fSACF: Functional Spherical Autocorrelation Function (fSACF) Plot

In FTSgof: White Noise and Goodness-of-Fit Tests for Functional Time Series

Functional Spherical Autocorrelation Function (fSACF) Plot

Description

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.

Usage

fSACF(f_data, H = 20, alpha = 0.05)

Arguments

f_data	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.
H	A positive integer value. The maximum lag for which to compute the coefficients and confidence bounds.
alpha	A numeric value between 0 and 1 specifying the significance level to be used for the confidence bounds.

Details

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.

Value

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.

References

[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.

Examples

data(Spanish_elec) # Daily Spanish electricity price profiles
fSACF(Spanish_elec)

FTSgof documentation built on Oct. 4, 2024, 1:06 a.m.