fCH_test: Test for Conditional Heteroscedasticity of Functional Time...

fCH_testR Documentation

Test for Conditional Heteroscedasticity of Functional Time Series

Description

It tests the null hypothesis that the objective functional curve data is not conditionally heteroscedastic. If a small p-value rejects the null hypothesis, the curves exhibit conditional heteroscedasticity.

Usage

fCH_test(f_data, H = 10, stat_Method = "functional", pplot = FALSE)

Arguments

f_data

A J \times N matrix of functional time series data, where J is the number of discrete points in a grid and N is the sample size.

H

A positive integer specifying the maximum lag for which test statistic is computed.

stat_Method

A string specifying the test method to be used in the "ch" test. Options include:

"norm"

Uses V_{N,H}.

"functional"

Uses M_{N,H}.

pplot

A Boolean value. If TRUE, the function will produce a plot of p-values of the test as a function of maximum lag H, ranging from H=1 to H=20, which may increase the computation time.

Details

Given the objective curve data X_i(t), for 1\leq i \leq N, t\in[0,1], the test aims at distinguishing the hypotheses:

H_0: the sequence X_i(t) is IID;
H_1: the sequence X_i(t) is conditionally heteroscedastic.

Two portmanteau type statistics are applied:

1. the norm-based statistic: V_{N,H}=N\sum_{h=1}^H\hat{\gamma}^2_{X^2}(h), where \hat{\gamma}^2_{X^2}(h) is the sample autocorrelation of the time series ||X_1||^2,\dots,||X_N||^2, and H is a pre-set maximum lag length.

2. the fully functional statistic M_{N,H}=N\sum_{h=1}^H||\hat{\gamma}_{X^2,N,h}||^2, where the autocovariance kernel \hat{\gamma}_{X^2,N,h}(t,s)=N^{-1}\sum_{i=1}^{N-h}[X_i^2(t)-\bar{X}^2(t)][X^2_{i+h}(s)-\bar{X}(s)], for ||\cdot || is the L^2 norm, and \bar{X}^2(t)=N^{-1}\sum_{i=1}^N X^2_i(t).

Value

A list that includes the test statistic and the p-value will be returned.

References

Rice, G., Wirjanto, T., Zhao, Y. (2020). Tests for conditional heteroscedasticity of functional data. Journal of Time Series Analysis. 41(6), 733-758. <doi:10.1111/jtsa.12532>.

Examples



# generate discrete evaluations of the iid curves under the null hypothesis.
yd_ou = dgp.ou(50, 100)

# test the conditional heteroscedasticity.
fCH_test(yd_ou, H=5, stat_Method="functional")


FTSgof documentation built on Oct. 4, 2024, 1:06 a.m.