pvmr.par: Proportion of variance attributable to mean reversion

In partialAR: Partial Autoregression

Description

Proportion of variance attributable to mean reversion of a partially autoregressive model

Usage

pvmr.par(rho, sigma_M, sigma_R)

Arguments

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

Details

This routine determines the proportion of variance attributable to mean reversion for a partially autoregressive model. The partially autoregressive model is given by the specification:

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

The proportion of variance attributable to mean reversion is defined as

R^2[MR] = Var((1 - B) M[t]) / Var((1 - B) X[t])

where M[t] is the mean-reverting component of the system at time t, X[t] is the state of the entire system at time t, and B is the backshift operator.

It will be a value between zero and one, with zero indicating that none of the variance is attributable to the mean reverting component, and one indicating that all of the variance is attributable to the mean-reverting component.

In the case of the partially autoregressive model, the proportion of variance attributable to mean reversion is given by the following formula:

R^2[MR] = 2 sigma_M^2 / (2 sigma_M^2 + (1 + rho) sigma_R^2)

Value

Returns the proportion of variance attributable to mean reversion for the parameter values (rho, sigma_M, 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

pvmr.par(0,0,1)  # -> 0
pvmr.par(0,1,0)  # -> 1
pvmr.par(0,1,1)  # -> 0.6667
pvmr.par(0.5,1,1) # -> 0.5714
pvmr.par(0.5,1,2) # -> 0.25

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