the right formula

encouraged by finding the right formula and the brief distraction of writing a blog post, i put on the most sugar-y sweet happy music I have, and went to town to solve the problem.

i realized that it was similar to a problem I had posted to our class discussion board earlier in the week, so i check it... and noticed that I had done root-mean square (the forecast check to determine how accurate your forcast is) wrong. So I happily fixed it. Yeah, score extra points before it's graded.

so I get back to working at the problem at hand... and noticed something else.

when you're doing an exponential smoothing forecast, you have several elements. let's take a look at the formula:

Ft+1 =wAt + (1 - w)Ft

Essentially, Ft+1 is what you're solving for... it's the forecast for the next year.  For example, you might be trying to find what the forecast would be for the year 2000.  To find it you have three elements:

1) w: w is for a weight that you choose, between 0 and 1.  The point of this weight is to determine how much "weight" you're giving to the forecast from real data and forecasted data.

2) At: a is for the Actual amount from the year you are using to solve the forecast.  If you were trying to forecast for 2000, you would use the actual data for the year 1999.

3) Ft: f is for the Forecast you previously did to solve the current forecast.  Again, if you were trying to forecast for 2000, you would use the forecast data for the year 1999.

so what did i do wrong?

well, when you have a set of actual data, you start at the beginning and forecast through all the years you have leading up to the coming year that you're going to forecast for.  you do this so in the end you can check the root-mean square and find out how accurate your forecast is.  well, you have to start somewhere so, to get the very first Ft, you just take an average of all the real data you have.

when i originally solved the problem, I used the average every time instead of the previous forecast.

but, that wasn't the end of my troubles.

because of the way I wrote out the problem, using a grid, i ended up using the WRONG FORMULA.   i was doing this:

Ft+1 =wAt+1 + (1 - w)Ft

sigh.  so... i finally found all my errors (as far as I can tell) my fourth time through.  the good thing about this is I'll never forget this experience and the frustration, but continual excitement at "getting it right".  It's amazing that you can think you've got a problem right four times...

of course, from a psychological point of view, it makes you second guess yourself a lot and wonder how you got it wrong so many times.  in something like this i have two options:

1) decide in my mind that i just am never going to understand it

2) decide in my mind that after four tries, my answer is correct and i have mastery over the subject (which is why i wrote this post... so i could prove to myself that I understand the concepts).  if my answer is still wrong... at least I know my answer is more correct than my version 4 times ago.

which would you choose?