Method for determining house prices indices

• US 7,822,691 B1
• Filed: 12/26/2002
• Issued: 10/26/2010
• Est. Priority Date: 12/28/2001
• Status: Active Grant

• Current Assignee: Fannie Mae
• Original Assignee: Fannie Mae
• Inventors: Kuo, Chionglong
• Primary Examiner(s): Weiss; John G
• Assistant Examiner(s): Cumarasegaran; Vern
• Application Number:
  US10/328,172
• Time in Patent Office: 2,861 Days
• Field of Search: 705/1
• US Class Current: 705/313
• CPC Class Codes: G06Q 30/0202 Market predictions or forecasting for commercial activities
• CPC Class Codes: G06Q 30/0206 Price or cost determination based on market factors
• CPC Class Codes: G06Q 30/06 Buying, selling or leasing transactions
• CPC Class Codes: G06Q 50/16 Real estate

Abstract

A method for estimating a real estate price index based on a repeat sales model. The method includes the steps of eliminating corrupt portions of data used to determine price indices; regressing a difference in a log price of a second sale minus a log price of a first sale for a property on a set of dummy variables, eliminating the observations with zero residuals for estimating the dispersion function; using a quadratic formula to model a dispersion of residual values with respect to time interval; using the quadratic formula to solve for a dispersion for each time interval starting with a minimum positive value; determining a minimum dispersion value that is a value calculated from the quadratic formula; determining a maximum dispersion value that is calculated from the quadratic formula for each time interval starting with a minimum positive value, wherein the dispersion values are prevented from decreasing with increasing time intervals; repeating the step of regressing using the inverse of the square root of fitted values from the quadratic formula as weights; identifying and selecting the time periods and associated data for estimating a price index that covers a particular time period; excluding the index values which are determined to be unreliable; and obtaining an index series for a lower geographic level by using the index series of a higher geographic level.

Claims

1. A computer-implemented method for determining a real estate price index based on a repeat sales model, the method comprising the steps of:

a processor executing in a first stage regression, regressing the difference in a log price of a second sale minus a log price of a first sale for a property on a set of dummy variables, each log price representing a time period except a base period;

a processor executing in a second stage regression, using a quadratic formula to model, and estimate a dispersion of residual values with respect to time interval and determining a modified dispersion by determining a minimum dispersion value corresponding to a first point in time and a maximum dispersion value corresponding to a second point in time, wherein the modified dispersion is configured such that the dispersion value is not below zero at times less than, the first point in time and is held at the maximum dispersion value at times greater than the second point in time;

a processor executing in a third stage regression, repeating the first stage regression using the inverse of the square root of fitted values from the quadratic formula from the second stage regression as weights;

determining the real estate price index resulting from the first, second and third stage regressions; and

storing the determined real estate price index in a computer memory.

2. The method of claim 1, wherein the second stage excludes those observations that have zero residuals in the first-stage regression due to limited data availability.

3. The method of claim 2, further comprising the step of identifying the zero residuals by determining (1) if the first-stage residual is zero, and (2) if there is only one observation for a pair of sale and resale time points, and (3) if the diagonal element for the first sale of the inverse of the frequency matrix with the row and column for the second sale excluded is equal to one.

4. The method of claim 2, further comprising the step of identifying the zero residuals by determining if the first-stage residual is zero.

5. The method of claim 2, further comprising the step of identifying the zero residuals by determining if there is only one observation for a pair of sale and resale time points.

6. The method of claim 1, wherein determining the minimum residual value includes selecting the minimum positive value that is a low value that is assured to be more than a small amount greater than zero.

7. The method of claim 1, wherein determining the minimum residual value includes setting the minimum dispersion value to equal one-half of a second positive dispersion value that is calculated from the quadratic formula.

8. The method of claim 1, wherein determining the minimum dispersion value includes setting the minimum dispersion value to equal a second positive dispersion value that is calculated from the quadratic formula.

