Page 86 - Special Topic Session (STS) - Volume 4

STS566 Richard Finlay
A VECM is similar the ECM above, except that instead of estimating a
separate equation for each denomination, one estimates all denominations
concurrently, which allows shocks to one denomination to effect demand for
another. Mathematically, the equation we estimate has the same basic form
as the ECM above, except that scalars and vectors become vectors or matrixes
(with yt now a vector of the log demand of each denomination at time t).
To compare the ARMA and ECM models we use rolling out-of-sample
forecast performance. Graphs 1-5 below show the mean absolute percentage
error (MAPE), relative to observed outcomes, for forecast horizons from one
month to three years into the future, where our sample starts in 2003 and runs
to between 2008 and November of 2015 (mean squared percentage errors
show a similar profile).
One can see that in terms of forecasting performance, the ARMA model is
as good as or better than the ECM for all denominations except the $50. The
superior forecast performance of the ECM for the $50 denomination (but not
the other denominations) appears to be due to a better fitting ECM model,
and in particular demand for $50 banknotes being more closely aligned with
the macro factors considered than is the case for the other denominations (for
example more factors are significant in the ECM than for the other
denominations, and the adjusted R2 is over twice as high as for the next-best
model). This likely reflects that the $50 is the main ATM banknote, and so is
the denomination that will respond most to changes in consumer spending.
This is also reflected in the $50 displaying the most seasonality of all
denominations. In contrast, the lower denominations, which are used as
change, appear to adjust velocity rather than quantity in response to changes
in spending, while demand for the $100 is in general hard to model accurately.

3. Determining contingency stocks
While we make every effort to forecast future banknote demand as
accurately as possible, our forecasts will inevitably contain errors, sometimes
large ones. Historically, the median absolute forecast error one year ahead,
expressed as a percentage of total outstanding banknotes, has ranged from
slightly less than 1 per cent for the $10 denomination to 3 per cent for the $50
denomination. The largest error, which occurred around the onset of the
global financial crisis for the $50 denomination, was 11 per cent. Given that
the Reserve Bank has a strong aversion to running out of banknotes in the
event of a spike in demand, we hold substantial contingency stocks. These are
calibrated to cover, for each denomination, a one-year outage to the
printworks during which time no new banknotes are delivered, and, on top of
this, an increase in demand proportional to that seen during the global
financial crisis. This delivers a contingency stock ranging from about 15 per
cent of circulation for the $100 denomination to 35 per cent of circulation for
the $50 denomination. Holding contingency stocks is not costless, although

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