estimate.par: Estimates the parameters of a partially autoregressive fit...

In partialAR: Partial Autoregression

Description

Estimates the parameters of a partially autoregressive fit using lagged variances

Usage

estimate.par(X, useR = FALSE, rho.max = 1)

Arguments

X	A numeric vector or zoo vector representing the time series whose parameters are to be estimated
useR	If TRUE, the estimation is performed using R code. If FALSE, the estimation is performed using a faster C++ implementation. Default: FALSE.
rho.max	An artificial upper bound to be imposed on the value of rho.

Details

The method of lagged variances provides an analytical formula for the parameter estimates in terms of the variances of the lags X[t+1] - X[t], X[t+2] - X[t] and X[t+3] - X[t]. Let

V[k] = var(X[t+k] - X[t]).

Then, the estimated parameter values are given by the following formulas:

rho = -(V[1] - 2 V[2] + V[3]) / (2 V[1] - V[2])

sigma_M^2 = (1/2) ((rho + 1)/(rho - 1)) (V[2] - 2 V[1])

sigma_R^2 = (1/2) (V[2] - 2 sigma_M^2)

Value

Returns a numeric vector containing three named components

rho	The estimated value of rho
sigma_M	The estimated value of sigma_M
sigma_R	The estimated value of sigma_R

Author(s)

Matthew Clegg [e-mail]

References

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

See Also

fit.par

Examples

set.seed(1)
x <- rpar(1000, 0.5, 1, 2)  # Generate a random PAR sequence
estimate.par(x)
fit.par(x)  # For comparison

partialAR documentation built on April 14, 2020, 6:05 p.m.