Instructions:

1.   You are allowed to use computer programming and/or Excel, but codes

and/or Excel worksheets and/or snapshots of computations should be provided to gain higher marks.

2.   We only accept submissions in the format of pdf, docx, xlsx (i.e.,Excel) and

jpeg. Sloppy submissions with unclear photos might cause mark reductions.

3.   You could upload multiple files if needed.

Question 1. [40 marks] A time series dataset is provided in the Excel file “data.xlsx” which contains 156 data points.

(1)  Describe the  dataset. Consider various aspects, for example the graph, the “ pattern”, the trend, etc.

(2) Treat   the   data   points   as   they   follow   a   linear   trend   model.   Generate 157, 158, … , 208    by   using   Double   Exponential  Smoothing   method  with S0  = 30, B0  = 10, α = 0.3, β = 0.1   and   present   the   forecasts   and   real observations   in   one   graph.   Round   your   answers   to   3   decimal   places. Conceptually do you think this is appropriate for this particular dataset? Why?

(3)  Use  a  different way to  produce  157, 158, … , 208   and  make  a  comparison with your result in (2), provide sufficient explanation/reasoning. Again present the forecasts and  real observations in one graph.  Round your answers to 3 decimal places.

Question 2. [30 marks] Caspar owns a Company which manufactures electronic chips and  his  business  partner,  Martin, would  like to order 200,000 chips, which would make the whole  company work full time for  a week,  each  chip  profits  $5  but  if Caspar couldn’t finish, he has no gain and needs to pay liquidated damage  $500,000; or Martin orders 100,000 chips, each profit  $4, in which case the company would work part-time, the liquidated damage is  $150,000. Also Caspar could choose not to take any orders from Matin and let the company not work for now. Due to the recent spread of COVID-19 in the city, all the companies are monitored by the government. So there is a 50% chance that a company with full time operations will be urged to close  temporarily   and   20%  for   companies  with   part  time   operations.  As   an alternative, companies could conduct a nucleic acid testing (costing  $10,000) before their productions, the ones with “all negative” would be allowed to work (regardless