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We're now going to move on
to a Mean
Forecast Error.
We're looking at Chapter Four, Slide Nineteen,
or excuse me! Eighteen,
and Nineteen.
The Mean Forecast Error,
or MFE,
looks for a bias of errors towards forecasting, over forecasting, or under
forecasting.
We're looking for the running sum of forecast errors or RSFE
RSFE,
and that's nothing more
than the deviation
at the actual forecast minus
the actual demand, excuse me, minus the forecasted demand, and we ideally
want this to be zero.
So, if we look at this,
on Slide Nineteen,
we've actually done the math here before.
The actual deviation, again, for our same six time periods,
one, two, three, four, five, and six,
are
the negative five, one twenty minus
one twenty five,
five, or one thirty minus a hundred and twenty five,
negative fifteen,
one ten minus a hundred and twenty five,
positive fifteen for the one forty minus a hundred and twenty five,
negative fifteen, a hundred and ten minus one twenty five,
and five again,
for the one thirty minus one twenty five.
Again,
our "MFE"
or uh...
Mean Forecast Error
is the running sum of the forecast errors divided
by "n," or the number of time periods,
which in actuality
is
the sum of each actual
minus forecasted demand,
divided by "n."
Just like we've done each and every single time, we're gonna take that deviation,
A minus F here,
and we're going to sum it up.
So, negative five plus five is zero, plus
negative fifteen is a negative fifteen,
plus fifteen,
we're back to zero,
minus fifteen is a negative fifteen,
plus five is a negative
ten.
So our numerator here, or the running sum forecast error is a negative ten,
and we are dividing this, again, by our number of time periods,
which was six,
and if we do the math quickly we should get a negative 1.67
1.67.
Now,
looking at this, remember we said that a positive MFE
is under forecasting, a positive MFE is under forecasting
because our actual demand is higher than the forecasted demand.
So,
a negative
MFE, we're over forecasting! Our actual demand is lower than the forecasted
demand.
So, what we're looking at here is a negative MFE.
What does this mean? It means that we have
over
forecasted here.
Our actual
demand is less than,
on average, what we have been forecasting.
Again, that is the MFE,
or mean forecast error,
and we're going to continue on
to the Mean
Absolute
Percentage Error (MAPE).
In Chapter Four,
on Slide Twenty here, and Slide Twenty- one, we're looking at a Mean Absolute
Percentage Error,
and this is actually a percentage. This is where we can actually take a look at
a forecasting method and say
"Oh look, this is what happened"
and
the formula in your book is a little bit different than the one I'm
going to give you, but if you take a look at
the math in it, it's still the same,
but I like to be repetetive and if you noticed,
with
uh... mean absolute deviation, mean squared error,
mean forecast error,
MAD, MSE, and MFE,
we sort of followed the same pattern.
I like patterns. I understand the pattern.
I can get in that mode and just keep going with it and so we've tweaked the
formula a little bit
so that it fits that same pattern.
So, literally,
what we are going to do is take the sum
of
one hundred times the actual demand minus the forecasted demand
divided by the actual demand
and divide that by
the number of observations or the number of time periods that we have
taken.
So, when we go to Slide Twenty-one to actually calculate,
you'll see again the same things that you've seen before,
the actual
demand
in that first column, the forecasted demand
in the second,
the deviation A minus F in the third.
Here we're going to have the absolute deviation of A minus F
and then working towards that absolute percentage of error, which writing the
formula above that is actually going to be one hundred
times the absolute value of A
minus F divided by A.
So, in my time periods again,
one, two, three,
four, five, and six,
I'm going to take my deviation
and I'm just going to quickly write these in because we've already
looked at these, we've already computed
these numbers
when we worked on our
MAD, our MSE, and then our MFE, we had these same numbers all the way
across
and now let's get that absolute deviation
back from where we did the MAD,
so, negative five would be five, a positive five would be five,
negative fifteen will be fifteen,
fifteen will be fifteen,
negative fifteen will be fifteen, and five will be five.
Now comes the computation.
In order to do this computation,
I'm going to take
this column, my absolute deviation,
and divide it by
my actual demand,
so...
and then I'm going to multiply it
by one hundred
to get my absolute percentage of errors.
So I'm going to take five
and divide it by a hundred and twenty and multiply by
one hundred
and...
let me write that...
in black...
and you should get four point one seven (4.17).
