Package 'SimIndep'

Title: WISE: a Weighted Similarity Aggregation Test for Serial Independence
Description: A fast implementation of the weighted information similarity aggregation (WISE) test for detecting serial dependence, particularly suited for high-dimensional and non-Euclidean time series. Includes functions for constructing similarity matrices and conducting hypothesis testing. Users can use different similarity measures and define their own weighting schemes. For more details see Q Zhu, M Liu, Y Han, D Zhou (2025) <doi:10.48550/arXiv.2509.05678>.
Authors: Qihua Zhu [aut, cre], Mingshuo Liu [aut], Yuefeng Han [aut], Doudou Zhou [aut]
Maintainer: Qihua Zhu <[email protected]>
License: GPL-3
Version: 0.1.2
Built: 2026-05-13 07:35:10 UTC
Source: https://github.com/cran/SimIndep

Help Index

Calculate an n by n similarity matrix

Description

Returns an n by n similarity matrix.

Usage

wise_sim(data, measure = "distance", metric = "manhattan", k = NULL)

Arguments

data

an n by p data matrix, with n being the sample size and p being the dimension.
measure

the similarity measure: "distance" for distance-based measure; "graph" for k-nearest neighbor graph-based measure. The default is "distance".
metric

character string specifying the distance metric or graph weight. "manhattan" for Manhattan distance (default), "euclidean" for Euclidean distance.
k

the Number of nearest neighbors used in k-nearest neighbor graph. k = floor(sqrt(n)) if not specified.

Value

an n by n similarity matrix.

Examples

X <- matrix(rnorm(100), nrow = 10)
wise_sim(X, measure = "distance", metric = "manhattan")

Conducts the serial independence test (WISE) based on a similarity matrix

Description

Returns the p-value of WISE, the squared test statistic, and related quantities (the chi-square critical value, permutation mean, permutation variance).

Usage

wise_test(sim, dependence = "proximity", alpha = 0.05, weight = NULL, h = 4)

Arguments

sim

an n by n similarity matrix, typically generated from wise_sim().
dependence

design for the weight matrix W: if "proximity", Wij=(1/(∣i−j∣2+1))−1W_{ij} = (1 / (|i - j|^2 + 1))-1; if "periodicity", then Wij=∣cos(∣i−j∣π/h)∣−1W_{ij} = |cos(|i-j|\pi/h)|-1; If "customized", users should input their self-defined weight matrix through the parameter "weight". The default is "proximity"
alpha

the nominal significance level (default is 0.05).
weight

an n by n weight matrix with zero diagonal (only used if dependence = "customized").
h

the estimated periodicity (default is 4). The parameter is used only if dependence = "periodicity".

Value

A list containing:

p_value

The p-value of the test.
test_statistic_sq

The value of the squared test statistic.
critical_value

The chi-square critical value at the given significance level.
t

The unstandardized test statistic.
permutation_mean

The mean of t under the permutation null.
permutation_variance

The variance of t under the permutation null.

Examples

library(MASS)
n <- 100
p <- 50

# Example 1: iid data
set.seed(123)
data_iid <- mvrnorm(n = n, mu = rep(0, p) , Sigma = diag(p))
wise_test(
 wise_sim(data_iid, measure = "distance", metric = "manhattan"),
 dependence = "proximity",
 alpha = 0.05
)

# Example 2: AR(1)
set.seed(123)
data_ar <- matrix(0, nrow = n, ncol = p)
error <- mvrnorm(n = n, mu = rep(0,p), Sigma = diag(p))
data_ar[1,] <- error[1,]
phi <- 0.1 * diag(p)
for (t in 2:n) {
  data_ar[t, ] <- phi %*% data_ar[t - 1, ] + error[t,]
}
wise_test(
 wise_sim(data_ar, measure = "distance", metric = "manhattan"),
 dependence = "proximity",
 alpha = 0.05
)

# Example 3: NMA(2)
set.seed(123)
data_nma <- matrix(0, nrow = n, ncol = p)
error <- mvrnorm(n = n, mu = rep(0,p), Sigma = diag(p))
data_nma[1:2, 1:p] <-error[1:2,1:p]
for (i in 3:n) {
  data_nma[i, ] <- error[i,]*error[i-1,]*error[i-2,]
}
wise_test(
 wise_sim(data_nma, measure = "distance", metric = "manhattan"),
 dependence = "proximity",
 alpha = 0.05
)