2 For Exponential Smoothing we will use the Excel Spreadsheet in this module. I created the spreadsheet so there is no copyright; do as you please Statistical Software

3 Before defining what Exponential Smoothing is, here is an example of a case that needs this wonderful tool: Why would I need something like Exponential Smoothing?

4 Exponential Smoothing Motivation Suppose you are investigating Alaska Airlines flight delays at Ted Stevens International in Anchorage, Alaska. Ted Stevens is a vital connection between Asia and the United States, and is has the third largest cargo traffic in the United States. Thus there is good reason why you are concerned with on time arrivals as cargo is often time dependent. Your goal is to predict the flight delays for the next three years. There are many ways to do this, and we have discussed one already: Using a regression line. However, sometimes data is not linear, and the data may actual depend on past data! Would this be a case of that?....Think it over as we learn Exponential Smoothing.

5 Examining the Data Take a look at the data in the spreadsheet titled Exponential Smoothing. This data looks to be quite chaotic, but let’s try Exponential smoothing to attempt to predict the next few values.

6 Exponential Smoothing (1) The idea behind Exponential Smoothing is to use past values to predict the future values, with more emphasis on the most recent values. We weight past values, add them together, and estimate the next value. All the weights must add up to 1 or 100%

7 Exponential Smoothing (2) For example, using the data in our spreadsheet, let’s try to predict the number of delays in August 2013 by using 70% of the previous month’s delays and adding that to 30% of the delays from two months ago. Thus we would have: 0.3(D i-1 ) +0.7( i-2 )=D i where D i is the number of delays of the i th month. See the results on the Smoothing All Data Tab.

8 Exponential Smoothing (3) Reviewing our results, we see that our delays look to approach 140, and if we keep going, this is the number of delays we will predict throughout. Also note that in this model we start with the first two months data, and then use solely our predictions from there on out. This is what is taught in most courses, but obviously does not serve us well in this case!

9 Exponential Smoothing (3) Reviewing our results, we see that our delays look to approach 140, and if we keep going, this is the number of delays we will predict throughout. Also note that in this model we start with the first two months data, and then use solely our predictions from there on out. This is what is taught in most courses, and has great benefits, but obviously does not serve us well in this case!

10 Exponential Smoothing (4) Let’s try with just the final six months in our data set. See the sheet Smoothing with Six Months. This seems to work better, but I am still not satisfied. Perhaps we should reexamine the original data.

11 Reexamining the Data Note that this is Alaska, and we should probably take into account the time of year. Look back over the winter delays versus the summer delays; there seem to be more of a pattern here. You can use any smoothing technique you see fit and any model as long as you justify it. I encourage you to explore other options when smoothing your data, and do not hesitate to contact me if you have questions.

12 Directions for Smoothing 1.Determine what your alpha will be 2.Put your alpha (between 0 and 1) in the cell G2. 3.Paste your data column A starting with A1. 4.Drag the cell B3 all the way down your data going one or two past your data value (these are your predicted values-see video).

13 Final Thoughts Remember to use common sense and examine the data If you use more than two previous values, be sure all the weights add up to 1. If you need help, ask!