FTS_identification {fdaACF}

Obtain the auto- and partial autocorrelation functions for a given FTS

Description

Estimate both the autocorrelation and partial autocorrelation function for a given functional time series and its distribution under the hypothesis of strong functional white noise. Both correlograms are plotted to ease the identification of the dependence structure of the functional time series.

Usage

FTS_identification(Y, v, nlags, n_harm = NULL, 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 autocorrelation functions.

n_harm

Number of principal components that will be used to fit the ARH(p) models. If this value is not supplied, n_harm will be selected as the number of principal components that explain more than 95 % of the variance of the original data. By default, n_harm = NULL.

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_FACF: Autocorrelation coefficients for each lag of the functional time series.

• rho_FPACF: 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

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 (Toy example)

N <- 50
v <- seq(from = 0, to = 1, length.out = 10)
sig <- 2
set.seed(15)
Y <- simulate_iid_brownian_bridge(N, v, sig)
FTS_identification(Y,v,3)


# Example 2

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