8 Correlated Errors

8 Correlated Errors - Statistics 191: Introduction to...

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Unformatted text preview: Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Statistics 191: Introduction to Applied Statistics Correlated Errors, Whitening Jonathan Taylor Department of Statistics Stanford University February 22, 2010 1 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Correlated Erorrs Topics Autocorrelation. Whitening. 2 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Correlated errors Autocorrelation In the random effects model, outcomes within groups were correlated. Other regression applications also have correlated outcomes (i.e. errors). Common examples: time series data. Why worry? Can lead to underestimates of SE inflated t s false positives. 3 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Correlated errors Autocorrelation Suppose we plot Palo Altos daily average temperature clearly we would see a pattern in the data. Sometimes, this pattern can be attributed to a deterministic phenomenon (i.e. predictable seasonal fluctuations). Other times, patterns are due to correlations in the noise, maybe small time fluctuations in the stock market, economy, etc. Example: financial time series, monthly bond return. Example: residuals regressing consumer expenditure on money stock. 4 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Average Max Temp in Palo Alto 5 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Monthly bond return R code 6 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Monthly bond return, ACF R code 7 / 1 Statistics 191:...
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8 Correlated Errors - Statistics 191: Introduction to...

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