Price Indexing

Abstract

Among other things, transactions involving assets (for example, real estate assets) that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. The parameters do not include an offset parameter representing possible shifts in the value spectrum over time. An index is formed of values associated with the assets using at least one of the determined parameters. The parameters may include at least one shape parameter determined by fitting data over multiple days and at least one position parameter determined by fitting data either over a single day or multiple days, the probability density function for at least one of the components comprising a power law. A subindex is formed of values of the assets that are associated with a subset of fewer than all of the data points of the set, the subset being selected to represent a range of one or more of a demographic, geographic, value, or other attribute of the transactions.

1 . A computer-based method comprising
 representing transactions involving assets that share a common characteristic, as respective data points associated with values of the assets, the data points including transaction value information,   determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time, and   forming an index of values associated with the assets using at least one of the determined parameters.   
   
   
       2 . The computer-based method of  claim 1  in which data points are excluded that are associated with values that are outside defined cutoffs. 
   
   
       3 . The computer-based method of  claim 2  in which the defined cutoffs include a lower cutoff that is a function of a minimum value of any of the data points. 
   
   
       4 . The computer-based method of  claim 2  in which the defined cutoffs include an upper cutoff that corresponds to a maximum value of any of the data points. 
   
   
       5 . A computer-based method comprising
 representing transactions involving assets that share a common characteristic, as respective data points associated with values of the assets, the data points including transaction value information,   determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, and   providing a median derived from the fitted probability density function as an index of values associated with the assets using at least one of the determined parameters.   
   
   
       6 . A computer-based method comprising
 representing transactions involving assets that share a common characteristic, as respective data points associated with values of the assets, the data points including transaction value information,   determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters being separated into parameters that characterize a shape of the probability density function but not its position and at least one parameter that characterizes its position but not its shape, and   forming an index of values associated with the assets using at least one of the determined parameters.   
   
   
       7 . The method of  claim 6  in which there is a single parameter that characterizes the position of the probability distribution function. 
   
   
       8 . The method of  claim 6  in which the shape parameters are fit using data for many days and the single position parameter is fit using data for a single day. 
   
   
       9 . A computer-based method comprising
 representing transactions involving assets that share a common characteristic, as a set of respective data points associated with values of the assets, the data points including transaction value information,   the set of data points sufficing to form an index of the values of the assets, using parameters that are determined by fitting probability density functions to at least one component of a value spectrum of the data points, the parameters including at least one shape parameter determined by fitting data over multiple days and at least one position parameter determined by fitting data either over a single day or multiple days, the probability density function for at least one of the components comprising a power law, and   forming a subindex of values of the assets that are associated with a subset of fewer than all of the data points of the set, the subset being selected to represent a range of one or more of a demographic, geographic, value, or other attribute of the transactions.   
   
   
       10 . The method of  claim 9  in which the subindex is formed by determining parameters that fit probability density functions to at least one component of a value spectrum of the subset of data points. 
   
   
       11 . The method of  claim 9  in which the subindex comprises an approximation based on scaling the index of the set by a ratio of medians of, respectively, the subset of values associated with the subindex and the set of values associated with the index. 
   
   
       12 . The method of  claim 9  in which the subindex comprises an approximation based on scaling the index of the set by a ratio of the means of, respectively, the subset of values associated with the subindex and the set of values associated with the index.