obtain_FPACF {fdaACF}

Obtain the partial autocorrelation function for a given FTS.

Description

Estimate the partial autocorrelation function for a given functional time series and its distribution under the hypothesis of strong functional white noise.

Usage

obtain_FPACF(Y, v, nlags, n_harm, 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 (n x m), where n is the number of curves and m is the number of points observed in each curve.

v

Discretization points of the curves.

nlags

Number of lagged covariance operators of the functional time series that will be used to estimate the partial autocorrelation function.

n_harm

Number of principal components that will be used to fit the ARH(p) models.

ci

A value between 0 and 1 that indicates the confidence interval for the i.i.d. bounds of the partial autocorrelation function. By default ci = 0.95.

estimation

Character specifying the method to be used when estimating the distribution under the hypothesis of functional white noise. Accepted values are:

• "MC": Monte-Carlo estimation.

• "Imhof": Estimation using Imhof's method.

By default, estimation = "MC".

figure

Logical. If TRUE, plots the estimated partial autocorrelation function with the specified i.i.d. bound.

...

Further arguments passed to the plot_FACF function.

Value

Return a list with:

• Blueline: The upper prediction bound for the i.i.d. distribution.

• rho: Partial autocorrelation coefficients 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

Examples

# Example 1

N <- 100
v <- seq(from = 0, to = 1, length.out = 5)
sig <- 2
set.seed(15)
Y <- simulate_iid_brownian_bridge(N, v, sig)
obtain_FPACF(Y,v,10, n_harm = 2)


# Example 2

data(elec_prices)
v <- seq(from = 1, to = 24)
nlags <- 30
obtain_FPACF(Y = as.matrix(elec_prices), 
v = v,
nlags = nlags,
n_harm = 5, 
ci = 0.95,
figure = TRUE)