Question

Consider the following time series data: Month 1 2 3 4 5 6 7 Value 25 13 21 13 20 22 14 (a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8

Answer 1

Answer:

a. MSE = 64.8

b. Forecast for month 8 is 14.

Step-by-step explanation:

$MSE = \frac{sum (error)^{2} }{n-1}$

where $error= value-forecast$

Using the most recent value as the forecast for the next period, we have forecasts for the months as;

(1,-) , (2,25) , (3,13) , (4,21) , (5,13) , (6,20) , (7,22)

$error$ = (-, -12, 8, -8, 7, 2, -8, -)

$error^{2}$ = (-, 144, 64, 64, 49, 4, 64, -)

$sum(error^{2} ) = 389$

$MSE = \frac{389}{7-1} = 64.833333$

Therefore, MSE = 64.8 (1 decimal place).

The Forecast for month 8 is 14 since we are using the most recent value as the forecast for the next period.

Answer 2

Answer:

MSE = 64.8 to 1d.

The forecast for the 8 months is 14.

Check attachment for solution and diagram

Step-by-step explanation:

The table was computed using the following analysis

1. Forecast value: we are told to use the most recent value for the next period, so we take values from the previous time series values.

2. Forecast error:

time-series value — Forecast Value

3. Absolute Value of forecast error: absolute value means modulus of a number and it returns a positive value of that number e.g. |-x| = x

4. Squared forecast error: this means multiplying the error with it self. i.e. (forecast error)²

5. % error:

(forecast error) / (time series value) ×100

6. Absolute forecast error: same as number 3.

Therefore,

MSE= total square forecast error / frequency

MSE = 389 / 6

MSE = 64.83

To 1d.p

MSE = 64.8

The forecast for the eight month is 14. This is the last time series value and it will be 8 month forecast value.