DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION

Slides:



Advertisements
Similar presentations
Regression Analysis.
Advertisements

Christopher Dougherty EC220 - Introduction to econometrics (chapter 11) Slideshow: static models and models with lags Original citation: Dougherty, C.
Christopher Dougherty EC220 - Introduction to econometrics (chapter 13) Slideshow: cointegration Original citation: Dougherty, C. (2012) EC220 - Introduction.
COINTEGRATION 1 The next topic is cointegration. Suppose that you have two nonstationary series X and Y and you hypothesize that Y is a linear function.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(LGDPI) Method: Least Squares Sample (adjusted): Included observations: 44 after adjustments.
Chapter 11 Autocorrelation.
Christopher Dougherty EC220 - Introduction to econometrics (chapter 13) Slideshow: tests of nonstationarity: example and further complications Original.
============================================================ Dependent Variable: LGHOUS Method: Least Squares Sample: Included observations:
AUTOCORRELATION 1 The third Gauss-Markov condition is that the values of the disturbance term in the observations in the sample be generated independently.
FITTING MODELS WITH NONSTATIONARY TIME SERIES 1 Detrending Early macroeconomic models tended to produce poor forecasts, despite having excellent sample-period.
Welcome to Econ 420 Applied Regression Analysis Study Guide Week Three Ending Tuesday, September 11 (Note: You must go over these slides and complete every.
Chapter 4 Using Regression to Estimate Trends Trend Models zLinear trend, zQuadratic trend zCubic trend zExponential trend.
1 TIME SERIES MODELS: STATIC MODELS AND MODELS WITH LAGS In this sequence we will make an initial exploration of the determinants of aggregate consumer.
Angela Sordello Christopher Friedberg Can Shen Hui Lai Hui Wang Fang Guo.
Chapter 13 Additional Topics in Regression Analysis
Factors Determining the Price Of Used Mid- Compact Size Vehicles Team 4.
TAKE HOME PROJECT 2 Group C: Robert Matarazzo, Michael Stromberg, Yuxing Zhang, Yin Chu, Leslie Wei, and Kurtis Hollar.
Marietta College Week 14 1 Tuesday, April 12 2 Exam 3: Monday, April 25, 12- 2:30PM Bring your laptops to class on Thursday too.
Is There a Difference?. How Should You Vote? Is “Big Government” better?Is “Big Government” better? –Republicans want less government involvement. –Democrats.
Global Warming: Is It True? Peter Fuller Odeliah Greene Amanda Smith May Zin.
Economics 310 Lecture 15 Autocorrelation. Correlation between members of series of observations order in time or space. For our classic model, we have.
Determents of Housing Prices. What & WHY Our goal was to discover the determents of rising home prices and to identify any anomies in historic housing.
Why Can’t I Afford a Home? By: Philippe Bonnan Emelia Bragadottir Troy Dewitt Anders Graham S. Matthew Scott Lingli Tang.
1 Motor Vehicle Accidents Hunjung Kim Melissa Manfredonia Heidi Braunger Yaming Liu Jo-Yu Mao Grace Lee December 1, 2005 Econ 240A Project.
Determining what factors have an impact on the burglary rate in the United States Team 7 : Adam Fletcher, Branko Djapic, Ivan Montiel, Chayaporn Lertarattanapaiboon,
Violent Crime in America ECON 240A Group 4 Thursday 3 December 2009.
Lecture Week 3 Topics in Regression Analysis. Overview Multiple regression Dummy variables Tests of restrictions 2 nd hour: some issues in cost of capital.
California Expenditure VS. Immigration By: Daniel Jiang, Keith Cochran, Justin Adams, Hung Lam, Steven Carlson, Gregory Wiefel Fall 2003.
So far, we have considered regression models with dummy variables of independent variables. In this lecture, we will study regression models whose dependent.
GDP Published by: Bureau of Economic Analysis Frequency: Quarterly Period Covered: prior quarter Volatility: Moderate Market significance: very high Web.
1 Power Fifteen Analysis of Variance (ANOVA). 2 Analysis of Variance w One-Way ANOVA Tabular Regression w Two-Way ANOVA Tabular Regression.
Zhen Tian Jeff Lee Visut Hemithi Huan Zhang Diana Aguilar Yuli Yan A Deep Analysis of A Random Walk.
