Consider the following time series data in average temperatures for the year of 2021 in San Antonio.

Using the same time series to answer questions 11 - 15, develop a 4-month MVA and and use = 0.25 to compute the exponential smoothing values:

Month	Value
January	74
February	78
March	83
April	87
May	88
June	85
July	81
August	80
September	80
October	78
November	75
December

Compute the forecast for December for a four-month moving average for this time series:

What is the MSE for the four-month moving average time series?

What is the forecast for December using = 0.25 to compute the exponential smoothing values for the time series?

What is the MSE for the exponential smoothing time series using = 0.25?

Using the same forecast values for problem 11, calculate a three-month weighted moving average with the following weights:

1/4 for the most recent observation

1/3 for the second most recent observation

2/5 for the third most recent observation

What is the MSE for the three-moving weighted average time series?

By comparing the four-month MVA from question 11 to the three-month WMVA, which forecast is better?

By comparing the four-month MVA from question 11 to the three-month WMVA, which forecast is better?

Extra Credit - Construct a time series plot. What type of pattern exists in the data?