Download or view correlation.frink in plain text format
/** This library calculates the correlation between items in lists. */
/** This calculates the autocorrelation of a single numeric list, that is, it
identifies the periods at which sequences appear to repeat. The result
is a sorted list containing pairs of [offset, correlation] with the terms
of strongest correlation being first in the list.
If you just want a single most likely autcorrelation period, it is found at
result@0@0
see correlationTest.frink for an example of using it.
*/
autocorrelation[list] :=
{
results = new array
size = length[list]
average = sum[list] / size
// Scale the list around its average
normalizedList = new array[size+1]
denom = 0
for i = 1 to size
{
term = list@(i-1) - average
normalizedList@i = term
denom = denom + term^2
}
for offset=1 to size
{
sum = 0
for i = 1 to size-offset
sum = sum + normalizedList@i * normalizedList@(i+offset)
results.push[[offset, sum/denom]]
}
return sort[results, byColumn[1]]
}
/** This is the partial autocorrelation of a series. The partial
autocorrelation is useful because it eliminates the effects of smaller
offsets. For example, the partial autocorrelation at offset k is the
autocorrelation not accounted for by offsets 1 through k-1. That means
that, for example, if a sequence has a perfect autocorrelation with a
offset of 5, this will *not* display any partial autocorrelation at
10, 15, etc.
For equation:
https://support.minitab.com/en-us/minitab/20/help-and-how-to/statistical-modeling/time-series/how-to/autocorrelation/methods-and-formulas/methods-and-formulas/
*/
partialAutocorrelation[list] :=
{
results = new array
size = length[list]
average = sum[list] / size
// Scale the list around its average
normalizedList = new array[size+1]
denom = 0
for i = 1 to size
{
term = list@(i-1) - average
normalizedList@i = term
denom = denom + term^2
}
for offset=1 to size
{
sum = 0
for t = offset+1 to size-offset
sum = sum + normalizedList@(t-offset) * normalizedList@(t)
results.push[[offset, sum/denom]]
}
return sort[results, byColumn[1]]
}
Download or view correlation.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 18 hours, 20 minutes ago.