notrend_test: Sieve Bootstrap Based Test for the Null Hypothesis of no...

In funtimes: Functions for Time Series Analysis

Sieve Bootstrap Based Test for the Null Hypothesis of no Trend

Description

A combination of time series trend tests for testing the null hypothesis of no trend, versus the alternative hypothesis of a linear trend (Student's t-test), or monotonic trend (Mann–Kendall test), or more general, possibly non-monotonic trend (WAVK test).

Usage

notrend_test(
  x,
  B = 1000,
  test = c("t", "MK", "WAVK"),
  ar.method = "HVK",
  ar.order = NULL,
  ic = "BIC",
  factor.length = c("user.defined", "adaptive.selection"),
  Window = NULL,
  q = 3/4,
  j = c(8:11)
)

Arguments

x	a vector containing a univariate time series. Missing values are not allowed.
B	number of bootstrap simulations to obtain empirical critical values. Default is 1000.
test	trend test to implement: Student's t-test ("t", default), Mann–Kendall test ("MK"), or WAVK test ("WAVK", see WAVK).
ar.method	method of estimating autoregression coefficients. Default "HVK" delivers robust difference-based estimates by \insertCiteHall_VanKeilegom_2003;textualfuntimes. Alternatively, options of ar function can be used, such as "burg", "ols", "mle", and "yw".
ar.order	order of the autoregressive model when ic = "none", or the maximal order for IC-based filtering. Default is round(10*log10(length(x))), where x is the time series.
ic	information criterion used to select the order of autoregressive filter (AIC of BIC), considering models of orders p= 0,1,...,ar.order. If ic = "none", the AR(p) model with p= ar.order is used, without order selection.
factor.length	method to define the length of local windows (factors). Used only if test = "WAVK". Default option "user.defined" allows to set only one value of the argument Window. The option "adaptive.selection" sets method = "boot" and employs heuristic m-out-of-n subsampling algorithm \insertCiteBickel_Sakov_2008funtimes to select an optimal window from the set of possible windows length(x)*q^j whose values are mapped to the largest previous integer and greater than 2. Vector x is the time series tested.
Window	length of the local window (factor), default is round(0.1*length(x)). Used only if test = "WAVK". This argument is ignored if factor.length = "adaptive.selection".
q	scalar from 0 to 1 to define the set of possible windows when factor.length = "adaptive.selection". Used only if test = "WAVK". Default is 3/4. This argument is ignored if factor.length = "user.defined".
j	numeric vector to define the set of possible windows when factor.length = "adaptive.selection". Used only if test = "WAVK". Default is c(8:11). This argument is ignored if factor.length = "user.defined".

Details

This function tests the null hypothesis of no trend versus different alternatives. To set some other shape of trend as the null hypothesis, use wavk_test. Note that wavk_test employs hybrid bootstrap, which is an alternative to the sieve bootstrap employed by the current function.

Value

A list with class "htest" containing the following components:

method	name of the method.
data.name	name of the data.
statistic	value of the test statistic.
p.value	p-value of the test.
alternative	alternative hypothesis.
estimate	list with the following elements: employed AR order and estimated AR coefficients.
parameter	window that was used in WAVK test, included in the output only if test = "WAVK".

Author(s)

Vyacheslav Lyubchich

References

\insertAllCited

See Also

ar, HVK, WAVK, wavk_test, vignette("trendtests", package = "funtimes")

Examples

## Not run: 
# Fix seed for reproducible simulations:
set.seed(1)

#Simulate autoregressive time series of length n with smooth linear trend:
n <- 200
tsTrend <- 1 + 2*(1:n/n)
tsNoise <- arima.sim(n = n, list(order = c(2, 0, 0), ar = c(0.5, -0.1)))
U <- tsTrend + tsNoise
plot.ts(U)

#Use t-test
notrend_test(U)

#Use Mann--Kendall test and Yule-Walker estimates of the AR parameters
notrend_test(U, test = "MK", ar.method = "yw")

#Use WAVK test for the H0 of no trend, with m-out-of-n selection of the local window:
notrend_test(U, test = "WAVK", factor.length = "adaptive.selection")
# Sample output:
##	Sieve-bootstrap WAVK trend test
##
##data:  U
##WAVK test statistic = 21.654, moving window = 15, p-value < 2.2e-16
##alternative hypothesis: (non-)monotonic trend.
##sample estimates:
##$AR_order
##[1] 1
##
##$AR_coefficients
##    phi_1
##0.4041848

## End(Not run)

funtimes documentation built on March 31, 2023, 7:35 p.m.