obtain_FACF {fdaACF} | R Documentation |
Obtain the autocorrelation function for a given functional time series.
Description
Estimate the lagged autocorrelation function for a given functional time series and its distribution under the hypothesis of strong functional white noise. This graphic tool can be used to identify seasonal patterns in the functional data as well as auto-regressive or moving average terms. i.i.d. bounds are included to test the presence of serial correlation in the data.
Usage
obtain_FACF(Y, v, nlags, ci = 0.95, estimation = "MC", figure = TRUE,
...)
Arguments
Y |
Matrix containing the discretized values
of the functional time series. The dimension of the
matrix is |
v |
Discretization points of the curves, by default
|
nlags |
Number of lagged covariance operators of the functional time series that will be used to estimate the autocorrelation function. |
ci |
A value between 0 and 1 that indicates
the confidence interval for the i.i.d. bounds
of the autocorrelation function. By default
|
estimation |
Character specifying the method to be used when estimating the distribution under the hypothesis of functional white noise. Accepted values are:
By default, |
figure |
Logical. If |
... |
Further arguments passed to the |
Value
Return a list with:
-
Blueline
: The upper prediction bound for the i.i.d. distribution. -
rho
: Autocorrelation values for each lag of the functional time series.
References
Mestre G., Portela J., Rice G., Muñoz San Roque A., Alonso E. (2021). Functional time series model identification and diagnosis by means of auto- and partial autocorrelation analysis. Computational Statistics & Data Analysis, 155, 107108. https://doi.org/10.1016/j.csda.2020.107108
Mestre, G., Portela, J., Muñoz-San Roque, A., Alonso, E. (2020). Forecasting hourly supply curves in the Italian Day-Ahead electricity market with a double-seasonal SARMAHX model. International Journal of Electrical Power & Energy Systems, 121, 106083. https://doi.org/10.1016/j.ijepes.2020.106083
Kokoszka, P., Rice, G., Shang, H.L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity Journal of Multivariate Analysis, 162, 32–50. https://doi.org/10.1016/j.jmva.2017.08.004
Examples
# Example 1
N <- 100
v <- seq(from = 0, to = 1, length.out = 5)
sig <- 2
Y <- simulate_iid_brownian_bridge(N, v, sig)
obtain_FACF(Y,v,20)
# Example 2
data(elec_prices)
v <- seq(from = 1, to = 24)
nlags <- 30
obtain_FACF(Y = as.matrix(elec_prices),
v = v,
nlags = nlags,
ci = 0.95,
figure = TRUE)