TED (version 1.0)

noiseTests: Perform noise tests for a time series

Description

This function performs noise tests on the sliding subsequences extracted from a time series.

Usage

noiseTests(x, w, noiseType = c("white", "red"), parallel = FALSE)

Arguments

x

a vector or a time series.

w

a scalar specifying the size of the sliding window.

noiseType

background noise assumed for x. There are two options: ``white' or ``red' .

parallel

logical, if TRUE then codes are executed in parallel using the foreach package. The user must register a parallel backend to use by the doMC package.

Value

• test p value series for the time series x.

Details

When using this function, the user needs to choose the background noise type via noiseType according to the application context. In atmospheric turbulence, red noise is used. We first use the Phillips-Perron (PP) Unit Root Test to test for the unit root process. For the stationary processes, red noise tests are performed to test for events. For those cases tested to be unit root processes, we have to take into consideration a special situation when there is a structural break in the process. The reason comes from the difficulty for PP test to distinguish random walk processes from a stationary process contaminated by a structural break, both of which result in non-rejection of the null hypothesis. Random-walk processes are not considered as events since they are known to be brownian noise, but stationary processes with structure breaks are, so it is essential to distinguish them. To this end, an additional test called Zivot & Andrews (ZA) unit root test is introduced.This test allows for a structural break in either the intercept or in the slope of the trend function of the underlying series. Rejection of the null hypothesis indicates a potential event (stationary process with a structural break). Random walk processes result in non-rejection of the null hypothesis.

References

Pierre Perron (1998). Trends and random walks in macroeconomic time series: Further evidence from a new approach. Journal of economic dynamics and control, 12(2), 297-332. http://dx.doi.org/10.1016/0304-3932(82)90012-5.

Eric Zivot and Donald W K Andrews (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 20(1), 25-44. http://dx.doi.org/10.1198/073500102753410372.

Yanfei Kang, Danijel Belusic and Kate Smith-Miles (2014). Detecting and Classifying Events in Noisy Time Series. J. Atmos. Sci., 71, 1090-1104. http://dx.doi.org/10.1175/JAS-D-13-0182.1.

See Also

eventExtraction, plotevents

Examples

set.seed(123)
n=128
types=c('box','rc','cr','sine')
shapes=matrix(NA,20,n)
for (i in 1:20){
  shapes[i,]=cbfs(type=types[sample(1:4,1)])
}
whitenoise=ts2mat(rnorm(128*20),128)
# generate x which randomly combine the four types of events with each two of them
# seperated by noise
x=c(t(cbind(shapes,whitenoise)))
plot(x,ty='l')
w=128
# execute loops sequentially
tests=noiseTests(x,w,'white',parallel=FALSE)
# execute loops in parallel using doMC package (for non-Windows users)
# tests=noiseTests(x,w,'white',parallel=TRUE)