Computes maximum likelihood estimates of parameters for an ARMA model with p and q autoregressive and moving average terms respectively.
For a list of all members of this type, see ARMAMaxLikelihood Members.
System.Object
Imsl.Stat.ARMAMaxLikelihood
Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.
ARMAMaxLikelihood
computes estimates of parameters for a nonseasonal ARMA model given a sample of observations, , for where
z.Length
. The class is derived from the maximum likelihood estimation algorithm described by Akaike, Kitagawa, Arahata and Tada (1979), and the XSARMA routine published in the TIMSAC-78 Library.
The stationary time series with mean can be represented by the nonseasonal autoregressive moving average (ARMA) model by the following relationship:
where B is the backward shift operator defined by and TheARMAMaxLikelihood
class estimates the AR coefficients and the MA coefficients using maximum likelihood estimation.
ARMAMaxLikelihood
checks the initial estimates for both the autoregressive and moving average coefficients to ensure that they represent a stationary and invertible series respectively.
If
are the initial estimates for a stationary series then all (complex) roots of the following polynomial will fall outside the unit circle:If
are initial estimates for an invertible series then all (complex) roots of the polynomial will fall outside the unit circle.By default, the order of the lags for the autoregressive terms is and for the moving average terms. However, this cannot be overridden.
Initial values for the AR
and MA
coefficients can be supplied via the SetAR
and SetMA
methods. Otherwise, initial estimates are computed internally by the method of moments. The class computes the roots of the associated polynomials. If the AR
estimates represent a nonstationary series, ARMAMaxLikelihood
issues a warning message and replaces the intial AR
estimates with initial values that are stationary. If the MA
estimates represent a noninvertible series, a terminal error is issued and new initial values must be sought.
ARMAMaxLikelihood
also validates the final estimates of the AR
coefficients to ensure that they too represent a stationary series. This is done to guard against the possibility that the internal log-likelihood optimizer converged to a nonstationary solution. If nonstationary estimates are encountered, an exception will be thrown.
For model selection, the ARMA
model with the minimum value for AIC might be preferred, , where L is the value of the maximum likelihood function evaluated at the parameter estimates.
ARMAMaxLikelihood
can also handle white noise processes, i.e. processes.
Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll)
ARMAMaxLikelihood Members | Imsl.Stat Namespace | Example