sample.likelihood_ratio.par: Generates random samples of the likelihood ratio for the...
In partialAR: Partial Autoregression

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

Generates random samples of the likelihood ratio for the partially autoregressive model

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sample.likelihood_ratio.par(n = 500, rho = 0.8, sigma_M = 1, sigma_R = 1, 
  nrep = 1000, use.multicore = TRUE, robust = FALSE, 
  nu = par.nu.default(), seed.start = 0)

`n`	Length of the randomly generated sequence. Possibly a vector.
`rho`	The coefficient of mean reversion. Possibly a vector.
`sigma_M`	Standard deviation of the innovations of the mean-reverting process. Possibly a vector.
`sigma_R`	Standard deviation of the innovations of the random walk process. Possibly a vector.
`nrep`	Number of repetitions to perform
`use.multicore`	If `TRUE`, then the `parallel` package is used to speed up processing.
`robust`	If `TRUE`, then sequences containing t-distributed errors are generated, and robust fits are performed. Possibly a vector.
`nu`	If `robust` is `TRUE`, then this is the degrees-of-freedom parameter to be used. Possibly a vector.
`seed.start`	Starting seed to use for the random number generator.

The purpose of this function is to facilitate studying the behavior of the fit.par function by generating random partially autoregressive sequences and determining the maximum likelihood fits to them. For each combination of parameter values given by n, rho, sigma_M, sigma_R, robust and nu, generates nrep random partially autoregressive sequences with these parameters. Then, uses fit.par to fit the sequence using the partially autoregressive model, the pure random walk model and the pure mean reversion model. Returns a data.frame containing the results of the fits.

A data.frame with the following columns

`n`	The length of the sequence
`rho`	The value of `rho` that was used for generating the sequence
`sigma_M`	The value of `sigma_M` that was used for generating the sequence
`sigma_R`	The value of `sigma_R` that was used for generating the sequence
`robust`	0 if normally distributed innovations, 1 if t-distributed innovations
`nu`	If t-distributed innovations, the value of the degrees of freedom parameter
`seed`	The value used for seeding the random number generator
`rw_rho`	The value of `rho` estimated using the pure random walk model (always 0)
`rw_sigma_M`	The value of `sigma_M` estimated using the pure random walk model (always 0)
`rw_sigma_R`	The value of `sigma_R` estimated using the pure random walk model
`rw_negloglik`	The negative log likelihood of the fit obtained with the pure random walk model
`mr_rho`	The value of `rho` estimated using the pure mean-reversion model
`mr_sigma_M`	The value of `sigma_M` estimated using the pure mean-reversion model
`mr_sigma_R`	The value of `sigma_R` estimated using the pure mean-reversion model (always 0)
`mr_negloglik`	The negative log likelihood of the fit obtained with the pure mean-reversion model
`par_rho`	The value of `rho` estimated using the PAR model
`par_sigma_M`	The value of `sigma_M` estimated using the PAR model
`par_sigma_R`	The value of `sigma_R` estimated using the PAR model
`par_negloglik`	The negative log likelihood of the fit obtained with the PAR model
`rw_lrt`	The log likelihood ratio of the random walk model vs. the PAR model
`mr_lrt`	The log likelihood ratio of the mean-reversion model vs. the PAR model
`kpss_stat`	Statistic computed by the KPSS test (see `ur.kpss`)
`kpss_p`	p-value associated with `kpss_stat`
`pvmr`	Proportion of variance attributable to mean reversion found for PAR fit

Matthew Clegg matthewcleggphd@gmail.com

Clegg, Matthew. Modeling Time Series with Both Permanent and Transient Components using the Partially Autoregressive Model. Available at SSRN: http://ssrn.com/abstract=2556957

fit.par