Compute functional autocorrelation function at various lags
Usage
facf(fun_data, lag_value_range = seq(0, 20, by = 1))
Value
A vector of functional autocorrelation function at various lags
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
Author
Han Lin Shang
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.