SpuriousMemory (version 1.0.0)

Longmemorytest: Testing true long memory against spurious long memory

Description

Tests the null hypothesis of true long memory against the alternative of spurious long memory (e.g., due to level shifts or trends) using the Qu (2011) test.

Usage

Longmemorytest(
  x,
  demean = TRUE,
  alpha = 0.05,
  filter = TRUE,
  print_results = TRUE
)

Value

A list with elements:

d_estimate

Local Whittle estimate of the long memory parameter.

test_stat_eps02

Test statistic with trimming parameter epsilon = 0.02.

test_stat_eps05

Test statistic with trimming parameter epsilon = 0.05.

critical_value_eps02

Critical value for epsilon = 0.02 at the chosen significance level alpha.

critical_value_eps05

Critical value for epsilon = 0.05 at the chosen significance level alpha.

reject_eps02

Logical, TRUE if the null is rejected for epsilon = 0.02.

reject_eps05

Logical, TRUE if the null is rejected for epsilon = 0.05.

alpha

Significance level.

m

Bandwidth parameter m.

n

Sample size.

Arguments

x

Numeric vector of time series data

demean

Logical, demean the series (default: TRUE)

alpha

Numeric, significance level: 0.01, 0.025, 0.05, or 0.10 (default: 0.05)

filter

Logical, apply a pre-whitening filter to reduce short-memory dynamics that may otherwise affect the size of the test in finite samples (default: TRUE).

print_results

Logical, print results (default: TRUE)

Details

The test uses bandwidth parameter m = n^0.7 with trimming parameters 0.02 or 0.05 as recommended by Qu (2011). Critical values are based on these settings. Whether the pre-whitening filter is applied does not affect the asymptotic critical values.

References

Qu, Z. (2011). A Test Against Spurious Long Memory. Journal of Business & Economic Statistics, 29(3), 423-438.

Examples

data(RV5min)
result <- Longmemorytest(log(RV5min))

# Simulated example: ARFIMA(0,d,0) with d = 0.3 (true long memory)
set.seed(123)
n  <- 2000
d0 <- 0.3
e  <- rnorm(n)
x  <- fracdiff::fracdiff.sim(n, d = d0)$series

# Apply the test (null = true long memory)
out <- Longmemorytest(x, alpha = 0.05)
out$reject_eps02    # typically FALSE
out$d_estimate

# Example: Spurious long memory due to a structural break
set.seed(123)
n <- 2000
x <- c(rnorm(n/2, 0, 1), rnorm(n/2, 2, 1))   # one-time mean shift

out <- Longmemorytest(x, alpha = 0.05)
out$reject_eps02
out$reject_eps05