Two-stage change-point estimators in smooth regression models

Change-point regression models are often used to develop building energy baselines that can be used to predict energy use and determine energy savings during a given performance period. However, the reliability of building energy baselines can depend on how well the change-point model fits the data measured during the baseline period. This research proposes the use of segmented linear regression models with one or two change points for automatically driving best-fit building energy baseline models, along with an algorithm using a data-driven grid search to find the optimal change point(s) within a given data boundary for the proposed models. The algorithm was programmed and tested with actual measured data (e.g., daily gas and electricity use) for case-study buildings. Graphical and statistical analysis was also performed to validate its reliability within acceptable deviations of an overall coefficient of variation of the root mean squared error (i.e., CV(RMSE)) of 1%, as compared to the results derived from the ASHRAE Inverse Model Toolkit (IMT) that was developed as a public domain program to manually derive the change-point model with user specified parameters. Consequently, it is expected that the algorithm can be applied for automatically deriving best-fit building energy baseline models with optimal change point(s) from measured data.

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BAYESIAN IDENTIFICATION OF OUTLIERS AND CHANGE-POINTS IN MEASUREMENT ERROR MODELS

Advances in Complex Systems ◽

10.1142/s0219525905000567 ◽

2005 ◽

Vol 08 (04) ◽

pp. 433-449 ◽

Cited By ~ 8

Author(s):

FERNANDO A. QUINTANA ◽

PILAR L. IGLESIAS ◽

HELENO BOLFARINE

Keyword(s):

Linear Regression ◽

Outlier Detection ◽

Change Point ◽

Regression Models ◽

Point Problem ◽

Linear Regression Models ◽

Outlier Identification ◽

Change Point Problem ◽

Error In Variables ◽

The Relationship

The problem of outlier and change-point identification has received considerable attention in traditional linear regression models from both, classical and Bayesian standpoints. In contrast, for the case of regression models with measurement errors, also known as error-in-variables models, the corresponding literature is scarce and largely focused on classical solutions for the normal case. The main object of this paper is to propose clustering algorithms for outlier detection and change-point identification in scale mixture of error-in-variables models. We propose an approach based on product partition models (PPMs) which allows one to study clustering for the models under consideration. This includes the change-point problem and outlier detection as special cases. The outlier identification problem is approached by adapting the algorithms developed by Quintana and Iglesias [32] for simple linear regression models. A special algorithm is developed for the change-point problem which can be applied in a more general setup. The methods are illustrated with two applications: (i) outlier identification in a problem involving the relationship between two methods for measuring serum kanamycin in blood samples from babies, and (ii) change-point identification in the relationship between the monthly dollar volume of sales on the Boston Stock Exchange and the combined monthly dollar volumes for the New York and American Stock Exchanges.

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