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Godfrey test.
IV. A General Test of Autocorrelation:
The Breusch–Godfrey (BG) Test
30
To avoid some of the pitfalls of the Durbin–Watson 
d
test of autocorrelation, statisticians
Breusch and Godfrey have developed a test of autocorrelation that is general in the sense
that it allows for (1) nonstochastic regressors, such as the lagged values of the regressand;
(2) higher-order autoregressive schemes, such as AR(1), AR(2), etc.; and (3) simple or
higher-order 
moving averages
of white noise error terms, such as 
ε
t
in Eq. (12.2.1).
31
Without going into the mathematical details, which can be obtained from the refer-
ences, the 
BG test,
which is also known as the 
LM test,
32
proceeds as follows: We use the
438
Part Two
Relaxing the Assumptions of the Classical Model
28
Ibid., p. 161.
29
Fumio Hayashi, 
Econometrics,
Princeton University Press, Princeton, NJ, 2000, p. 45.
30
See, L. G. Godfrey, “Testing Against General Autoregressive and Moving Average Error Models
When the Regressor Includes Lagged Dependent Variables,’’ 
Econometrica,
vol. 46, 1978,
pp. 1293–1302, and T. S. Breusch, “Testing for Autocorrelation in Dynamic Linear Models,’’
Australian Economic Papers,
vol. 17, 1978, pp. 334–355.
31
For example, in the regression 
Y
t
=
β
1
+
β
2
X
t
+
u
t
the error term can be represented as
u
t
=
ε
t
+
λ
1
ε
t
−
1
+
λ
2
ε
t
−
2
, which represents a three-period moving average of the white noise error
term 
ε
t
.
32
The test is based on the