SepTest (version 0.0.1)

random.shift: Apply a circular random shift to the temporal component of a spatio-temporal point pattern

Description

Performs a circular random shift of the temporal coordinate in a spatio-temporal point pattern. This operation preserves the spatial configuration while randomizing the temporal component under the assumption of temporal stationarity. The shift amount is drawn uniformly from \([0, 1]\) and applied modulo 1, ensuring that the time window is maintained. The resulting dataset can be used to construct null models for hypothesis testing of first-order separability or temporal independence.

Usage

random.shift(X, shifted_col = 3)

Value

A matrix or data frame (matching the input type) with the time column shifted modulo 1.

Arguments

X

A numeric matrix or data frame containing the spatio-temporal point pattern. Must include at least one numeric column representing time.

shifted_col

Integer index specifying which column to shift (typically the time coordinate). Default is 3.

Details

The circular random shift is a common resampling procedure for generating null models of temporal randomness while preserving the overall temporal marginal distribution and spatial structure.

For each dataset, a single uniform random shift value \(\Delta \sim \mathrm{Uniform}(0,1)\) is drawn and added to the temporal coordinate. The shifted times are then wrapped around the unit interval:

$$ t_i^{*} = (t_i + \Delta) \bmod 1, \quad i = 1, \dots, n. $$

References

Ghorbani, M., Vafaei, N., Dvořák, J., and Myllymäki, M. (2021). Testing the first-order separability hypothesis for spatio-temporal point patterns. Computational Statistics & Data Analysis, 161, 107245.

Examples

set.seed(123)
X <- cbind(runif(100), runif(100), runif(100))  # x, y, t
X_shifted <- random.shift(X)

# Compare original and shifted time values
head(X[,3])
head(X_shifted[,3])

# Verify shift visually
plot(X[, 3], type = "o", col = "blue", ylab = "Time", xlab = "Index",
     main = "Original vs Shifted Times")
lines(X_shifted[, 3], type = "o", col = "red")
legend("topright", legend = c("Original", "Shifted"),
       col = c("blue", "red"), lty = 1, pch = 1)