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Activity Number: 133
Type: Contributed
Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
Sponsor: Business and Economic Statistics Section
Abstract - #305000
Title: Constrained Regression for Interval-Valued Data: The Daily Low/High Interval of SP500 Returns
Author(s): Wei Lin*+ and Gloria González-Rivera
Companies: University of California at Riverside and University of California at Riverside
Address: 3122 Sproul Hall, Riverside, CA, 92521,
Keywords: Interval-valued Data ; Inverse of the Mill's Ratio ; Maximum Likelihood Estimation ; Minimum Distance Estimator ; Truncated Probability Density Function
Abstract:

Current regression models for interval-valued data do not guarantee that the predicted lower bound of the interval is always smaller than its upper bound. We propose a constrained regression model that preserves the order of the interval either for fitted intervals or for interval forecasts. In interval time series, we specify a bivariate system for the two bounds of the intervals. By imposing the order of the interval bounds, the bivariate PDF of the errors is conditionally truncated, causing the OLS estimators inconsistent. MLE is possible but it is computationally burdensome due to the nonlinearity of the estimator when truncation occurs. We propose a two-step method that combines MLE and LS estimation, and a modified two-step method that combines MLE and minimum-distance estimation. Both estimators are consistent. The latter method is superior at identifying the model regardless of the severity of the truncation, and overcomes possible multicollinearity. Simulations show good finite sample properties of our estimators. We model the daily SP500 returns, and find that truncation is severe since the financial crisis of 2008, suggesting that a modified two-step method be used.


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