ptestReg: Test short time series for periodicity with maximum...
In CliffordLai/harper: Harmonic Regression and Periodicity Test

Description Usage Arguments Details Value Author(s) References See Also Examples

This function is used to test the existence of the periodicity for a short time series (length<=100). Likelihood ratio tests under the Gaussian or the Laplace assumptions are provided with the response surface method implemented for efficiently obtaining accurate p-values under the default setting.

1 2	ptestReg(z, t = 1:n, lambdalist = (ceiling(1001/length(z)):500)/1001, method = c("LS", "L1", "rank", "MRobust"), returnPvalue = TRUE)

`z`	A vector or a matrix containg series as columns.
`t`	Length of a series.
`lambdalist`	A vector containg all plausible values of frequencies.
`method`	The statistical test to be used. See details for more information.
`returnPvalue`	Whether the p-value of the test is returned.

The null hypothesis is set as no peridicities, H0: f=0. Discriptions of different test statistics (methods) are as follow:

LS: The -2 loglikelihood ratio test statistic based on the likelihood ratio test with normal noises, where the p-values are efficiently computed by the response surface method.

L1: The -2 loglikelihood ratio test statistic based on the likelihood ratio test with Laplace noises, where the p-values are efficiently computed by the response surface method.

Object of class "Htest" produced.

An object of class "Htest" is a list containing the following components:

`obsStat`	Vector containing the observed test statistics.
`pvalue`	Vector containing the p-values of the selected tests.
`freq`	Vector containing the estimated frequencies.

Yuanhao Lai and A.I. McLeod

Islam, M.S. (2008). Peridocity, Change Detection and Prediction in Microarrays. Ph.D. Thesis, The University of Western Ontario.

Li, T. H. (2010). A nonlinear method for robust spectral analysis. Signal Processing, IEEE Transactions on, 58(5), 2466-2474.

MacKinnon, James (2001) : Computing numerical distribution functions in econometrics, Queen's Economics Department Working Paper, No. 1037.

ptestg, hreg.

# Simulate the harmonic regression model with standard Gaussian error terms
set.seed(193)
# Non-Fourier frequency
z <- shreg(10, f=2.5/10, hpar=list(snr=10), model="Gaussian")
ptestReg(z,method = "LS") #Normal likelihood ratio test
ptestReg(z,method = "L1") #Laplace likelihood ratio test  
fitHRegLS(z)
fitHRegL1(z)   

z <- shreg(11, f=0.42, hpar=list(snr=10), model="Laplace")
ptestReg(z,method = "LS") #Normal likelihood ratio test
ptestReg(z,method = "rank")
                                                                                  
# Performe tests on the alpha factor experiment
data(alpha)
## Eliminate genes with missing observations
alpha.nonNA <- alpha[complete.cases(alpha),]
## Transpose the data set so that each column stands for a gene
alpha.nonNA <- t(alpha.nonNA)
result <- ptestReg(alpha.nonNA[,1:10], method = "LS") 
str(result)       


# The movtivating example: gene ORF06806 in Cc
data(Cc)
x <- Cc[which(rownames(Cc)=="ORF06806"),]
plot(1:length(x),x,type="b", main="ORF06806",
     xlab="time",ylab="Gene expression")
ptestg(x,method="Fisher") #Fail to detect the periodicity
ptestReg(x,method="LS") #The periodicity is significantly not zero
ptestReg(x,method="rank") #The periodicity is significantly not zero
ptestReg(x,method="L1") #The periodicity is significantly not zero