# notrend_test: Sieve Bootstrap Based Test for the Null Hypothesis of no... In funtimes: Functions for Time Series Analysis

 notrend_test R Documentation

## 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 (Mannâ€“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",
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), Mannâ€“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

`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.