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 \(h = 1:H\).
sacf(X, lag.max = 20, alpha = 0.05, figure = TRUE)List with sACF values and plots
A dfts object or data which can be automatically converted to that
format. See dfts().
A positive integer value. The maximum lag for which to compute the coefficients and confidence bounds.
Significance in [0,1] for intervals when forecasting.
Logical. If TRUE, prints plot for the estimated
function with the specified 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.
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.
sacf(electricity)
sacf(generate_brownian_motion(100))
Run the code above in your browser using DataLab