gen_ar1blocks: Generate AR(1) Blocks Process

Description Usage Arguments Value Note Author(s) Examples

View source: R/avns.R

Description

This function allows us to generate a non-stationary AR(1) blocks process.

Usage

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gen_ar1blocks(phi, sigma2, n_total, n_block, scale = 10, 
title = NULL, seed = 135, ...)

Arguments

phi

A double value for the autocorrection parameter phi.

sigma2

A double value for the variance parameter sigma^2.

n_total

An integer indicating the length of the whole AR(1) blocks process.

n_block

An integer indicating the length of each block of the AR(1) blocks process.

scale

An integer indicating the amount of decomposition performed at each level. The default value is 10.

title

A string of the time series data name.

seed

An integer set for simulation replication purpose.

...

Additional parameters.

Value

A vector containing the AR(1) blocks process.

Note

This function helps generate a non-stationary process example, AR(1) blocks, whose theoretical maximum overlapping allan variance (MOAV) is different and can be distinguished from the theoretical MOAV of a stationary AR(1) process. This difference of allan variance between stationary and non-stationary processes is proved to be able to be captured by the calculation of theoretical allan variance raised 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.

Author(s)

Yuming Zhang and Haotian Xu

Examples

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Xt = gen_ar1blocks(phi = 0.9, sigma2 = 1, 
n_total = 1000, n_block = 10, scale = 100)
plot(Xt)

Yt = gen_ar1blocks(phi = 0.5, sigma2 = 5, n_total = 800, 
n_block = 20, scale = 50)
plot(Yt)

SMAC-Group/simts documentation built on Jan. 30, 2018, 6:39 a.m.