Question

Special Note: The teacher wants the question to be explain step by step, not worked out.

Given is a historical time series for job services demand in the prior 6 months. Month Demand 1 11 2 13 3 14 4 12 5 13 6 14 a) In your own words, explain (do not show how to solve) how to compute MSE based on the 3 months moving average method b) In your own words, explain (do not show how to solve) how to compute MAD based on the 3 months moving average method c) In your own words, explain (do not show how to solve) how to compute MAD based on the Exponential smoothing α = 0.2 method The teacher wants question to be explain step by step not worked out.

Answer 1

(a)

MSE is the Mean Squared error

First we need to find the forecasted values. Since we are using 3 months moving average, we will find the forecasted values for months 4, 5 and 6. The 3 months moving average is the average of last 3 months services demand i.e. F_t = (A_t-1 + A_t-2 + A_t-3)/3

Now we need to find the squared error for these 3 months. The squared error is the square of the difference between the actual value and the forecasted vale. Find this for months 4, 5, 6.

Once we find the squared errors, we find the average of the squared errors for months 4, 5, and 6. This average value is the MSE

(b)

MAD is the Mean Absolute error

First we need to find the forecasted values. Since we are using 3 months moving average, we will find the forecasted values for months 4, 5 and 6. The 3 months moving average is the average of last 3 months services demand i.e. F_t = (A_t-1 + A_t-2 + A_t-3)/3

Now we need to find the absolute error for these 3 months. The absolute error is the absolute difference between the actual value and the forecasted vale. Find this for months 4, 5, 6.

Once we find the absolute errors, we find the average of the squared errors for months 4, 5, and 6. This average value is the MAD

(c)

We need to first find the exponential smoothened forecast using the exponential smoothening coefficient. For period 1 we assume that the forecast is same as the actual value.

Exponential forecast values for other months is calculated as sum of forecast for previous month plus the smoothened difference between the actual value in last month and forecast in last month i.e. F_t = F_t-1 + α(A_t-1 + F_t-1)

Now we need to find the absolute error for months 1 to 6. The absolute error is the absolute difference between the actual value and the forecasted vale. Find this for months 1, 2, 3, 4, 5, 6.

Once we find the absolute errors, we find the average of the squared errors for months 1, 2, 3, 4, 5, and 6. This average value is the MAD