partialAR (version 1.0.3)

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

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.

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

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: $$rho = -(V[1] - 2 V[2] + V[3]) / (2 V[1] - V[2])$$ $$sigma_M^2 = (1/2) ((rho + 1)/(rho - 1)) (V[2] - 2 V[1])$$ $$sigma_R^2 = (1/2) (V[2] - 2 sigma_M^2)$$

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