third: Third-order Moment

In season: Seasonal Analysis of Health Data

Third-order Moment

Description

Estimated third order moment for a time series.

Usage

third(data, n.lag, centre = TRUE, outmax = TRUE, plot = TRUE)

Arguments

data	a vector of equally spaced numeric observations (time series).
n.lag	the number of lags, maximum = length of time series.
centre	centre series by subtracting mean (default=TRUE).
outmax	display the (x,y) lag co-ordinates for the maximum and minimum values (default=TRUE).
plot	contour plot of the third order moment (default=TRUE).

Details

The third-order moment is the extension of the second-order moment (essentially the autocovariance). The equation for the third order moment at lags (j,k) is: n^{-1}∑ X_t X_{t+j} X_{t+k}. The third-order moment is useful for testing for non-linearity in a time series, and is used by nonlintest.

Value

waxis	The axis –n.lag to n.lag.
third	The estimated third order moment in the range –n.lag to n.lag, including the symmetries.

Author(s)

Adrian Barnett [e-mail]

Examples

data(CVD)
third(CVD$cvd, n.lag=12)

season documentation built on March 21, 2022, 9:10 a.m.