acfGarchTest: Tests for weak white noise

In sarima: Simulation and Prediction with Seasonal ARIMA Models

Tests for weak white noise

Description

Carry out tests for weak white noise under GARCH, GARCH-type, and stochastic volatility null hypotheses.

Usage

acfGarchTest(acr, x, nlags, interval = 0.95)

acfWnTest(acr, x, nlags, interval = 0.95, ...)

Arguments

acr	autocorrelations.
x	time series.
nlags	how many lags to use.
interval	If not NULL, compute also confidence intervals with the specified coverage probability.
...	additional arguments for the computation of the variance matrix under the null hypothesis, passed on to nvarOfAcfKP.

Details

Unlike the autocorrelation IID test, the time series is needed here to estimate the covariance matrix of the autocorrelations under the null hypothesis.

acfGarchTest performs a test for uncorrelatedness of a time series. The null hypothesis is that the time series is GARCH, see \insertCiteFrancqZakoian2010garch;textualsarima.

acfWnTest performs a test for uncorrelatedness of a time series under a weaker null hypothesis. The null hypothesis is that the time series is GARCH-type or from a stochasitc volatily model, see \insertCitekokoszka2011nonlinearity;textualsarima.

See the references for details and precise specification of the hypotheses.

The format of the return value is the same as for acfIidTest.

Value

a list with components "test" and "ci"

Author(s)

Georgi N. Boshnakov

References

\insertAllCited

See Also

whiteNoiseTest, acfIidTest;

plot-methods for graphical representations of results

Examples

## see also the examples for \code{\link{whiteNoiseTest}}
set.seed(1234)
n <- 5000
x <- sarima:::rgarch1p1(n, alpha = 0.3, beta = 0.55, omega = 1, n.skip = 100)
x.acf <- autocorrelations(x)
x.pacf <- partialAutocorrelations(x)

acfGarchTest(x.acf, x = x, nlags = c(5,10,20))
acfGarchTest(x.pacf, x = x, nlags = c(5,10,20))

# do not compute CI's:
acfGarchTest(x.pacf, x = x, nlags = c(5,10,20), interval = NULL)

## plot methods call acfGarchTest() suitably if 'x' is given:
plot(x.acf, data = x)
plot(x.pacf, data = x)

## use 90% limits:
plot(x.acf, data = x, interval = 0.90)

acfWnTest(x.acf, x = x, nlags = c(5,10,20))
nvarOfAcfKP(x, maxlag = 20)
whiteNoiseTest(x.acf, h0 = "arch-type", x = x, nlags = c(5,10,20))

sarima documentation built on May 29, 2024, 3:22 a.m.