For the data in the following table compute the adjusted...

For the data in the following table, compute the adjusted exponential smoothing forecast of the retail gasoline price using $\alpha = 0.5$ and $\beta = 0.1$. Assume that the forecast component for the first period is the actual time series data and the initial trend is zero. Determine the MAPD and express it as a percentage. Round your answer to two decimal places. Month-Year Gas Price Aug-11 $3.696 Sep-11 $3.667 Oct-11 $3.506 Nov-11 $3.443 Dec-11 $3.326 Jan-12 $3.440 Feb-12 $3.640 Mar-12 $3.907 Apr-12 $3.958 May-12 $3.791

Transcript

00:01 All right, so for this problem to begin, i'll note that when we're using exponential smoothing, the idea is that the forecasted value for time t is going to be equal to alpha times the actual value at time t minus 1, plus 1 minus alpha times the forecasted value for time t minus 1.

00:22 So, if we're setting alpha to be equal to 0 .1, we'd have that the forecast at time t is equal to 0 .1 times 1 .5 .1, we'd have that the forecast at time t is equal to 0 .1 times 1.

00:31 The actual value at time t minus 1 plus 0 .9 times the forecast value for time t minus 1.

00:39 Now i'm going to do all the calculations here using excel just because this is a kind of tedious process, just a lot of almost identical calculations, but i will be showing the explicit procedure here.

00:53 So of course we can't actually have a meaningful result for our first week, but then from that point on, we can do 0 .1 times previous week, plus, pardon me, so for this to actually be calculable, we need to go with some value just to put in as the forecast value for our initial period, and so i'm just going to go for the pretend, so to speak, forecast for that initial period as just being 17.

01:19 Then we can use our exponential smoothing from that point on.

01:27 So we have all of our different possible values found using alpha equals 0 .1.

01:32 We know that.

01:33 We know that.

01:33 We know that we know that that we're also going to want to do this for alpha equals 0 .2 as well.

01:37 So let's calculate that out here.

01:42 So we have, again, just match it up at the first week, and then from that point on, we'd have 0 .2 times the actual, times the previous actual value, times 0 .8 times the previous forecast value, and apply that procedure for the rest.

01:58 And then, actually, one thing that i'm just going to do here is shift these over to the side, because we're going to want to find the error values for each one of these.

02:09 So of course the error is just going to be the actual value minus the forecast of value.

02:16 And do that for the 0 .2 version as well, actual minus forecast.

02:22 And then we are trying to answer a few questions about the mean squared error and the mean absolute error.

02:31 So we have that the mean squared error is equal to one over the number of values we're using, times the sum of the squared difference between the actual value at time step t and the forecast value at time step t.

02:52 So looking at our different values here, to get the mean squared error, actually one second here, i need to add another column for each of these, because we're going to want to have the squared error.

03:06 Actually, we'll need two more columns...

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