ptestReg {ptest} | R Documentation

## Test short time series for periodicity with maximum likelihood ratio tests

### Description

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.

### Usage

    ptestReg(z, method = c("LS", "L1"), multiple = FALSE)

### Arguments

`z` | A series or a matrix containg series as columns
`method` | The statistical test to be used. See details for more information.
`multiple` | Indicating whether z contains multiple series.

### Details

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.

### Value

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.

### Author(s)

Yuanhao Lai and A.I. McLeod

### References

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.

### See Also

`fitHReg, ptestg`

### Examples

    # Simulate the harmonic regression model with standard Gaussian error terms
    set.seed(193)
    # Non-Fourier frequency
    z <- simHReg(n = 14, f=2/10, A = 2, B = 1, model="Gaussian",sig=1)
    ptestReg(z,method = "LS") #Normal likelihood ratio test
    ptestReg(z,method = "L1") #Laplace likelihood ratio test
    fitHReg(z, algorithm="exact") #the nls fitted result

    # Performe tests on the alpha factor experiment
    data(alpha)
    ## Eliminate genes with missing observations
    alpha.nonNA <- alpha[complete.cases(alpha),]
    ## Using the multiple option to do the test for all the genes
    ## Transpose the data set so that each column stands for a gene
    alpha.nonNA <- t(alpha.nonNA)
    result <- ptestReg(alpha.nonNA, method = "LS",multiple=TRUE)
    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="L1") #The periodicity is significantly not zero

[Package ptest version 1.0-8 Index]