TIME SERIES FORECASTING

Based on the success of the first season, Mr. Lee decided to expand his Alumni Games for students on a larger scale. A monthly number of participants for each of the past 3 years are provided below. A forecast of participant numbers for the next year is needed in the determination of the rewards.

	Year 1	Year 2	Year 3
Jan	438	484	550
Feb	420	465	538
Mar	414	463	534
Apr	318	385	438
May	280	345	402
June	240	286	354
Jul	220	290	350
Aug	216	273	331
Sep	198	255	324
Oct	225	283	343
Nov	270	308	389
Dec	315	365	435

1. You may need to smooth out the patterns by a 12-month WMA to discuss any apparent components of the time series. Plot a 12-month WMA on the same graph in part (a)

2. Smooth out the patterns that include everything the model learned so far based on the historical record of the number of participants. The forecast in the first month was 430. You are free to choose an appropriate smoothing coefficient to smooth out the pattern and preserve the given time series components.

Please answer the whole question.