confint: Confidence and acceptance intervals in package sarima

In GeoBosh/sarima: Simulation and Prediction with Seasonal ARIMA Models

Confidence and acceptance intervals in package sarima

Description

Compute confidence and acceptance intervals for sample autocorrelations under assumptions chosen by the user.

Usage

## S4 method for signature 'SampleAutocorrelations'
confint(object, parm, level = 0.95, se = FALSE, maxlag, ..., assuming)

Arguments

object	an object containing sample autocorrelations (sacfs).
parm	which parameters to include, as for stats::confint.
level	coverage level, such as 0.95.
se	If TRUE return also standard errors.
assuming	under what assumptions to do the computations? Currently can be "iid", "garch", a fitted model, or a theoretical model, see Details.
maxlag	maximal lag to include
...	further arguments for se.

Details

For lags not fixed by the assumed model the computed intervals are confidence intervals.

The autocorrelations postulated by the null model (argument assuming) are usually fixed for some lags. For such lags it doesn't make sense to talk about confidence intervals. We use the term acceptance interval in this case since the sacfs for such lags fall in the corresponding intervals with high probability if the null model is correct.

If assuming is "iid" (strong white noise), then all autocorrelations in the null model are fixed (to zero) and the limits of the resulting acceptance intervals are ethose from the familiar plots produced by base-R's function acf.

If assuming is a fitted MA(q) model, e.g. obtained from arima(), then for lags 1,\ldots,q we get confidence intervals, while for lags greater than q the intervals are acceptance intervals.

The autocorrelations of ARMA models with non-trivial autoregressive part may also have structural patterns of zeroes (for example some seasonal models), leading to acceptance intervals for such lags.

If assuming specifies a theoretical (non-fitted) model, then the autocorrelation function of the null model is completely fixed and we get acceptance intervals for all lags.

The return value is a matrix with one row for each requested lag, containg the lag, lower bound, upper bound, estimate for acf(lag) and the value of acf(lag) under H0 (if fixed) and NA if not fixed under H0. The null model is stored as attribute "assuming".

Note: When assuming = "garch" it is currently necessary to submit the time series from which the autocorrelations were computed as argument x.

Value

a matrix as described in section ‘Details’;

if se = TRUE, a column giving the standard errors of the sample autocorrelations is appended.

See Also

se

vignette("white_noise_tests", package = "sarima")

vignette("garch_tests_example", package = "sarima")

Examples

set.seed(1234)
v1 <- arima.sim(n = 100, list(ma = c(0.8, 0.1), sd = 1))
v1.acf <- autocorrelations(v1, maxlag = 10)

confint(v1.acf, parm = 1:4, assuming = "iid")
confint(v1.acf,  assuming = "iid", maxlag = 4) # same

## a fitted MA(2) - rho_1, rho_2 not fixed, the rest fixed
ma2fitted <- arima(v1, order = c(0,0,2), include.mean=FALSE)
confint(v1.acf, assuming = ma2fitted, maxlag = 4)

## a theoretical MA(2) model, all acfs fixed under H0
ma2 <- MaModel(ma = c(0.8, 0.1), sigma2 = 1)
confint(v1.acf, assuming = ma2, maxlag = 4)

# a weak white noise null
confint(v1.acf, assuming = "garch", maxlag = 4, x = v1)

GeoBosh/sarima documentation built on March 27, 2024, 6:31 p.m.