season (version 0.3.16)

third: Third-order Moment

Description

Estimated third order moment for a time series.

Usage

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

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.

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).

Author

Adrian Barnett

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: \(n^{-1}\sum X_t X_{t+j} X_{t+k}\). The third-order moment is useful for testing for non-linearity in a time series, and is used by nonlintest.

Examples

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