Price indexing

1. A computer-based method comprising performing, with one or more computers, the steps of:

representing transactions involving sales of real estate assets in a geographical region, as respective sets of data points associated with values of the real estate assets, the data points including transaction value information including price per unit area and transaction date for each transaction,

determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the value spectrum being a log-log spectrum of a number of sales in the geographical region on a given transaction date versus price per unit area, the probability density function for at least one of the components comprising a triple power law including a first power law, a second power law, and a third power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time, the first power law applying between a price per unit area a and a price per unit area b, the second power law applying between the price per unit area b and a price per unit area c, the third power law applying between the price per unit area c and a price per unit area d, wherein the triple power law comprises:

f

⁡

(

x

)

=

{

h

b

⁡

(

x

-

a

b

-

a

)

β

L

;

a

≤

x

≤

b

h

c

⁡

(

x

-

a

c

-

a

)

β

M

;

b

≤

x

≤

c

h

c

⁡

(

x

-

a

c

-

a

)

β

R

⁢

c

≤

x

≤

d

wherein h b is a height of the value spectrum at b, h c is a height of the value spectrum at c, β L is an exponent of the first power law, β M is an exponent of the second power law, β R is an exponent of the third power law; and

forming a daily index of values associated with the assets using at least one of the determined parameters, wherein for each day, the daily index provides a price per unit area for transactions involving real estate assets on said each day in the geographical region.

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 performing, with one or more computers, the steps of

representing transactions involving sales of real estate assets in a geographical region, as respective sets of data points associated with values of the real estate assets, the data points including transaction value information including price per unit area and transaction date for each transaction,

determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the value spectrum being a log-log spectrum of a number of sales in the geographical region on a given transaction date versus price per unit area, 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, wherein the power law comprises a triple power law including first power law, a second power law, and a third power law, the first power law applying between a price per unit area a and a price per unit area b, the second power law applying between the price per unit area b and a price per unit area c, the third power law applying between the price per unit area c and a price per unit area d, wherein the at least one parameter that characterizes its position but not its shape includes b, and wherein the parameters that characterize a shape of the probability density function but not its position include p, h c , β L and β M , and wherein the triple power law comprises:

f

⁡

(

x

)

=

s

⁢

{

x

′β

L

;

x

min

′

<

x

′

≤

1

h

c

⁡

(

x

′

p

)

β

M

;

1

<

x

′

<

p

h

c

⁡

(

x

′

p

)

β

R

;

p

≤

x

′

≤

x

max

′

where x′=x/b, x min /b, s is a constant, and x max ′=x max /b,

where c=pb, 1<p,

where x min is a minimum price per unit area value of the value spectrum, x max is a maximum price per unit area value of the value spectrum, h c is a height of the value spectrum at c, β L is an exponent of the first power law, β M is an exponent of the second power law, β R is an exponent of the third power law; and

forming a daily index of values associated with the assets using at least one of the determined parameters, wherein for each day, the daily index provides a price per unit area for transactions involving real estate assets on said each day in the geographical region.

6. The method of claim 5 in which there is only a single parameter that characterizes the position of the probability distribution function.

7. The method of claim 5 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.

8. A computer-based method comprising performing, with one or more computers, the steps of:

representing transactions involving sales of real estate assets in a geographical region, as respective sets of data points associated with values of the real estate assets, the data points including transaction value information including price per unit area and transaction date for each transaction,

determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the value spectrum being a log-log spectrum of a number of sales in the geographical region on a given transaction date versus price per unit area, the probability density function for at least one of the components comprising a triple power law including a first power law, a second power law, and a third power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time, the first power law applying between a price per unit area a and a price per unit area b, the second power law applying between the price per unit area b and a price per unit area c, the third power law applying between the price per unit area c and a price per unit area d, wherein a is defined as a minimum price per unit area value of the value spectrum x min , d is defined as a maximum price per unit area value of the value spectrum x max , and the triple power law comprises

f

⁡

(

x

)

=

{

h

b

⁡

(

x

b

)

β

L

;

x

min

≤

x

≤

b

h

c

⁡

(

x

c

)

β

M

;

b

≤

x

≤

c

h

c

⁡

(

x

c

)

β

R

;

⁢

c

≤

x

≤

x

max

wherein h b is a height of the value spectrum at b, h c is a height of the value spectrum at c, β L is an exponent of the first power law, β M is an exponent of the second power law, β R is an exponent of the third power law.

9. A computer-based method comprising performing, with one or more computers, the steps of:

representing transactions involving sales of real estate assets in a geographical region, as respective sets of data points associated with values of the real estate assets, the data points including transaction value information including price per unit area and transaction date for each transaction,

determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the value spectrum being a log-log spectrum of a number of sales in the geographical region on a given transaction date versus price per unit area, the probability density function for at least one of the components comprising a triple power law including a first power law, a second power law, and a third power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time, the first power law applying between a price per unit area a and a price per unit area b, the second power law applying between the price per unit area b and a price per unit area c, the third power law applying between the price per unit area c and a price per unit area d, wherein the triple power law comprises:

f

⁡

(

x

)

=

s

⁢

{

x

′β

L

;

x

min

′

<

x

′

≤

1

h

c

⁡

(

x

′

p

)

β

M

;

1

<

x

′

<

p

h

c

⁡

(

x

′

p

)

β

R

;

p

≤

x

′

≤

x

max

′

where x′=x/b, x min ′=x min /b, s is a constant, and x max ′=x max /b,

where c=pb, 1<p,

where is a minimum price per unit area value of the value spectrum, x max is a maximum price per unit area value of the value spectrum, h c is a height of the value spectrum at c, β L is an exponent of the first power law, β M is an exponent of the second power law, β R is an exponent of the third power law.