autocorrelations {sarima}

Compute autocorrelations and related quantities

Description

Generic functions for computation of autocorrelations, autocovariances and related quantities. The idea is to free the user from the need to look for specific functions that compute the desired property for their object.

Usage

autocovariances(x, maxlag, ...)

autocorrelations(x, maxlag, lag_0, ...)

partialAutocorrelations(x, maxlag, lag_0 = TRUE, ...)

partialAutocovariances(x, maxlag, ...)

partialVariances(x, ...)

Arguments

x

an object for which the requested property makes sense.

maxlag

the maximal lag to include in the result.

lag_0

if TRUE include lag zero.

...

further arguments for methods.

Details

autocorrelations is a generic function for computation of autocorrelations. It deduces the appropriate type of autocorrelation from the class of the object. For example, for models it computes theoretical autocorrelations, while for time series it computes sample autocorrelations.

The other functions described are similar for other second order properties of x.

These functions return objects from suitable classes, all inheriting from "Lagged". The latter means that indexing starts from zero, so the value for lag zero is accessed by r[0]). Subscripting always returns the underlying data unclassed (i.e. ordinary vectors or arrays). In particular, "[]" extracts the underlying data.

Functions computing autocorrelations and partial autocorrelations have argument lag_0 — if it is set to FALSE, the value for lag zero is dropped from the result and the returned object is an ordinary vector or array, as appropriate.

See the individual methods for the format of the result and further details.

There are plot methods for sample autocorrelations and sample partial autocorrelations with overlaid significance limits under null hypotheses for independence or weak white noise, see plot-methods and the examples there. More details can be found in the vignettes, see section ‘See also’ below.

Value

an object from a class suitable for the requested property and x

Author(s)

Georgi N. Boshnakov

See Also

plot-methods for plotting with significance limits computed under strong white noise and weak white noise hypotheses;

autocorrelations-methods, partialAutocorrelations-methods for details on individual methods;

vignette("white_noise_tests", package = "sarima") and
vignette("garch_tests_example", package = "sarima") for extensive worked examples.

armaccf_xe, armaacf

Examples

set.seed(1234)
v1 <- rnorm(100)
autocorrelations(v1)
v1.acf <- autocorrelations(v1, maxlag = 10)

v1.acf[1:10] # drop lag zero value (and the class)
autocorrelations(v1, maxlag = 10, lag_0 = FALSE) # same

partialAutocorrelations(v1)
partialAutocorrelations(v1, maxlag = 10)

## compute 2nd order properties from raw data
autocovariances(v1)
autocovariances(v1, maxlag = 10)
partialAutocovariances(v1, maxlag = 6)
partialAutocovariances(v1)
partialVariances(v1, maxlag = 6)
pv1 <- partialVariances(v1)

## compute 2nd order properties from raw data
autocovariances(AirPassengers, maxlag = 6)
autocorrelations(AirPassengers, maxlag = 6)
partialAutocorrelations(AirPassengers, maxlag = 6)
partialAutocovariances(AirPassengers, maxlag = 6)
partialVariances(AirPassengers, maxlag = 6)

acv <- autocovariances(AirPassengers, maxlag = 6)
autocovariances(acv) # no-op
autocovariances(acv, maxlag = 4) # trim the available lags

## compute 2nd order properties from sample autocovariances
acr <- autocorrelations(acv)
acr
partialAutocorrelations(acv)
partialAutocovariances(acv)
partialVariances(acv)

## compute 2nd order properties from sample autocorrelations
acr
partialAutocorrelations(acr)

## These cannot be computed, since the variance is needed but unknown:
##     autocovariances(acr)
##     partialAutocovariances(acr)
##     partialVariances(acr)

## to treat autocorrelations as autocovariances, 
## convert them to autocovariances explicitly:
as(acr, "Autocovariances")
as(acr, "SampleAutocovariances")

partialVariances(as(acr, "Autocovariances"))
partialVariances(as(acr, "SampleAutocovariances"))