vse4ts: Identify Memory Patterns in Time Series Using Variance Scale Exponent

Description

Methods for calculating the variance scale exponent to identify memory patterns in time series data. Includes tests for white noise, short memory, and long memory. See Fu, H. et al. (2018) doi:10.1016/j.physa.2018.06.092.

Author(s)

Maintainer: Mengyang Zheng mengyang.zheng@outlook.com

Authors:

• Hui Fu hui_fu@hotmail.com

See Also

Useful links:

• https://z-my-cn.github.io/vse4ts/

• Report bugs at https://github.com/z-my-cn/vse4ts/issues

Testing Long Memory in Time Series

Description

The function SLmemory.test computes the test statistic for long memory in time series based on the variance scale exponent. The null hypothesis is that the time series is white noise or short memory, while the alternative hypothesis is that the time series has long memory.

Usage

SLmemory.test(x, m = 0.5, n = NULL)

Arguments

Value

A list with class "SLmemory.test" containing the following components:

References

Fu, H., Chen, W., & He, X.-J. (2018). On a class of estimation and test for long memory. In Physica A: Statistical Mechanics and its Applications (Vol. 509, pp. 906–920). Elsevier BV. https://doi.org/10.1016/j.physa.2018.06.092

Examples

## Test long memory in time series
library(pracma)

set.seed(123)
data("brown72")
x72 <- brown72                          #  H = 0.72
xgn <- rnorm(1024)                      #  H = 0.50
xlm <- numeric(1024); xlm[1] <- 0.1     #  H = 0.43
for (i in 2:1024) xlm[i] <- 4 * xlm[i-1] * (1 - xlm[i-1])

SLmemory.test(x72)
SLmemory.test(xgn)
SLmemory.test(xlm)

Testing White Noise in Time Series

Description

The function Wnoise.test computes the test statistic for white noise in time series based on the variance scale exponent. The null hypothesis is that the time series is independent white noise, while the alternative hypothesis is that the time series is a non-independent stochastic process.

Usage

Wnoise.test(x, m = 0.5, n = NULL)

Arguments

Value

A list with class "Wnoise.test" containing the following components:

References

Fu, H., Chen, W., & He, X.-J. (2018). On a class of estimation and test for long memory. In Physica A: Statistical Mechanics and its Applications (Vol. 509, pp. 906–920). Elsevier BV. https://doi.org/10.1016/j.physa.2018.06.092

Examples

## Test white noise in time series
library(pracma)

set.seed(123)
data("brown72")
x72 <- brown72                          #  H = 0.72
xgn <- rnorm(1024)                      #  H = 0.50
xlm <- numeric(1024); xlm[1] <- 0.1     #  H = 0.43
for (i in 2:1024) xlm[i] <- 4 * xlm[i-1] * (1 - xlm[i-1])

Wnoise.test(x72)
Wnoise.test(xgn)
Wnoise.test(xlm)

Calculate the Variance Scale Exponent of a Time Series

Description

Calculate the variance scale exponent of a time series.

Usage

vse(x, m = 0.5, n = NULL, type = c("weak", "strong"))

Arguments

Value

The variance scale exponent.

References

Fu, H., Chen, W., & He, X.-J. (2018). On a class of estimation and test for long memory. In Physica A: Statistical Mechanics and its Applications (Vol. 509, pp. 906–920). Elsevier BV. https://doi.org/10.1016/j.physa.2018.06.092

Examples

## Compute the variance scale exponent of a time series
# Generate a random time series
set.seed(123)
x <- rnorm(1024) # F = H = 0.5 also d = 0
vse(x)

## Compare the result with the Hurst exponent
library(pracma)

# A time series with Hurst exponent 0.72
data("brown72")
x <- brown72     # F = H = 0.72 also d = 0.22
hurstexp(x)
vse(x)

# A time series with Hurst exponent 0.43
xlm <- numeric(1024); xlm[1] <- 0.1
for (i in 2:1024) xlm[i] <- 4 * xlm[i-1] * (1 - xlm[i-1])
x <- xlm         # F = H = 0.43 also d = -0.07
hurstexp(x)
vse(x)