ftsa (version 5.5)

facf: Functional autocorrelation function

Description

Compute functional autocorrelation function at various lags

Usage

facf(fun_data, lag_value_range = seq(0, 20, by = 1))

Arguments

fun_data

A data matrix of dimension (n by p), where n denotes sample size; and p denotes dimensionality

lag_value_range

Lag value

Value

A vector of functional autocorrelation function at various lags

Details

The autocovariance at lag \(i\) is estimated by the function \(\widehat{\gamma}_i(t,s)\), a functional analog of the autocorrelation is defined as $$\widehat{\rho}_i = \frac{\|\widehat{\gamma}_i\|}{\int \widehat{\gamma}_0(t,t)dt}.$$

References

L. Horv\'ath, G. Rice and S. Whipple (2016) Adaptive bandwidth selection in the long run covariance estimator of functional time series, Computational Statistics and Data Analysis, 100, 676-693.

Examples

Run this code
# NOT RUN {
facf_value = facf(fun_data = t(ElNino_ERSST_region_1and2$y))
# }

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