rpar: Random partially autoregressive sequence
In partialAR: Partial Autoregression

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

Random partially autoregressive sequence

1 2	rpar(n, rho, sigma_M, sigma_R, M0 = 0, R0 = 0, include.state = FALSE, robust = FALSE, nu = par.nu.default())

`n`	Length of sequence to generate
`rho`	The coefficient of mean reversion
`sigma_M`	The standard deviation of the innovations of the mean-reverting component
`sigma_R`	The standard deviation of the innovations of the random walk component
`M0`	Initial state of mean-reverting component
`R0`	Initial state of random walk component
`include.state`	If `TRUE`, a `data.frame` is returned containing the states of the mean-reverting and random walk components. Otherwise, a numeric vector is returned containing the state of the system. Default: `FALSE`.
`robust`	If TRUE, innovations are t-distributed. Otherwise, they are normally distributed. Default: `FALSE`.
`nu`	If `robust` is `TRUE`, then this is the degrees of freedom parameter to be used in the t-distributed innovations.

Generates a random sequence according to the specification of the partially autoregressive model. The partially autoregressive model is given as

X[t] = M[t] + R[t]

M[t] = rho * M[t-1] + epsilon_M[t]

R[t] = R[t-1] + epsilon_R[t]

-1 < rho < 1

To generate the random sequence, the sequences epsilon_M[t] and epsilon_R[t] are first generated. These are then used to build up the sequences M[t], R[t] and X[t].

If include.state is FALSE, then returns the sequence X[t]. Otherwise, returns a data.frame with the following columns:

`X`	State of the system
`M`	State of the mean-reverting component
`R`	State of the random walk component
`eps_M`	Innovations in the mean-reverting component
`eps_R`	Innovations in the random walk component

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

set.seed(1)
x <- rpar(10000, 0.5, 2, 1)
library(tseries)
adf.test(x)      # Seems to contain a unit root, as expected
estimate.par(x)  # Estimate parameters using lagged variances
fit.par(x)       # Maximum likelihood estimate