sacf | R Documentation |
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)
X |
A dfts object or data which can be automatically converted to that
format. See |
lag.max |
A positive integer value. The maximum lag for which to compute the coefficients and confidence bounds. |
alpha |
Significance in [0,1] for intervals when forecasting. |
figure |
Logical. If |
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.
List with sACF values and plots
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.
acf()
sacf(electricity)
sacf(generate_brownian_motion(100))
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