pvar (version 1.0.9)

PvarBreakTest: Structural break test

Description

This function performs structural break test based on p-variation.

Usage

PvarBreakTest(x, TimeLabel = as.vector(time(x)), alpha = 0.05, FullInfo = TRUE) 

## S3 method for class 'PvarBreakTest':
summary(object, ...)

## S3 method for class 'PvarBreakTest':
plot(x, main1 = "Data", main2 = "Bridge transformation", 
    ylab1 = x$dname, ylab2 = "BridgeT(" \%.\% x$dname \%.\% ")", sub2=NULL, 
	col.PP = 3, cex.PP = 0.5, col.BP = 2, cex.BP = 1, cex.DP = 0.5, ...)
	
BreakPoints(object)

Arguments

x

a numeric vector of data values or an object of class pvar.

TimeLabel

numeric, a time index of x. Used only for plotting.

alpha

a small number greater then 0. It indicates the significant level of the test.

FullInfo

logical. If TRUE (the default) the function will return an object of the class PvarBreakTest that saves all useful information. Otherwise only the statistics will by returned.

object

the object of the class PvarBreakTest.

main1

the main parameter of the data graph.

main2

the main parameter of the Bridge transformation graph.

ylab1

the ylab parameter of the data graph.

ylab2

the ylab parameter of the Bridge transformation graph.

sub2

the sub parameter of the Bridge transformation graph. By default it reports the number of break points.

cex.DP

the cex of data points.

col.PP

the color of partition points.

cex.PP

the cex of partition points.

col.BP

the color of break points.

cex.BP

the cex of break points.

...

further arguments.

Value

• If FullInfo=TRUE then function returns an object of the class PvarBreakTest. It is the list that contains:
• Stat
  a value of statistics (p-variation of transformed data).
• CriticalValue
  the critical value of the test according to significant level.
• alpha
  the significant level.
• p.value
  approximate p-value.
• reject
  logical. If TRUE, the H0 was rejected.
• dname
  the name of data vector.
• p
  the power in p-variation calculus. The test performs only with the p=4.
• x
  a vector of original data.
• y
  a vector of transformed data (y=BridgeT(x)).
• Timelabel
  time label of x. Used only for ploting.
• BreakPoints
  the indexes of break points suggestion.
• Partition
  a vector of indexes that indicates the partition of y that achieves the p-variation maximum.
• SplitPoints
  the indexes of y that indicates the points where y might be spited and analysed separately.
• info
  the list of extra information about the calculation.
• The info is a list that contains:
• PartitionN
  the length of the partition.
• AnalysedPointsN
  the length of the prepared y, i.e. after removing monotonic points and meaningless pints in small intervals.
• SegmentsN
  the number of segments the y was splinted.
• sizeN
  the inner sizeN parameter
• TakesTime
  the total time taken for calculation.

Details

Lets x be a data that should be tested of structial breaks. Then the p-variation of the BridgeT(x) with p=4 is the test's statistics. The quantiles of H0 distribution is based on Monte-Carlo simulation of 140 millions iterations. The test is reliable then length(x) is between 100 and 10000. The test might work with other lengths too, but it is not tested well. The test will not compute then length(x)<20< code="">.

References

[1] R. Norvaisa, A. Rackauskas. Convergence in law of partial sum processes in p-variation norm. Lth. Math. J., 2008., Vol. 48, No. 2, 212-227.

See Also

Tests statistics is pvar of the data BridgeT(x)(see BridgeT) with (p=4). The critical value and the approximate p-value of the test might by found by functions PvarQuantile and PvarPvalue.

Examples

set.seed(1)
# x contains 4 blocks with diferent mean.
x = c(rnorm(250,0),rnorm(250,0.3), rnorm(250,0), rnorm(250,0.3))

# run test
PVBT = PvarBreakTest(x); PVBT
PVBTSummary = summary(PVBT); PVBTSummary

# the plot of the test
plot(PVBT)

# the sugestion of break points. True points are 250, 500 and 750
BreakPoints(PVBT)

# if we only interesting in main numbers.
PvarBreakTest(x, FullInfo = FALSE)

##################################
# the statistic maigth by find with pvar
Y = BridgeT(x)
pv = pvar(Y, p = 4)
pv

# critical value
PvarQuantile(n=length(x), prob = c(0.95))
# apricimal p-value
PvarPvalue(n=length(x), stat=pv$value)