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.
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 asfloor(N^m).
Value
A list with class "Wnoise.test" containing the following components:
- Wnoise
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 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
#>
#> Wnoise statistic: 135.1091
#> degrees of freedom: 31
#> p-value: 5.884182e-15
#>
#> alternative hypothesis: non-independent stochastic process
Wnoise.test(xgn)
#> Wnoise Test
#>
#> Wnoise statistic: 27.9873
#> degrees of freedom: 31
#> p-value: 0.3781797
#>
#> alternative hypothesis: non-independent stochastic process
Wnoise.test(xlm)
#> Wnoise Test
#>
#> Wnoise statistic: 19.58707
#> degrees of freedom: 31
#> p-value: 0.05575128
#>
#> alternative hypothesis: non-independent stochastic process