multiscale_test: Carries out the multiscale test given that the values the...

In marina-khi/multiscale: Multiscale Inference for Nonparametric Time Trend(s)

Carries out the multiscale test given that the values the estimatates of long-run variance have already been computed.

Description

Carries out the multiscale test given that the values the estimatates of long-run variance have already been computed.

Usage

multiscale_test(
  data,
  sigma = 1,
  sigma_vec = 1,
  n_ts = 1,
  grid = NULL,
  ijset = NULL,
  alpha = 0.05,
  sim_runs = 1000,
  deriv_order = 0,
  correction = TRUE,
  epidem = FALSE
)

Arguments

data	Vector (in case of n_ts = 1) or matrix (in case of n_ts > 1) that contains (a number of) time series that needs to be analyzed. In the latter case, each column of the matrix must contain one time series.
sigma	The estimator of the square root of the long-run variance \sigma in case of n_ts = 1, or the estimator of the overdispersion parameter \sigma in case of n_ts > 1 and epidemic = TRUE.
sigma_vec	Vector that consists of estimators of the square root of the long-run variances \sigma_i in case of n_ts > 1 and epidemic = FALSE.
n_ts	Number of time series analysed. Default is 1.
grid	Grid of location-bandwidth points as produced by the functions construct_grid or construct_weekly_grid, it is a list with the elements 'gset', 'bws', 'gtype'. If not provided, then the defalt grid is used. For the construction of the default grid, see construct_grid.
ijset	In case of multiple time series (n_ts > 1), we need to know which pairs of time series to compare. This matrix consists of all pairs of indices (i, j) that we want to compare. If not provided, then all possible pairwise comparison are performed.
alpha	Significance level. Default is 0.05.
sim_runs	Number of simulation runs to produce quantiles. Default is 1000.
deriv_order	In case of a single time series, this denotes the order of the derivative of the trend that we estimate. Default is 0.
correction	Logical variable, TRUE (by default) is we are using a_k and b_k.
epidem	Logical variable, TRUE if we are using dealing with epidemic time trends. Default is FALSE.

Value

In case of n_ts = 1, the function returns a list with the following elements:

testing_result	A string that contains the result of the testing: either the null hypothesis is rejected or not, what is the confidence level and what is value of the test statistic.
quant	Quantile that was used for testing calculated from the Gaussian distribution.
statistics	Value of the multiscale statistics.
test_matrix	Matrix of the test results for the multiscale test defined in Khismatullina and Vogt (2019). The matrix is coded as follows: test_matrix[i,j] = -1: test rejects the null for the j-th location u and the i-th bandwidth h and indicates a decrease in the trend; test_matrix[i,j] = 0: test does not reject the null for the j-th location u and the i-th bandwidth h; test_matrix[i,j] = 1: test rejects the null for the j-th location u and the i-th bandwidth h and indicates an increase in the trend; test_matrix[i,j] = 2: no test is carried out at j-th location u and i-th bandwidth h (because the point (u, h) is excluded from the grid as specified by the 'deletions' option in the function construct_grid) .
gset_with_vals	A matrix that contains the values of the normalised kernel averages and test results for each pair of location-bandwidth with the corresponding location and bandwidth.

In case of n_ts > 1, the function returns a list with the following elements:

quant	Quantile that was used for testing calculated from the gaussian distribution.
statistics	Value of the multiscale statistics.
stat_pairwise	Matrix of the values of the pairwise statistics.
ijset	The matrix that consists of all pairs of indices (i, j) that we compared. The order of these pairs corresponds to the order in the list gset_with_vals.
gset_with_vals	A list of matrices, each matrix corresponding to a specific pairwise comparison. The order of the list is determined by ijset. Each matrix contains the values of the normalisedkernel averages for each pair of location-bandwidth with the corresponding location and bandwidth.

marina-khi/multiscale documentation built on Jan. 15, 2025, 7:28 a.m.