Optimal instrumental variables estimation for ARMA models

42 Pages·1999·1.8 MB·English

by  Kuersteiner, Guido M

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DEWB
HB31
M415
•
working paper
department
economics
of
OPTIMAL INSTRUMENTAL VARIABLES
ESTIMATION FORARMA MODELS
Guido Kuersteiner
No. 99-07 March, 1999
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139

WORKING PAPER
DEPARTMENT
OF ECONOMICS
OPTIMAL INSTRUMENTAL VARIABLES
ESTIMATION FORARMA MODELS
Guido Kuersteiner
No. 99-07 March, 1999
MASSACHUSETTS
OF
INSTITUTE
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142
riTUTE
10GY
R 1 4 1999
—
ARMA
Optimal Instrumental Variables Estimation for
Models
By Guido M. Kuersteiner1
In this paper a new class of Instrumental Variables estimators for linear
ARMA
processes and in particular models is developed. Previously, IV esti-
mators based on lagged observations as instruments have been used to account
for unmodelled MA(q) errors in the estimation of the AR parameters. Here it
is shown that these IV methods can be used to improve efficiency oflinear time
series estimators in the presence of unmodelled conditional heteroskedasticity.
Moreover an IV estimator for both the AR and MA parts is developed. One
consequence of these results is that Gaussian estimators for linear time series
models are inefficient members of this IV class. A leading example of an inef-
ficient member is the OLS estimator for AR(p) models which is known to be
efficient under homoskedasticity.
Keywords: ARMA, conditional heteroskedasticity, instrumental variables, efficiency lower-
bound, frequency domain.
1Address: MIT Dept. of Economics, 50 Memorial Drive, Cambridge, MA 02142, USA. Email:
[email protected].