Hi k9queen!
Here are the answers to your questions:
1) A possible question that could be asked is: what will be the amount
of sales of the supermarket X in the next quarter? In order to answers
this question, it's possible to use any of the three models described
above.
· Moving average model: this model should predict that the sales next
quarter should be equal to the average of sales of the current and
possibly some previous quarters. Thus this model is better fit for
short term movements: the forecast for future sales is the average of
recent sales. The length of the moving average (i.e., how many periods
you're averaging) will determine how "recent" are the sales that are
used for the forecast.
The equation for this model would be (assume we're at time t), and
sales are represented by 'y':
y(t+1) = (y(t)+y(t-1)+...+y(t-n))/n
(n is the length of the moving average)
· Trend model: this model should predict that the sales next quarter
follow the trend of sales of the sample from where the trend line was
obtained. Thus the trend model would best fit long-term movements. For
example, if the supermarket opened three years ago, it could be the
case that sales have been generally rising (although there could be a
few downward movements), because the supermarket is becoming more
known among the neighboring people. So -in this case- the forecast for
the next quarter would be that the sales next quarter are greater than
the ones in the current quarter. The equation for this model would be:
y(t+1) = a + b*(t+1)
(a and b are the coeffcients of the trend line)
· Causal model (regression): the prediction from this model would
depend on the predicted values for the causes of sales. A causal model
would establish that sales each quarter depend on a number of
variables (unemployment, income level, advertising spending, etc.).
Therefore, in order to make a forecast for the sales next quarter, we
must know (or have another forecast) the value of the variables that
will affect sales. For example, if we find that sales depends
positively on advertising spending; then, if the supermarket plans to
rise this spending next quarter, and everything else is held equal,
then the forecast would be that sales will rise. If several of the
variables are changing, then the final forecast would depend on the
combined effect of these variables. The equation for the causal model
would be:
y(t+1) = A + B1*X1(t+1) + B2*X2(t+1) + B3*X3(t+1) + ...
(X1, X2,... are variables -causes- that affect sales)
a) Let's assume that the causal model is not taking in account the
effect of the passage of time (and thus it doesn't take in account the
general trend). Then, in order for the three forecasts to be
approximately equal, we must have that:
· The trend line is flat (so sales trend is neither increasing nor decreasing)
· This and the previous quarters are very similar in terms of sales figures
· The variables of the causal model aren't expected to change much next quarter
In this case, all the forecasts would be approximately the same; in
fact the forecast would be that the sales next quarter are equal to
the sales of the current quarter. Of course, it would be extremely
rare that all these conditions happen at the same time.
b) Basically, the opposite to everything stated in the previous answer
would have to happen:
· Suppose the trend line is increasing, so that the average *growth*
of sales is about $1,000 per quarter. The trend model would then
predict that sales next quarter are $1,000 more than sales this
quarter.
· However, the current quarter could be October-December, when
everyone goes Christmas shopping, so the sales are significantly
higher than in any other quarters. The moving average model would thus
predict extremely high sales for the next quarter (a growth of more
than $1,000)
· Yet the income level is expected to fall significantly next quarter,
because the Congress is about to issue a tax rise. Under this
conditions, a causal model that takes income level as an input could
predict that sales will fall rather than grow.
c) There is no superior model, as each one is best suited according to
the specific situations. Consider the situation in which sales have
always been rising, but have stopped doing so in the last year (maybe
because another supermarket opened in the same area). The trend line
would predict that sales next quarter will be higher, but this would
not be an adequate forecast. A moving average based forecast could beb
better, because it would take in account the lately there has been a
slowdown in sales. On the other hand, if this slowdown is only
temporary, then the trend line would make a better forecast than the
moving average. On the other hand, a causal model would be best when
the general situation has changed and the trend line or moving average
are no long valid. A change in the "general situtation" could be a
change in income level, a new supermarket opening, etc; conditions
than can't be taken in account by a trend line or average. The
drawback of the causal model is that it's difficult to decide which
variables affect sales, and it's also difficult to forecast the values
of these variables in the next period.
d) If you are sure you have a good causal model (i.e., you have taken
all the relevant variable into account) and you have good predictions
for the variables in this model, then the causal model is generally
preferred over the other two. If for any reason you can't trust the
causal model, or yoiu don't have forecasts for the variables, you
should turn to some of the other two models. In this case, if you
expect sales to continue with the long-term trend, it would be best to
use the trend line model. However, if you have no reason to believe
that this trend will be followed in the future, then you should use
the moving average model, which assumes the future will be "similar"
to the present and recent past.
I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification before rating it.
Otherwise I await your rating and final comments.
Best wishes!
elmarto |
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