1 Power Fifteen Analysis of Variance (ANOVA). 2 Analysis of Variance w One-Way ANOVA Tabular Regression w Two-Way ANOVA Tabular Regression.
Forecasting Fed Funds Rate Group 4 Neelima Akkannapragada Chayaporn Lertrattanapaiboon Anthony Mak Joseph Singh Corinna Traumueller Hyo Joon You.
Introduction to Regression Analysis, Chapter 13,
EC220 - Introduction to econometrics (chapter 12)
12 Autocorrelation Serial Correlation exists when errors are correlated across periods -One source of serial correlation is misspecification of the model.
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 12-1 Chapter 12 Simple Linear Regression Statistics for Managers Using.
Regression Method.
Multiple Regression. In the previous section, we examined simple regression, which has just one independent variable on the right side of the equation.
Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Chapter Inference on the Least-Squares Regression Model and Multiple Regression 14.
What decides the price of used cars? Group 1 Jessica Aguirre Keith Cody Rui Feng Jennifer Griffeth Joonhee Lee Hans-Jakob Lothe Teng Wang.
Welcome to Econ 420 Applied Regression Analysis Study Guide Week Five Ending Wednesday, September 26 (Note: Exam 1 is on September 27)
1 Economics 240A Power Eight. 2 Outline n Maximum Likelihood Estimation n The UC Budget Again n Regression Models n The Income Generating Process for.
SPURIOUS REGRESSIONS 1 In a famous Monte Carlo experiment, Granger and Newbold fitted the model Y t =  1 +  2 X t + u t where Y t and X t were independently-generated.
Welcome to Econ 420 Applied Regression Analysis Study Guide Week Four Ending Wednesday, September 19 (Assignment 4 which is included in this study guide.
PARTIAL ADJUSTMENT 1 The idea behind the partial adjustment model is that, while a dependent variable Y may be related to an explanatory variable X, there.
AUTOCORRELATION 1 Assumption C.5 states that the values of the disturbance term in the observations in the sample are generated independently of each other.
Christopher Dougherty EC220 - Introduction to econometrics (chapter 4) Slideshow: exercise 4.5 Original citation: Dougherty, C. (2012) EC220 - Introduction.
2010, ECON Hypothesis Testing 1: Single Coefficient Review of hypothesis testing Testing single coefficient Interval estimation Objectives.
AUTOCORRELATION: WHAT HAPPENS IF THE ERROR TERMS ARE CORRELATED?
FUNCTIONAL FORMS OF REGRESSION MODELS Application 5.
Air pollution is the introduction of chemicals and biological materials into the atmosphere that causes damage to the natural environment. We focused.
MEASURES OF GOODNESS OF FIT The sum of the squares of the actual values of Y (TSS: total sum of squares) could be decomposed into the sum of the squares.
Christopher Dougherty EC220 - Introduction to econometrics (chapter 6) Slideshow: exercise 6.13 Original citation: Dougherty, C. (2012) EC220 - Introduction.
EC208 – Introductory Econometrics. Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models)
TESTING FOR NONSTATIONARITY 1 This sequence will describe two methods for detecting nonstationarity, a graphical method involving correlograms and a more.
Partial Equilibrium Framework Empirical Evidence for Argentina ( )
Significance Tests for Regression Analysis. A. Testing the Significance of Regression Models The first important significance test is for the regression.
TESTING FOR NONSTATIONARITY 1 This sequence will describe two methods for detecting nonstationarity, a graphical method involving correlograms and a more.
F TESTS RELATING TO GROUPS OF EXPLANATORY VARIABLES 1 We now come to more general F tests of goodness of fit. This is a test of the joint explanatory power.
An Assessment of Climate Change
Correlation and Simple Linear Regression
المبادلة بين العائد و المخاطرة دراسة قياسية السنة الدراســــــــية:
Correlation and Simple Linear Regression
Introduction to Econometrics, 5th edition Chapter 12: Autocorrelation
Simple Linear Regression and Correlation
Table 4. Regression Statistics for the Model
Correlation and Simple Linear Regression
Correlation and Simple Linear Regression
Presentation transcript:

