Convert ARMA model to AR model
returns
the coefficients of the truncated, infinite-order AR model approximation
to an ARMA model having AR and MA coefficients specified by ar
= arma2ar(ar0
,ma0
)ar0
and ma0
,
respectively.
arma2ar:
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.
To accommodate structural ARMA models, specify the
input arguments ar0
and ma0
as LagOp
lag operator polynomials.
To access the cell vector of the lag operator polynomial
coefficients of the output argument ar
, enter toCellArray(ar)
.
To convert the model coefficients of the output argument from lag operator notation to the model coefficients in difference-equation notation, enter
arDEN = toCellArray(reflect(ar));
arDEN
is
a cell vector containing at most numLags
+ 1
coefficients corresponding to the lag terms in ar.Lags
of
the AR model equivalent of the input ARMA model in difference-equation
notation. The first element is the coefficient of yt,
the second element is the coefficient of yt–1,
and so on.The software computes the infinite-lag polynomial of the resulting AR model according to this equation in lag operator notation:
where and
arma2ar
approximates the
AR 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 AR approximation to the
ARMA model (ar
) is stationary.
[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.