rlmtest: Robust Lagrange multiplier test for detecting ARCH/GARCH...

In gel-research-group/lawstat: Tools for Biostatistics, Public Policy, and Law

Description

The function performs two resampling techniques to find critical values of the Lagrange multiplier (LM) test, namely permutation and bootstrap, as well as the asymptotic parametric test.

Usage

rlmtest(
  y,
  x = NA,
  a.order = 1,
  sig.level = 0.05,
  crit.type = c("asymptotic", "nonparametric"),
  nonp.method = c("bootstrap", "permutation"),
  num.resamp = 1000,
  num.discard = 0
)

Arguments

y	A vector that contains univariate time series observations. Missing values are not allowed.
x	A matrix that contains control variable time series observations. Missing values are not allowed.
a.order	Order of the autoregressive model which must be a nonnegative integer number. Default value 1.
sig.level	Significance level for testing hypothesis of no ARCH effect. Default value is 0.05.
crit.type	Method of obtaining critical values: "asymptotic" (default) or "nonparametric" options.
nonp.method	Type of resampling if crit.type="nonparametric": "bootstrap" (default) or "permutation".
num.resamp	Number of resampling replications if crit.type="nonparametric". Default number is 1,000.
num.discard	Number of bootstrap sample discarded. Default value is 0.

Value

stats	Test statistic.
crit.val	Ressampling based critical value, with a given significance level sig.level.
p.values	p-value of the Lagrange multiplier test.

Author(s)

Meichen Huang, Tian Jiang, Yulia R. Gel

References

Engle R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica: Journal of the econometric society, 1982: 987-1007.

Gel Y R, Chen B. Robust Lagrange multiplier test for detecting ARCH/GARCH effect using permutation and bootstrap[J]. Canadian Journal of Statistics, 2012, 40(3): 405-426.

Examples

Collect daily high price (in USD) of Bitcoin and gold from June 1st, 2016 to May 31st, 2021,
and create a dataset with log-returned high price of Bitcoin and gold, named as "GoldBTC".
Test for ARCH effects with log-return of high price of Bitcoin and gold with conditions below:
H0: No ARCH effect.
Ha: There exist ARCH effects.

# Let's import dataset "GoldBTC":
data(GoldBTC)

# Fix seed for reproducible simulations:
set.seed(2021)

# We want to test ARCH effect in Gold.
rlmtest(GoldBTC$Gold, crit.type = "nonparametric",
        nonp.method = "bootstrap")

## The list of returned results are below:
## $stat
## [1] 65.84728
## $crit.val
## 95%
## 1.914901
## $p.value
## [1] 0.003
## Since p-value is 0.003, reject null hypothesis at 0.05,
## that is, ARCH effect exists in gold.

# We want to test for ARCH effects in Bitcoin.
rlmtest(GoldBTC$BTC, crit.type = "nonparametric",
        nonp.method = "bootstrap")

## The list of returned results are below:
## $stat
## [1] 8.189278
## $crit.val
## 95%
## 3.541198
## $p.value
## [1] 0.013
## Since p-value is 0.013, reject null hypothesis at 0.05,
## that is, ARCH effects exist in Bitcoin.

## We want to test ARCH effect in gold and Bitcoin.
rlmtest(GoldBTC$BTC, GoldBTC$Gold, crit.type = "nonparametric",
        nonp.method = "bootstrap")

## The list of returned results are below:
## $stat
## [1] 9.246483
## $crit.val
## 95%
## 3.478484
## $p.value
## [1] 0.015
## Since p-value is 0.015, reject null hypothesis at 0.05,
## that is, ARCH effects exist in Bitcoin controling gold.

gel-research-group/lawstat documentation built on Dec. 20, 2021, 9:50 a.m.