multiscale_test: Carries out the multiscale test given that the values the...
In MSinference: Multiscale Inference for Nonparametric Time Trend(s)

multiscale_test

R Documentation

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.