Repeat Sales Price Index Computation via Direct Matrix Calculation
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Solution Overview
Problem
Existing methods for determining real estate price indices using repeat sales data, such as the BMN and Case-Shiller models, require extensive calculations and significant computing power, leading to lengthy processing times.
Innovation Solution
A method that calculates the X′X and X′Y matrices directly without constructing the large X matrix, and uses a three-stage regression procedure to estimate dispersion functions, reducing the number of calculations and improving computational efficiency by eliminating multiplications by zero, allowing for efficient estimation of real estate price indices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the traditional repeat sales model (BMN or Case-Shiller) is used to estimate real estate price indices, then the estimation accuracy is maintained, but the computational time and processing power requirements increase significantly
Solution Approach 1:
The patent extracts and eliminates the unnecessary X matrix construction step from the traditional calculation process. By directly computing the X'X and X'Y matrices from the repeat sales data without forming the intermediate X matrix, the method removes computational redundancy while preserving the statistical accuracy of the price index estimation.
Solution Approach 2:
The patent segments the computational process into distinct phases: data preparation, direct matrix computation, and price index calculation. This segmentation allows for optimized computation at each stage, particularly in the direct matrix computation phase where the X'X and X'Y matrices are calculated efficiently without constructing the full X matrix, thereby reducing overall processing time.
2Quantity of substance
If the traditional repeat sales model is implemented with large datasets, then comprehensive price index coverage is achieved, but the computing power requirements and computational complexity increase
Solution Approach 1:
The patent extracts the essential computational elements (X'X and X'Y matrices) directly from the data without constructing the intermediate X matrix. This extraction approach reduces computational complexity while maintaining the ability to process large datasets, as the method only computes the necessary matrix products rather than manipulating the full N×T design matrix.
Solution Approach 2:
The patent changes the computational parameters by working directly with the aggregated matrix forms (X'X and X'Y) rather than the individual matrix elements. This parameter transformation reduces the computational burden from O(N×T) to O(N+T), enabling efficient processing of large datasets with numerous properties and time periods.
3Reliability
If the traditional method constructs the full X matrix for calculation, then the complete data structure is preserved, but the computational burden and memory requirements increase
Solution Approach 1:
The patent extracts only the necessary computational components (the products X'X and X'Y) directly from the data relationships without constructing the intermediate X matrix. This approach preserves the essential data structure information needed for accurate price index estimation while eliminating the computational energy required to create and manipulate the full N×T matrix.
Solution Approach 2:
The patent performs preliminary aggregation of the data into the X'X and X'Y matrix forms before conducting the regression analysis. This preliminary action consolidates the computational work into more efficient operations, reducing memory requirements and energy consumption while maintaining data integrity for the price index calculation.
Data Source
AI summary
The present invention relates to an efficient computer implemented method and system for generating a home price index based on a repeat sales model by calculating the time-dimension frequency matrices (X′X and X′Ω−1X) and price change matrices (X′Y and X′Ω−1Y) directly without the need to calculate the big X and Y matrices at the dimension of the number of repeat sales. The inventive method may further be used to estimate indices for multiple geographic levels without processing an entire data set to estimate the price indices for each geographic level.