pvarPseudoMonotonic: p-variation for a special form of `x`

Description

Calculates p-variation of special form of function (for a part of vector x, that satisfy the requirements). It is an inner function and should not be applied by users.

Usage

pvarPseudoMonotonic(x, p, a = 1, b = length(x), sizeN = 1)

Arguments

a numeric vector.

a number.

a number indicating the index the first member of subset of x that should be analysed.

a number indicating the index the last member of subset of x that should be analysed.

sizeN

a number indicating the length of 'small' interval. See pvar.

Value

The list:
ChBindicator of p-variation partition.
pvarVecThe vector of p-variations between partition points. It has meaning only for those points that ChB=TRUE, elsewier the numbers are meaningless.

Details

This function is applicable only for special form of sample. The requirements for the subset: 1. it should be pseudo-monotonic. i.e. min and max should be in the end points of the vector. 2. removed all monotonic points.

Examples

Run this code

############################################################
xx = c(0.9552822,  0.8317665,  0.9347037,  0.3861130,  0.6546701,  0.3600638,
	0.6767309,  0.1090384,  0.4675789,  0.3223871,  0.4312971,  0.3514759,
	0.4097339,  0.2601273,  0.4978533,  0.3255348,  0.7301583,  0.5317979,
	0.6366720,  0.5096362,  0.8123783, -0.8443095)
pvM = pvarPseudoMonotonic(x = xx, p = 2, a = 1, b = 22, sizeN = 7)
sum(pvM$pvarVec[pvM$ChB]) 
pvar(xx, 2)		#gives the same result.
		
############################################################
set.seed(51)
### get x
x = rbridge(1, 1000)		
### remuves monotonic points
xx = x[ChangePointsId(x)]
### splits into pseudo-monotonic parts
s = SplitByExtremum(xx)
### for parts we can calculate p-variaiotn the partitinio
pvM = pvarPseudoMonotonic(x = xx, p = 2, a = s[4], b = s[5], sizeN = 1)
sum(pvM$pvarVec[pvM$ChB]) 
pvar(xx[s[4]:s[5]], 2)		# the same result

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