGANIZATIONS ENGAGEMENT IN SOLVING SOCIETY S PROBLEMS Corina Şerban The Bucharest Academy of Economic Studies, Romania

### A Multiplicative Seasonal Box-Jenkins Model to Nigerian Stock Prices

A Multiplicative Seasonal Box-Jenkins Model to Nigerian Stock Prices Ette Harrison Etuk Department of Mathematics/Computer Science, Rivers State University of Science and Technology, Nigeria Email: ettetuk@yahoo.com

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### DOLLAR DEPRECIATION WILL NOT CONTRIBUTE TO U.S. INFLATION

DOLLAR DEPRECIATION WILL NOT CONTRIBUTE TO U.S. INFLATION Alan C. Stockman University of Rochester Prepared for the May 2, 2004 Meeting of the Shadow Open Market Committee Over the last 2 years, the dollar

### Instrumental Variables Regression. Instrumental Variables (IV) estimation is used when the model has endogenous s.

Instrumental Variables Regression Instrumental Variables (IV) estimation is used when the model has endogenous s. IV can thus be used to address the following important threats to internal validity: Omitted

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### Instrumental Variables & 2SLS

Instrumental Variables & 2SLS y 1 = β 0 + β 1 y 2 + β 2 z 1 +... β k z k + u y 2 = π 0 + π 1 z k+1 + π 2 z 1 +... π k z k + v Economics 20 - Prof. Schuetze 1 Why Use Instrumental Variables? Instrumental

### Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

### Parking slots in Europe: Results review and new model proposal. Phase 2: EPA s model improvement and design of a new survey

Parking slots in Europe: Results review and new model proposal Phase 2: EPA s model improvement and design of a new survey Research team: Jordi Suriñach (director) Manuela Alcañiz José Ramón García Montserrat

### Effects of bank mergers and acquisitions on small business lending in Nigeria

African Journal of Business Management Vol.2 (9), pp. 146-156, September 2008 Available online at http://www.academicjournals.org/ajbm ISSN 1993-8233 2008 Academic Journals Full Length Research Paper Effects

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### Bivariate Regression Analysis. The beginning of many types of regression

Bivariate Regression Analysis The beginning of many types of regression TOPICS Beyond Correlation Forecasting Two points to estimate the slope Meeting the BLUE criterion The OLS method Purpose of Regression

### Regression step-by-step using Microsoft Excel

Step 1: Regression step-by-step using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression

### 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,

### The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.

Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium

### Lectures 8, 9 & 10. Multiple Regression Analysis

Lectures 8, 9 & 0. Multiple Regression Analysis In which you learn how to apply the principles and tests outlined in earlier lectures to more realistic models involving more than explanatory variable and

### CORPORATE GOVERNANCE MECHANISM AND TAX PLANNING IN NIGERIA

CORPORATE GOVERNANCE MECHANISM AND TAX PLANNING IN NIGERIA UCHENDU, ODOEMELA Department of Accounting, Faculty of Management Sciences, University of Port Harcourt, Rivers State, Nigeria. Uchenduodoemela@yahoo.com

### Time Series Analysis

Time Series Analysis Descriptive analysis of a time series Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos

### Testing for Lack of Fit

Chapter 6 Testing for Lack of Fit How can we tell if a model fits the data? If the model is correct then ˆσ 2 should be an unbiased estimate of σ 2. If we have a model which is not complex enough to fit

### Sacred Heart University John F. Welch College of Business

Sacred Heart University John F. Welch College of Business CONNECTICUT ECONOMIC OUTLOOK for 2013-2015: A Perspective from Sacred Heart University Students in Business Economics Final Research Project for

### 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

### We extended the additive model in two variables to the interaction model by adding a third term to the equation.

Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic

### The Pecking Order Theory and the Static Trade Off Theory: Comparison of the Alternative Explanatory Power in French Firms

Journal of Business Studies Quarterly 2012, Vol. 4, No. 1, pp. 1-14 ISSN 2152-1034 The Pecking Order Theory and the Static Trade Off Theory: Comparison of the Alternative Explanatory Power in French Firms

### Estimation and Inference in Cointegration Models Economics 582

Estimation and Inference in Cointegration Models Economics 582 Eric Zivot May 17, 2012 Tests for Cointegration Let the ( 1) vector Y be (1). Recall, Y is cointegrated with 0 cointegrating vectors if there

