Functional autocorrelation function
Compute functional autocorrelation function at various lags
facf(fun_data, lag_value_range = seq(0, 20, by = 1))
fun_data |
A data matrix of dimension (n by p), where n denotes sample size; and p denotes dimensionality |
lag_value_range |
Lag value |
The autocovariance at lag i is estimated by the function \widehat{γ}_i(t,s), a functional analog of the autocorrelation is defined as
\widehat{ρ}_i = \frac{\|\widehat{γ}_i\|}{\int \widehat{γ}_0(t,t)dt}.
A vector of functional autocorrelation function at various lags
Han Lin Shang
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.
facf_value = facf(fun_data = t(ElNino_ERSST_region_1and2$y))
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