shreg: Simulate harmonic regression models
In CliffordLai/harper: Harmonic Regression and Periodicity Test

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

Simulates a harmonic regression or a semiparametric harmonic regression. Possible types of models are normal, t(5), Laplace, cubic and AR1.

shreg(n, f = 0, model = c("Gaussian", "ContaminatedNormal", "t5",
  "Laplace", "cubic", "AR1"), hpar = list(A = NA, B = NA, R = NA, zeta =
  NA, snr = NA), mu = 0, sig = 1, phi = 0.5, c = 3,
  g = function(x) {     x })

`n`	Length of series.
`f`	Frequency.
`model`	The model used for generating the error term. See details.
`hpar`	structural parameters that specify A and B. See details.
`mu`	constant term
`sig`	The standard error of the series.
`phi`	Only used if AR1 error distribution is selected.
`c`	Only used if Contaminated Normal error distribution is selected.
`g`	A function used to transform the harmonic component. See details.

Generate a harmonic series y with length n, where

y_t = mu+g( A*cos(2*pi*f*t)+B*sin(2*pi*f*t) )+sig*e_t,\ t=1,...,n,

and e_t comes from one of the following specified distributions with mean 0 and standard error 1 that are specified in the argument model:

Gaussian: A standard normal distribution (i.i.d.).

ContaminatedNormal: Generates a random sample from a normal mixture p*N(0,c^2)+(1-p)*N(0,1) where p=1/(1+c^2)).

t5: A t distribution with 5 degrees of freedom (i.i.d., standardized to mean 0 and variance 1).

Laplace: A Laplace (double exponential) distribution (i.i.d., standardized to mean 0 and variance 1).

cubic: A standard normal distribution for e, but the cube transform is used on the time series.

AR1: An AR(1) series with autocorrelation paramater phi (standardized to mean 0 and variance 1).

The argument hpar is a list that specifies the sinusoid. If components A and B are defined, these are used. Otherwise if components R and zeta are defined, these specify the amplitude and phase. Finally, snr may be used to generate a model with a specified signal-to-noise ratio and random phase.

Vector of length n, simulated harmonic series.

A.I. McLeod and Yuanhao Lai

hreg, ptestReg

#Simulate the harmonic regression model with standard Gaussian error terms
z <- shreg(10, f=2.5/10, hpar=list(snr=10))
plot(1:10,z,type="b")

#Simulate the AR(1) errors
z <- shreg(50, f=2.5/10, hpar=list(snr=2),model="AR1", phi=0.5, mu=100)
plot(z, type="o")
ans <- hreg(z)
plot(ans)
plot(ans, type="cp")

#Contaminated normal with large outlier
set.seed(77233)
z <- shreg(100, f=4/10, hpar=list(snr=10), model="ContaminatedNormal", c=25)
(out <- hreg(z))
plot(out)
(out <- hreg(z, method="MM",K=100))
plot(out)