FTSgof

This vignette provides an overview of how to perform exploratory data analysis, white noise hypothesis testing and the goodness-of-fit tests for functional time series (FTS) data using the functions fport_eda, fport_wn, fport_gof. Functional time series data consists of a sequence of curves, allowing for the analysis of complex data structures over time.

First, ensure you have the package installed and loaded:

library(FTSgof)

Exploratory Data Analysis with `fport_eda’

The fport_eda function provides a comprehensive exploratory data analysis for functional time series data.

# Load example data
data(Spanish_elec)  # Daily Spanish electricity price profiles

# Perform exploratory data analysis
fport_eda(Spanish_elec, H = 20, alpha = 0.05, wwn_bound = FALSE, M = NULL)

#> Hit <Return> to see next plot:

#> Hit <Return> to see next plot:

White Noise Hypothesis Testing with fport_wn

The fport_wn function computes various white noise tests for functional time series data. The available tests are “autocovariance”, “spherical”, and “arch”.


# Perform white noise hypothesis testing
fport_wn(Spanish_elec, test = "autocovariance", H = 10)
#> Autocovariance Test
#> 
#> Null hypothesis: the series is a weak white noise (sequentially uncorrelated).
#> sample size = 365
#> maximum lag H = 10
#> p-value = 0.000000
fport_wn(Spanish_elec, test = "spherical", H = 10, pplot = TRUE)

#> Spherical Test
#> 
#> Null hypothesis: the series is a strong white noise (iid).
#> sample size = 365
#> maximum lag H = 10
#> p-value = 0.000000

# Generate fGARCH(1) data for testing
yd_garch <- dgp.fgarch(J = 50, N = 200, type = "garch")$garch_mat
fport_wn(yd_garch, test = "ch", H = 10, stat_Method = "norm")
#> Test for Conditional Heteroscedasticity
#> 
#> Null hypothesis: the series is a strong white noise (iid).
#> sample size = 200
#> maximum lag H = 10
#> test type = norm
#> p-value = 0.000000

Goodness-of-fit Tests with fport_gof

The fport_gof function conducts goodness-of-fit tests for functional time series data. The available tests are “far”, “arch”, and “garch”.


# Perform goodness-of-fit tests
fport_gof(Spanish_elec, test = "far", H = 10)
#> Goodness-of-fit test for FAR(1)
#> 
#> Null hypothesis: FAR(1) model is adequate for the series.
#> sample size = 365
#> maximum lag H = 10
#> p-value = 0.000000

# Example with SP500 data
data(sp500)
fport_gof(OCIDR(sp500), test = "arch", M = 1, H = 5)
#> Warning in nloptr::cobyla(x0 = stav, fn = function_to_minimize2, lower =
#> c(rep(10^-20, : The old behavior for hin >= 0 has been deprecated. Please
#> restate the inequality to be <=0. The ability to use the old behavior will be
#> removed in a future release.
#> Goodness-of-fit test for fARCH(1)
#> 
#> Null hypothesis: fARCH(1) model is adequate for the series.
#> sample size = 251
#> maximum lag H = 5
#> p-value = 0.010181
fport_gof(OCIDR(sp500), test = "garch", M = 1, H = 5)
#> Warning in nloptr::cobyla(x0 = stav, fn = function_to_minimize2, lower =
#> c(rep(10^-20, : The old behavior for hin >= 0 has been deprecated. Please
#> restate the inequality to be <=0. The ability to use the old behavior will be
#> removed in a future release.
#> Goodness-of-fit test for fGARCH(1,1)
#> 
#> Null hypothesis: fGARCH(1,1) model is adequate for the series.
#> sample size = 251
#> maximum lag H = 5
#> p-value = 0.670733