annualnoise function

Annual noise color

The autocovariance function is estimated for the annual maxima in the series. An autoregressive model of the order of the highest significant lag is fit, using the Yule-Walker method to estimate the parameters. The function is transformed into the frequency domain, yielding an estimate theta.a of the annual noise color.

annualnoise(x)

Arguments

• x: A numeric vector of annual extremes. A streamflow object may also be used. If input is streamflow the function uses annual maximum discharge.

Returns

An object of S3 class annualnoise with the following attributes: - auto.corr: Sample autocorrelation.

• lm.fit: lm object from regression of log power spectrum on log frequency.

• interval: Upper and lower bounds of a 95% acceptance region when $\rho=0$.

• log.log: Matrix with log frequency and log power spectrum.

• reg.stats: Slope and intercept of regression of log power spectrum on log frequency, where slope is the annual noise color (theta.a).

• order: Indicates order of fitted AR model.

• fit.ar: Object of class ar summarizing the fitted AR model.

Details

To determine the order of the AR model, the ACF is calculated at all lags less than or equal to the highest power of 2 less than the length of the series. The order of the AR model is the lag with the highest significantly non-zero autocorrelation.

Examples

data(sycamore)
sycamore.flows<-asStreamflow(sycamore,river.name="Sycamore Creek")
syc.ar<-annualnoise(sycamore.flows)