Consider the following time series data.

$($a$)$ Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month $8?$

$($b$)$ Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month $8?$

$($c$)$ Which method appears to provide the better forecast?

Forecasts will be made using the most recent values known. There will be no forecast for the first month. The forecast value for month $2$ will be the observed value from month $1,$ so the forecast value for month $2$ is $|$

$].$ The forecast value for month $3$ will be the observed value from month $2,$ so the forecast value for month $3$ is

$.$ This pattern will continue for the rest of the months.

Complete the column for the forecast value in the table below.

Find the forecast for month $8$ using this pattern