I'm using the Forecasting module to analyze data on household electricity
use. My dataset is mean hourly electricity use from 195 households for a 6-
month period. On five days in this period, for four hours in the
afternoon, the utility sent a signal to each house to turn off the air
conditioner, and I want to use time series analysis to make the best
estimate of the size of the effect of these signals on mean electricity
use. In particular, I'd like to look at the size of the effect during each
individual hour of each four-hour signal period. The method I've used is
to specify each hour as an Event in Expert Modeler. That is, I've created
20 dummy variables, each of them is all zeros except for a one for the
hour of interest. These twenty events are entered into the model along
with other continuous external predictor variables of interest (e.g.
outdoor temperature), which is treated as a transfer function. The Output
I get specific to these events looks something like this:
Event1H1 No Transformation Numerator Lag 0 -.249
Event1H2 No Transformation Numerator Lag 0 -.265
Event1H3 No Transformation Numerator Lag 0 -.240
Event1H4 No Transformation Numerator Lag 0 -.182
where 'Event1' refers to signal day 1 of 5, and H1 ... H4 are the
individual hours within each 4-hour signal period.
My interpretation is that the numbers in the final column indicate the
direct effect of the signal event in that hour on the outcome variable
(mean electricity use), compared to what would have happened had the
events not taken place. Thus the effect of the utility signal was highest
during the second hour, and had begun to tail off by the fourth hour. This
is in line with expectations from similar work in other jurisdictions, and
makes sense from simple visual inspection of the data.
I just want to confirm that this interpretation is correct. I'm cautious
because the model is autoregressive and also contains Lag 1 terms (for
example) for the outcome variable. Thus each hour of the outcome variable
is dependent on the hour before. Does this mean that the effect size for
the H2 event in the table above needs to be interpreted with respect to
the effect size for the H1 event (the event hour preceding it), or is this
already taken into account in the model algorithms, meaning that the
effects in the table above can be interpreted independently, and thus my
initial interpretation is OK?
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