T_stationary: Testing stationarity of functional time series

Description

A hypothesis test for stationarity of functional time series.

Usage

T_stationary(sample, L = 49, J = 500, MC_rep = 1000, cumulative_var = .90, 
		    Ker1 = FALSE, Ker2 = TRUE, h = ncol(sample)^.5, pivotal = FALSE)

Arguments

sample

A matrix of discretised curves of dimension (p by n), where p represents the dimensionality and n represents sample size.

Number of Fourier basis functions.

Truncation level used to approximate the distribution of the squared integrals of Brownian bridges that appear in the limit distribution.

MC_rep

Number of replications.

cumulative_var

Amount of variance explained.

Ker1

Flat top kernel in (4.1) of Horvath et al. (2014).

Ker2

Flat top kernel in (7) of Politis (2003).

Kernel bandwidth.

pivotal

If pivotal = TRUE, a pivotal statistic is used.

Value

p-value

When p-value is less than any level of significance, we reject the null hypothesis and conclude that the tested functional time series is not stationary.

Details

As in traditional (scalar and vector) time series analysis, many inferential procedures for functional time series assume stationarity. Stationarity is required for functional dynamic regression models, for bootstrap and resampling methods for functional time series and for the functional analysis of volatility.

References

L. Horvath, P. Kokoszka, G. Rice (2014) "Testing stationarity of functional time series", Journal of Econometrics, 179(1), 66-82.

D. N. Politis (2003) "Adaptive bandwidth choice", Journal of Nonparametric Statistics, 15(4-5), 517-533.

A. Aue, G. Rice, O. S\"onmez (2018) "Detecting and dating structural breaks in functional data without dimension reduction", Journal of the Royal Statistical Society: Series B, 80(3), 509-529.

Examples

Run this code

# NOT RUN {
result = T_stationary(sample = pm_10_GR_sqrt$y)
result_pivotal = T_stationary(sample = pm_10_GR_sqrt$y, J = 100, MC_rep = 5000, 
				h = 20, pivotal = TRUE)
# }

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