This function allows us to generate a non-stationary AR(1) block process.
gen_ar1blocks(phi, sigma2, n_total, n_block, scale = 10, title = NULL, seed = 135, ...)
double value for the autocorrection parameter \(\phi\).
double value for the variance parameter \(\sigma ^2\).
integer indicating the length of the simulated AR(1) block process.
integer indicating the length of each block of the AR(1) block process.
integer indicating the number of levels of decomposition. The default value is 10.
string indicating the name of the time series data.
integer defined for simulation replication purposes.
vector containing the AR(1) block process.
This function generates a non-stationary AR(1) block process whose theoretical maximum overlapping allan variance (MOAV) is different from the theoretical MOAV of a stationary AR(1) process. This difference in the value of the allan variance between stationary and non-stationary processes has been shown through the calculation of the theoretical allan variance given in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al. (IEEE Signal Processing Letters, 2017), preprint available: https://arxiv.org/abs/1702.07795.