Testing Long Memory in Time Series

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

x

A time series vector.

m

A parameter to control the number of scales. Default is 0.5.

n

The number of scales. If NULL, it will be calculated as floor(N^m).

Value

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

SLmemory

the test statistic

df

the degrees of freedom of the test.

p.value

the p-value of the test.

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
#> 
#> SLmemory statistic: 21.20841 
#> degrees of freedom: 31 
#> p-value: 0.09369624 
#> 
#> alternative hypothesis: long memory
SLmemory.test(xgn)
#> SLmemory Test
#> 
#> SLmemory statistic: 29.06849 
#> degrees of freedom: 31 
#> p-value: 0.4343341 
#> 
#> alternative hypothesis: long memory
SLmemory.test(xlm)
#> SLmemory Test
#> 
#> SLmemory statistic: 33.53657 
#> degrees of freedom: 31 
#> p-value: 0.3453187 
#> 
#> alternative hypothesis: long memory