I'm going to take, for the second time period, five divided by a hundred and
thirty...
and you should get three point eight five (3.85).
Fifteen
divided by a hundred and ten times one hundred
and you should get
thirteen point six four (13.64).
Fifteen divided by a hundred and forty for the fourth period,
times one hundred is ten
point seven one (10.71).
Fifteen
divided by a hundred and ten
times one hundred is again
thirteen point six four (13.64),
and then five divided by a hundred and thirty times one hundred
is
three point eight five (3.85).
Again,
my mean absolute percentage of errors,
I am taking the sum of one hundred times the absolute value of the actual
minus the forecasted demand divided by the actual,
and dividing that
by "n."
So, I need to sum up
this last column.
So adding 4.17, 3.85, 13.64,
10.71, 13.64, and 3.85,
you should get
49.86,
so that number becomes my numerator,
and I'm going to divide that by "n," from the number of time periods,
which is six,
and the answer
should be 8.31, no now remember we said this was a percentage,
so we're making our forecasting errors
approximately 8.31% of the times.
So we actually can say here is a percentage, and we can take a look and of
course
when you're looking at errors do you want a larger percent or a lower percent?
I, personally, would prefer a lower percent of errors.
So
8.31%, we can take a look at... ten percent, two percent,
which are forecasting method is doing a better job?
Now, everything that we've looked at so far,
MAD,
uh... mean absolute deviation, MSE,
mean squared error, MFE, mean forecast errors,
uh... MAPE
a mean absolute percentage of errors,
have all been taking a look at forecasting methods and seeing how well
they're doing.
What happens if you actually want a forecast,
you actually want to find out that forecasting number?
There's ways to do that,
and were going to do that
looking at
simple moving averages.
Looking at
a simple moving average, we're in Chapter Four,
Slide Twenty-three.
A simple moving average
is nothing more than finding a mean, finding an average,
of a specific amount of data.
This problem looks at a three month
simple moving average.
That means, we're going to take
a mean of three months worth of information.
So here instead of time periods one, two, three, we're looking at months, twenty,
twenty one, twenty two, twenty three, twenty four, and twenty five,
and we want to start with
data to
get a forecasted demand
for that next month or for next year during this time period,
depending on what we're looking at,
so, what we do is we take three time periods, here three months,
and find the average of that.
So, to find the average
of months twenty, twenty one, and twenty two,
we're going to take
one twenty (120),
plus one thirty (130),
plus one ten (110),
and divide
by three,
which should give us
three sixty (360)
divided by three
or
this first
three-month uh...
simple moving average
is actually
a hundred and twenty (120).
We're then
going to just slide down one month
and pick up the next month.
So, we're going to be taking a look instead of time period twenty, twenty one, and twenty two,
we're now looking at twenty one, twenty-two, and twenty-three.
So, we're going to have
one thirty (130)
plus one ten (110)
plus one forty (140),
which should give us three hundred and eighty (380) and we're going to divide that by
three,
which should give us
a hundred and twenty six point six seven (126.67).
Again, we're going to slide down
just one month
to take the next simple moving average,
and it's going to be starting with time period
twenty-two, twenty-three,
and twenty four.
So, with this we're going to take one hundred and ten (110),
plus one hundred and forty (140),
plus one hundred and ten (110), which should be three hundred and sixty (360),
and divide by three, the number of time periods we're using in our
simple moving average.
So, three hundred and sixty (360) divided by three
is a hundred and twenty (120).
Using what we have left,
time period twenty three, twenty-four, and twenty five,
we're going to take
those three time periods and add them up, a hundred and forty (140),
plus a hundred and ten (110),
plus a hundred and thirty (130), which should give us three eighty (380),
and divide again by the number of time periods we're using,
which would give us
one twenty six point six events (126.67).
So, our simple moving average,
is literally taking an average of a subset of data.
And as long as we have the number of months or the number of time periods that
we're able to do,
we can continue moving on,
if we had a time period twenty six, I could move down one more.
I have to have at least three months
in this one, or three time periods
to be able to do
the average
because I want a three time period simple moving average.
If I moved down again with the information I have, I only had
time period twenty four and twenty five left, I don't have enough information to take
another simple moving average.
So, that is how you find the simple moving average
within forecasting.