### TOTAL FACTOR PRODUCTIVITY AND ECONOMIC GROWTH

İstanbul Ticaret Üniversitesi Sosyal Bilimler Dergisi Yıl:8 Sayı:15 Bahar 2009 s.49-56 TOTAL FACTOR PRODUCTIVITY AND ECONOMIC GROWTH Mehmet ADAK * ABSTRACT The causality between TFP (Total Factor Productivity)

### Multiple Regression - Selecting the Best Equation An Example Techniques for Selecting the "Best" Regression Equation

Multiple Regression - Selecting the Best Equation When fitting a multiple linear regression model, a researcher will likely include independent variables that are not important in predicting the dependent

### Pearson s Correlation

Pearson s Correlation Correlation the degree to which two variables are associated (co-vary). Covariance may be either positive or negative. Its magnitude depends on the units of measurement. Assumes the

### DEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests

DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also

### Regression Analysis. Data Calculations Output

Regression Analysis In an attempt to find answers to questions such as those posed above, empirical labour economists use a useful tool called regression analysis. Regression analysis is essentially a

### A Primer on Forecasting Business Performance

A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.

### Performing Unit Root Tests in EViews. Unit Root Testing

Página 1 de 12 Unit Root Testing The theory behind ARMA estimation is based on stationary time series. A series is said to be (weakly or covariance) stationary if the mean and autocovariances of the series

### PRICING OF FOREIGN CURRENCY OPTIONS IN THE SERBIAN MARKET

ECONOMIC ANNALS, Volume LIV, No. 180, January March 2009 UDC: 3.33 ISSN: 0013-3264 COMMUNICATIONS Irena Janković* DOI:10.2298/EKA0980091J PRICING OF FOREIGN CURRENCY OPTIONS IN THE SERBIAN MARKET ABSTRACT:

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### A Guide to Using EViews with Using Econometrics: A Practical Guide

A Guide to Using EViews with Using Econometrics: A Practical Guide In the Introduction: 1. Purpose of this guide 2. EViews help 3. EViews basics and objects 4. Mathematical expressions in EViews 5. Areas

### TIME SERIES ANALYSIS OF CHINA S EXTERNAL DEBT COMPONENTS, FOREIGN EXCHANGE RESERVES AND ECONOMIC GROWTH RATES. Hüseyin Çetin

TIME SERIES ANALYSIS OF CHINA S EXTERNAL DEBT COMPONENTS, FOREIGN EXCHANGE RESERVES AND ECONOMIC GROWTH RATES Hüseyin Çetin Phd Business Administration Candidate Okan University Social Science Institute,

### Regression Analysis (Spring, 2000)

Regression Analysis (Spring, 2000) By Wonjae Purposes: a. Explaining the relationship between Y and X variables with a model (Explain a variable Y in terms of Xs) b. Estimating and testing the intensity

### IAPRI Quantitative Analysis Capacity Building Series. Multiple regression analysis & interpreting results

IAPRI Quantitative Analysis Capacity Building Series Multiple regression analysis & interpreting results How important is R-squared? R-squared Published in Agricultural Economics 0.45 Best article of the

### Understanding Retention among Private Baccalaureate Liberal Arts Colleges

Understanding Retention among Private Baccalaureate Liberal Arts Colleges Thursday April 19, 2012 Author: Katherine S. Hanson 1 Abstract This paper attempts to analyze the explanatory variables that best

### Interaction between quantitative predictors

Interaction between quantitative predictors In a first-order model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors

### Evaluation of Vector Error Correction Models

Evaluation of Vector Error Correction Models in comparison with Simkins: Forecasting with Vector Autoregressive (VAR) Models Subject to Business Cycle Restrictions Stefan Zeugner 9851051 Seminar paper

### Online Appendices to the Corporate Propensity to Save

Online Appendices to the Corporate Propensity to Save Appendix A: Monte Carlo Experiments In order to allay skepticism of empirical results that have been produced by unusual estimators on fairly small

### ANALYSIS OF THE LIFE INSURANCE MARKET IN THE REPUBLIC OF MACEDONIA

ECONOMIC ANNALS, Volume LVII, No. 194 / July September 2012 UDC: 3.33 ISSN: 0013-3264 DOI:10.2298/EKA1294107A Cvetko Andreeski* Bratislav Milošević** Vladimir Njegomir*** ANALYSIS OF THE LIFE INSURANCE

### 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