Question

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

Date	A	B	C	D	Stock Exchange
9/3/10	127.37	18.34	21.03	15.51	10432.45
9/7/10	127.15	18.18	20.44	15.51	10334.67
9/8/10	124.92	17.88	20.57	15.82	10468.41
9/9/10	127.35	17.95	20.52	16.02	10498.61
9/10/10	128.37	17.82	20.42	15.98	10563.84
9/13/10	128.36	18.64	21.16	16.21	10616.07
9/14/10	128.61	18.83	21.29	16.22	10565.83
9/15/10	130.17	18.79	21.69	16.25	10627.97
9/16/10	130.34	19.16	21.76	16.36	10595.39
9/17/10	129.37	18.82	21.69	16.26	10517.99
9/20/10	130.97	19.12	21.75	16.41	10661.11
9/21/10	131.16	19.02	21.55	16.57	10687.95

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7).

I was also able to calculate the Mean Absolute Deviation (MAD) of each of the stocks: MAD of Stock A = 1.32 MAD of Stock B = 0.37 MAD of Stock C = 0.41 MAD of Stock D = 0.26 MAD of Stock Exchange = 83.85.

The Mean Square Error (MSE) of the stocks: MSE of Stock A = 2.22, MSE of Stock B = 0.17, MSE of Stock C = 0.21, MSE of Stock D = 0.08, MSE of Stock Exchange = 7963.44.

Help me to understand the concept of Mean Absolute Percentage Error (MAPE). I realize that MAPE is the average of absolute errors divided by actual observation values. I'm wondering if this is just the MAD divided by the total observation values for a particular stock. For example, for Stock A, If my understanding is correct (which I don't think it is), the MAPE of Stock A would be 1.32 / each of the observation values individually. Or, would it be [(127.15 - 127.37) / 127.15]. Or, do I need to add up all the absolute errors for Stock A and all the actual observation values for Stock A and divide the former by the latter and then multiply by 100. As you can see, I'm confused. Please help.

Answer 1

Solution: In order to calculate the MAPE for stock A follow steps as given below:

Step 1: Find the absolute error for the values of stock A.

Absolute error = | actual value - Forcasted value |

Step 2: Find the percentage absolute error for the values of stock A.

Absolute percentage error = (Absolute error × 100)/Actual value

Step 3: Now take the average of all the absolute percentage errors that you have calculated in step2. This average will be the Mean Absolute Percentage Error (MAPE).

The MAPE for Stock A is calculated below: