QUESTION:
Can
you tell me:
1.
For time series data that has not been detrended, what is the
significance of a statistically significant
2.
autocorrelation? Does this imply predictability?
3.
If a large AC does not imply predictability, what good is knowing it?
ANSWER:
The
autocorrelation is simply a regression coefficient. The model is Y(t)=
Constant + b*Y(t-1) + A(t). It
measures
the unconditional relationship between the two series Y and Y lagged 1 period.
It's
strengths and weaknesses are identical to the ordinary regression coefficient.
It can be effected by
model
specification bias.
Suppose
the true model was:
Y(t)=Constant
+ b*Y(t-1) + W*I(t) where I(t) is a pulse series (0,0,....1,0,,,..0)
or
perhaps a level shift series (0,0,0,0,1,1,1,1,1,...) or perhaps a seasonal dummy
series
(0,0,0,1,0,0,0,1,0,0,0,1,....0,0,0,1)
or perhaps a trend series (0,0,0,1,2,3,4,5,0,0,0,..
.0,0,0)
.
Additionally,
if the Var(A) is not constant and either changes deterministically over time or
changes
proportional
to the mean or median of the series Y then the estimate of b can be subject to
serious error.
In
summary, the AC can be meaningful but what is of more importance as a result of
estimation is the
self-checking
aspect where the Gaussian assumptions are internally verified.
AUTOBOX
not only checks these issues but the adequacy of the model over time leading to
locally
optimized
modeling.