This function offers a graphical summary of the fSACF of a functional time series (FTS) across different time lags \(h = 1:H\). It also plots \(100 \times (1-\alpha)\%\) confidence bounds developed under strong white noise (SWN) assumption for all lags \(h = 1:H\).
fSACF(f_data, H = 20, alpha = 0.05)Plot of the estimated autocorrelation coefficients for lags \(h\) in \(1:H\) with the SWN \((1-\alpha)100 \%\) upper and lower confidence bounds for each lag.
A \(J \times N\) matrix of functional time series data, where \(J\) is the number of discrete points in a grid and \(N\) is the sample size.
A positive integer value. The maximum lag for which to compute the coefficients and confidence bounds.
A numeric value between 0 and 1 specifying the significance level to be used for the confidence bounds.
This function computes and plots functional spherical autocorrelation coefficients at lag \(h\), for \(h = 1:H\). The fSACF at lag \(h\) is computed by the average of the inner product of lagged pairs of the series \(X_i\) and \(X_{i+h}\) that have been centered and scaled: $$ \tilde\rho_h=\frac{1}{N}\sum_{i=1}^{N-h} \langle \frac{X_i - \tilde{\mu}}{\|X_i - \tilde{\mu}\|}, \frac{X_{i+h} - \tilde{\mu}}{\|X_{i+h} - \tilde{\mu}\|} \rangle,\ \ \ \ 0 \le h < N, $$ where \(\tilde{\mu}\) is the estimated spatial median of the series. It also computes estimated asymptotic \((1-\alpha)100 \%\) confidence lower and upper bounds, under the SWN assumption.
[1] Yeh C.K., Rice G., Dubin J.A. (2023). Functional spherical autocorrelation: A robust estimate of the autocorrelation of a functional time series. Electronic Journal of Statistics, 17, 650–687.
# \donttest{
data(Spanish_elec) # Daily Spanish electricity price profiles
fSACF(Spanish_elec)
# }
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