Tools and Methods for Addressing Autocorrelation in Energy Modeling

Introduction

After reviewing SEM measurement and verification (M&V) protocols from different programs, the ETSP team identified autocorrelation as a common statistical issue in industrial data sets.  Understanding that autocorrelation has the potential to negatively affect the predictive capability of regression-based energy models used to create adjusted energy baselines, more consistent treatment of this issue may help improve confidence in SEM-based savings, and thereby address a potential market barrier.  The ETSP team compiled this paper for the purposes of outlining the implications of autocorrelation in the context of SEM measurement and verification, and providing examples of how program implementers have successfully identified and treated the presence of autocorrelation in regression-based energy models.

Statistical Interpretation

Autocorrelation is present when the error term in period t is related to the error term in period t-1.  More simply stated, there is a systematic pattern in the error term (residuals) of the model.  This systematic pattern may be due to omitted variables from the model, serially correlated predictors coupled with model specification error, or correlated disturbances that are beyond the scope of predictor variables.  The pattern in residuals also violates the ordinary least squares (OLS) assumption of independent error terms and may cause misinterpretation of regression results due to understated standard errors  (apparent accuracy/precision better than it really is).  The degree of autocorrelation is measured by the autocorrelation coefficient, also called the autocorrelation parameter, and can take on values between zero and one.  Autocorrelation is said to be present when the autocorrelation coefficient (ρ) is significantly greater than zero.  The Durbin-Watson test for autocorrelation is a popular approach for determining if the autocorrelation parameter is significantly greater than zero.  The test is applied by comparing the value of the Durbin-Watson statistic to upper and lower ranges.  Most statistical regression packages will calculate the autocorrelation coefficient, Durbin-Watson statistic, and results from the Durbin-Watson test.   

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