Convert ARMA model to MA model
returns
the coefficients of the truncated, infinite-order MA model approximation
to an ARMA model having AR and MA coefficients specified by ma
= arma2ma(ar0
,ma0
)ar0
and ma0
,
respectively.
arma2ma:
Accepts:
Vectors or cell vectors of matrices in difference-equation notation.
LagOp
lag
operator polynomials corresponding to the AR and MA polynomials in lag operator notation.
Accommodates time series models that are univariate
or multivariate (i.e., numVars
variables compose
the model), stationary or integrated, structural or in reduced form,
and invertible.
Assumes that the model constant c is 0.
The software computes the infinite-lag polynomial of the resulting MA model according to this equation in lag operator notation:
where and
arma2ma
approximates the
MA model coefficients whether ar0
and ma0
compose
a stable polynomial (a polynomial that is stationary or invertible).
To check for stability, use isStable
.
isStable
requires a LagOp
lag
operator polynomial as input. For example, if ar0
is
a vector, enter the following code to check ar0
for
stationarity.
ar0LagOp = LagOp([1 -ar0]); isStable(ar0LagOp)
A 0
indicates that the polynomial is not
stable.
You can similarly check whether the MA approximation to the
ARMA model (ma
) is invertible.
[1] Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. Time Series Analysis: Forecasting and Control 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.
[2] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[3] Lutkepohl, H. New Introduction to Multiple Time Series Analysis. Springer-Verlag, 2007.