9. The method of claim 1, further comprising:

eliminating corrupt portions of data used to determine price indices by using a model based process to eliminate an outlying data before estimating the real estate price index.

10. The method of claim 9, wherein eliminating corrupt portions of data further comprises:

determining a position of each property in a prediction gap distribution for a corresponding geographic area and in a gap distribution for an entire sample; and

excluding a data value if the data value falls within at least one predefined criterion.

11. The method of claim 10, wherein eliminating corrupt portions of data further comprises:

assuming that a data value is the outlying data if a prediction gap is at a tail end of the gap distribution.

12. The method of claim 10, wherein excluding a data value further comprises excluding the data value if it has a prediction gap at a predetermined tail end of a small geographic area gap distribution and also at a less-extreme tail end of the entire sample gap distribution.

13. The method of claim 10, wherein excluding a data value further comprises excluding the data value if the prediction gap for the data value is not at a predetermined tail end of a small geographic area gap distribution but at a far tail end of the entire sample gap distribution.

14. The method of claim 1, wherein estimating the real estate price index comprises

obtaining an index series for a relatively small geographic area by using the index series of a relatively large geographic area.

15. The method of claim 14, wherein obtaining the index series for the relatively small geographic area comprises:

establishing an exclusion criterion to exclude periods for which indices are deemed unreliable;

developing a frequency measure and a standard error measure combination to determine if an index estimate should be excluded;

filling in price indices predicted for a geographic region for the relatively small geographic area; and

executing the indices for the geographic region and the relatively small geographic area against the exclusion criterion.

16. The method of claim 1, further comprising:

determining an estimated real estate value using the determined price index and, displaying the estimated real estate value.

17. A computer-implemented method for obtaining an index series based on a repeat sales model, the method comprising the steps of:

eliminating corrupt portions of data used to determine price indices;

a processor executing in a first stage regression, regressing a difference in a log price of a second sale minus a log price of a first sale for a property on a set of dummy variables, each log price representing a time period except a base period;

eliminating the observations with zero residuals for estimating the dispersion function;

a processor executing in a second stage regression, using a quadratic formula to model and estimate a dispersion of residual values with respect to time interval and determining a modified dispersion by determining a minimum dispersion value corresponding to a first point in time and a maximum dispersion value corresponding to a second point in time, wherein the modified dispersion is configured such that the dispersion value is not below zero at times less than the first point in time and is held at the maximum dispersion value at times greater than the second point in time;

repeating the first stage regression using the inverse of the square root of fitted values from the quadratic formula from the second stage regression as weights;

identifying and selecting the time periods and associated data for estimating a price index that covers a particular time period;

excluding the time periods for which the index values are determined to be unreliable;

obtaining an index series for a relatively small geographic area by using an index series of a relatively large geographic area; and

storing the obtained index series for the relatively small geographic area in a computer memory.

18. The method of claim 17, further comprising:

determining an estimated real estate value using the index series for the relatively small geographic area and displaying the estimated real estate value.

19. A computer system for determining a real estate price index based on a repeat sales model, the system comprising:

a memory; and

a processor, for executing program instructions stored in the memory, the program instructions executed to provide operations comprising;

in a first stage regression, regressing the difference in a log price of a second sale minus a log price of a first sale for a property on a set of dummy variables, each log price representing a time period except a base period;

in a second stags regression, using a quadratic formula to model and estimate a dispersion of residual values with respect to time interval and determining a modified dispersion by determining a minimum dispersion value corresponding to a first point in time and a maximum dispersion value corresponding to a second point in time, wherein the modified dispersion is configured such that the dispersion value is not below zero at times less than the first point in time and is held at the maximum dispersion value at times greater than the second point in time;

in a third stage regression, repeating the first stage regression using the inverse of the square root of fitted values from the quadratic formula from the second stage regression as weights;

determining the real estate price index resulting from the first, second and third stage regressions; and

storing the determined real estate price index in a computer memory.

20. The system of claim 19, wherein the second stage excludes those observations that have zero residuals in the first-stage regression due to limited data availability.