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION The standard test statistic for autocorrelation of the AR(1) type is the Durbin–Watson d statistic, computed from the residuals as shown above. Most regression applications calculate it automatically and present it as one of the standard regression diagnostics. 1

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION In large samples It can be shown that in large samples d tends to 2 – 2r, where r is the parameter in the AR(1) relationship ut = rut–1 + et. 2

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION In large samples No autocorrelation If there is no autocorrelation, r is 0 and d should be distributed randomly around 2. 3

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION In large samples No autocorrelation Severe positive autocorrelation If there is severe positive autocorrelation, r will be near 1 and d will be near 0. 4

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION In large samples No autocorrelation Severe positive autocorrelation Severe negative autocorrelation Likewise, if there is severe positive autocorrelation, r will be near –1 and d will be near 4. 5

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation 2 4 Thus d behaves as illustrated graphically above. 6

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dcrit 2 dcrit 4 To perform the Durbin–Watson test, we define critical values of d. The null hypothesis is H0: r = 0 (no autocorrelation). If d lies between these values, we do not reject the null hypothesis. 7

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dcrit 2 dcrit 4 The critical values, at any significance level, depend on the number of observations in the sample and the number of explanatory variables. 8

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dcrit 2 dcrit 4 Unfortunately, they also depend on the actual data for the explanatory variables in the sample, and thus vary from sample to sample. 9

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dcrit dU 2 dcrit 4 However Durbin and Watson determined upper and lower bounds, dU and dL, for the critical values, and these are presented in standard tables. 10

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dcrit dU 2 dcrit 4 If d is less than dL, it must also be less than the critical value of d for positive autocorrelation, and so we would reject the null hypothesis and conclude that there is positive autocorrelation. 11

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dcrit dU 2 dcrit 4 If d is above than dU, it must also be above the critical value of d, and so we would not reject the null hypothesis. (Of course, if it were above 2, we should consider testing for negative autocorrelation instead.) 12

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dcrit dU 2 dcrit 4 If d lies between dL and dU, we cannot tell whether it is above or below the critical value and so the test is indeterminate. 13

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 (n = 45, k = 3, 5% level) Here are dL and dU for 45 observations and two explanatory variables, at the 5% significance level. 14

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) There are similar bounds for the critical value in the case of negative autocorrelation. They are not given in the standard tables because negative autocorrelation is uncommon, but it is easy to calculate them because are they are located symmetrically to the right of 2. 15

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) So if d < 1.43, we reject the null hypothesis and conclude that there is positive autocorrelation. 16

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) If 1.43 < d < 1.62, the test is indeterminate and we do not come to any conclusion. 17

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) If 1.62 < d < 2.38, we do not reject the null hypothesis of no autocorrelation. 18

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) If 2.38 < d < 2.57, we do not come to any conclusion. 19

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.43 1.62 2.38 2.57 (n = 45, k = 3, 5% level) If d > 2.57, we conclude that there is significant negative autocorrelation. 20

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION No autocorrelation Severe positive autocorrelation Severe negative autocorrelation positive autocorrelation no autocorrelation negative autocorrelation dL dU 2 4 1.24 1.42 2.58 2.76 (n = 45, k = 3, 1% level) Here are the bounds for the critical values for the 1% test, again with 45 observations and two explanatory variables. 21

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION Here is a plot of the residuals from a logarithmic regression of expenditure on housing services on income and the relative price of housing services. The residuals exhibit strong positive autocorrelation. 22

DURBIN–WATSON TEST FOR AR(1) AUTOCORRELATION ============================================================ Dependent Variable: LGHOUS Method: Least Squares Sample: 1959 2003 Included observations: 45 Variable Coefficient Std. Error t-Statistic Prob. C 0.005625 0.167903 0.033501 0.9734 LGDPI 1.031918 0.006649 155.1976 0.0000 LGPRHOUS -0.483421 0.041780 -11.57056 0.0000 R-squared 0.998583 Mean dependent var 6.359334 Adjusted R-squared 0.998515 S.D. dependent var 0.437527 S.E. of regression 0.016859 Akaike info criter-5.263574 Sum squared resid 0.011937 Schwarz criterion -5.143130 Log likelihood 121.4304 F-statistic 14797.05 Durbin-Watson stat 0.633113 Prob(F-statistic) 0.000000 dL dU 1.24 1.42 (n = 45, k = 3, 1% level) The d statistic is very low, below dL for the 1% significance test (1.24), so we would reject the null hypothesis of no autocorrelation. 23

Copyright Christopher Dougherty 2000–2006 Copyright Christopher Dougherty 2000–2006. This slideshow may be freely copied for personal use. 15.03.06