Autocorrelation Standard Error
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Autocorrelation Variance
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Autocorrelation Standard Error Underestimate
answer The best answers are voted up and rise to the top Why autocorrelation affects OLS coefficient standard errors? up vote 3 down vote favorite 1 It seems that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. But why residuals autocorrelation would affect the coefficient standard errors? From the Wikipedia article on autocorrelation: While it does not bias the OLS coefficient estimates, the standard standard error correlation errors tend to be underestimated (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive. regression standard-error autocorrelation share|improve this question edited Sep 6 '14 at 22:45 Glen_b♦ 147k19245509 asked Sep 6 '14 at 22:34 Robert Kubrick 1,25531837 Consider an extreme case of correlation. Suppose all the errors were perfectly positively correlated. In other words, somebody had generated a single random number and added it to all the response values. How certain would you be of (say) the intercept in the regression? Would you have any clues at all concerning the size of the random value that was added? –whuber♦ Sep 6 '14 at 22:55 Yes, but that is true of any missing predictor that could explain 99% of the variance and we just ignore. Why are making a specific case for $Y_{t-1}$? –Robert Kubrick Sep 6 '14 at 22:59 My example is not missing any predictors at all: it is only positing an extreme case of autocorrelation among the residuals. –whuber♦ Sep 7 '14 at 13:34 ok, but how is this different than the case where we don't have any residuals autocorrelation, but we're not including another critical predictor? We can draw
independent. This section discusses methods for dealing with dependent errors. In particular, the dependency
Robust Standard Errors Autocorrelation
usually appears because of a temporal component. Error terms correlated standard deviation autocorrelation over time are said to be autocorrelated or serially correlated. When error terms are autocorrelated, autocorrelation function some issues arise when using ordinary least squares. These problems are: Estimated regression coefficients are still unbiased, but they no longer have the minimum http://stats.stackexchange.com/questions/114564/why-autocorrelation-affects-ols-coefficient-standard-errors variance property. The MSE may seriously underestimate the true variance of the errors. The standard error of the regression coefficients may seriously underestimate the true standard deviation of the estimated regression coefficients. Statistical intervals and inference procedures are no longer strictly applicable. We also consider the setting where a https://onlinecourses.science.psu.edu/stat501/node/357 data set has a temporal component that affects the analysis. 14.1 - Autoregressive Models 14.2 - Regression with Autoregressive Errors 14.3 - Testing and Remedial Measures for Autocorrelation 14.4 - Examples of Applying Cochrane-Orcutt Procedure 14.5 - Advanced Methods 14.1 - Autoregressive Models › Printer-friendly version Navigation Start Here! Welcome to STAT 501! Search Course Materials Faculty login (PSU Access Account) Lessons Lesson 1: Simple Linear Regression Lesson 2: SLR Model Evaluation Lesson 3: SLR Estimation & Prediction Lesson 4: SLR Model Assumptions Lesson 5: Multiple Linear Regression Lesson 6: MLR Model Evaluation Lesson 7: MLR Estimation, Prediction & Model Assumptions Lesson 8: Categorical Predictors Lesson 9: Data Transformations Lesson 10: Model Building Lesson 11: Influential Points Lesson 12: Multicollinearity & Other Regression Pitfalls Lesson 13: Weighted Least Squares & Robust Regression Lesson 14: Time Series & Autocorrelation14.1 - Autoregressive Models 14.2 - Regression with Autoreg
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