WAVK Trend Test
Nonparametric test to detect (non-)monotonic parametric trends in time series if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="@based on@Lyubchich_etal_2013_wavk",package="funtimes",cached_env=.Rdpack.currefs) .
wavk_test( formula, factor.length = c("user.defined", "adaptive.selection"), Window = NULL, q = 3/4, j = c(8:11), B = 1000, method = c("boot", "asympt"), ar.order = NULL, ar.method = "HVK", ic = "BIC", out = FALSE )
formula: an object of class "formula", specifying the form of the parametric time trend to be tested. Variable should be used to specify the form, where is specified within the function as a regular sequence on the interval (0,1]. See Examples.
factor.length: method to define the length of local windows (factors). Default option
"user.defined" allows setting only one value of the argument Window. The option "adaptive.selection" sets method = "boot"
and employs heuristic -out-of- subsampling algorithm if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Bickel_Sakov_2008",package="funtimes",cached_env=.Rdpack.currefs) 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)), where x is the time series tested. 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". Default is . This argument is ignored if
factor.length = "user.defined".
j: numeric vector to define the set of possible windows when factor.length = "adaptive.selection". Default is c(8:11). This argument is ignored if
factor.length = "user.defined".
B: number of bootstrap simulations to obtain empirical critical values. Default is 1000.
method: method of obtaining critical values: from asymptotical ("asympt") or bootstrap ("boot") distribution. If factor.length = "adaptive.selection" the option "boot" is used.
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.
ar.method: method of estimating autoregression coefficients. Default "HVK" delivers robust difference-based estimates by if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Hall_VanKeilegom_2003;textual",package="funtimes",cached_env=.Rdpack.currefs) . Alternatively, options of ar function can be used, such as "burg", "ols", "mle", and "yw".
ic: information criterion used to select the order of autoregressive filter (AIC of BIC), considering models of orders 0,1,...,ar.order. If ic = "none", the AR() model with ar.order is used, without order selection.
out: logical value indicates whether the full output should be shown. Default is FALSE.
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: -value of the test.
alternative: alternative hypothesis.
parameter: window that was used.
estimate: list with the following elements: estimated trend coefficients; user-defined or IC-selected AR order; estimated AR coefficients; and, if factor.length = "adaptive.selection", test results for all considered windows.
See more details in if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Lyubchich_Gel_2016_synchronism;textual",package="funtimes",cached_env=.Rdpack.currefs)
and if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Lyubchich_2016_trends;textual",package="funtimes",cached_env=.Rdpack.currefs) .
# Fix seed for reproducible simulations: set.seed(1) #Simulate autoregressive time series of length n with smooth quadratic trend: n <- 100 tsTrend <- 1 + 2*(1:n/n) + 4*(1:n/n)^2 tsNoise <- arima.sim(n = n, list(order = c(2, 0, 0), ar = c(-0.7, -0.1))) U <- tsTrend + tsNoise plot.ts(U) #Test H0 of a linear trend, with m-out-of-n selection of the local window: ## Not run: wavk_test(U ~ t, factor.length = "adaptive.selection") ## End(Not run) # Sample output: ## Trend test by Wang, Akritas, and Van Keilegom (bootstrap p-values) ## ##data: U ##WAVK test statistic = 5.3964, adaptively selected window = 4, p-value < 2.2e-16 ##alternative hypothesis: trend is not of the form U ~ t. #Test H0 of a quadratic trend, with m-out-of-n selection of the local window #and output of all results: ## Not run: wavk_test(U ~ poly(t, 2), factor.length = "adaptive.selection", out = TRUE) ## End(Not run) # Sample output: ## Trend test by Wang, Akritas, and Van Keilegom (bootstrap p-values) ## ##data: U ##WAVK test statistic = 0.40083, adaptively selected window = 4, p-value = 0.576 ##alternative hypothesis: trend is not of the form U ~ poly(t, 2). ##sample estimates: ##$trend_coefficients ##(Intercept) poly(t, 2)1 poly(t, 2)2 ## 3.408530 17.681422 2.597213 ## ##$AR_order ##[1] 1 ## ##$AR_coefficients ## phi_1 ##[1] -0.7406163 ## ##$all_considered_windows ## Window WAVK-statistic p-value ## 4 0.40083181 0.576 ## 5 0.06098625 0.760 ## 7 -0.57115451 0.738 ## 10 -1.02982929 0.360 # Test H0 of no trend (constant trend) using asymptotic distribution of statistic. wavk_test(U ~ 1, method = "asympt") # Sample output: ## Trend test by Wang, Akritas, and Van Keilegom (asymptotic p-values) ## ##data: U ##WAVK test statistic = 25.999, user-defined window = 10, p-value < 2.2e-16 ##alternative hypothesis: trend is not of the form U ~ 1.
if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)
ar, HVK, WAVK, sync_test, vignette("trendtests", package = "funtimes")
Yulia R. Gel, Vyacheslav Lyubchich, Ethan Schaeffer
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