fCH_test | R Documentation |
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.
fCH_test(f_data, H = 10, stat_Method = "functional", pplot = FALSE)
f_data |
A |
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:
|
pplot |
A Boolean value. If TRUE, the function will produce a plot of p-values of the test
as a function of maximum lag |
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)
.
A list that includes the test statistic and the p-value will be returned.
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>.
# 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")
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