1 / 21

Linear Regression Basics III Violating Assumptions

Learn about violating assumptions, error variance, correlations, normality testing, and model construction in linear regression analysis. Understand the impact of omitting or adding variables, parameter stability, and error types.

kat
Télécharger la présentation

Linear Regression Basics III Violating Assumptions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fin250f: Lecture 7.2 Spring 2010 Brooks, chapter 4(skim) 4.1-2, 4.4, 4.5, 4.7, 4.9-13 Linear Regression Basics IIIViolating Assumptions

  2. Outline • Violating assumptions • Parameter stability • Model building

  3. OLS Assumptions • Error variances • Error correlations • Error normality • Functional forms and linearity • Omitting variables • Adding irrelevant variables

  4. Error Variance

  5. Error VarianceWhich is a bigger error? Y * * * * * * X

  6. Error Correlations • Patterns in residuals • Plot residuals/residual diagnostics • Further modeling necessary • If you can forecast u(t+1), need to work harder

  7. Error Normality • Skewness and kurtosis in residuals • Testing • Plots • Bera-Jarque test • How can this impact results?

  8. Bera-Jarque Test for Normality

  9. Nonnormal Errors: Impact • For some theory: No • In practice can be big problem • Many extreme data points • Forecasting models work hard to fit these extreme outliers • Some solutions: • Drop data points • Robust forecast objectives (absolute errors)

  10. Functional Forms • Y=a+bX • Actual function is nonlinear • Several types of diagnostics • Higher order (squared) terms (RESET) • Think about specific nonlinear models • Neural networks • Threshold models • Tricky: More later

  11. Omitting Variables Leave out x(2) If it is correlated with x(1) this is a problem. Beta(1) will be biased and inconsistent. Forecast will not be optimal

  12. Irrelevant Variables • Overfitting/data snooping • Model fits to noise • Impacts standard errors for coefficients • Coefficients still consistent and unbiased

  13. Parameter Stability • Known break point • Chow test • Predictive failure test • Unknown break • Quant likelihood ratio test • Recursive least squares

  14. Chow Test

  15. Chow Test

  16. Predictive Failure

  17. Predictive Failure

  18. Unknown Breaks • Search for break • Look for maximum Chow level • Distribution is tricky • Monte-carlo/bootstrap

  19. Recursive/rolling estimation • Recursive • Estimate (1,T1) move T1 to full sample T • See if parameters converge • Rolling • Roll bands (t-T,t) through data • Watch parameters move through time • We’ll use some of these

  20. Pure Out of Sample Tests • Estimate parameters over (1,T1) • Get errors over (T1+1,T)

  21. Model Construction • General -> specific • Less financial theory • More statistics • Problems: large unwieldy models • Simple -> general • More theory at the start • Problems: can leave out important stuff

More Related