Question: The daily evolution of a certain stock is recorded for the first 101 days of the year. Each of the following 101 numbers represents the gain a certain stock has at the end of the respective day. For example the first value in the vector below represents the gain after the first day, the second value below represents the gain after the second day, and the third value represents the gain after the third day and so on, till the last value which represents the gain of the stock after the 101-th day. By gain here we understand the value at the end of the day minus the value at the beginning of the day.

Assuming there are no events influencing the value of the stock between the end of one day and the beginning of the next day and that the initial value of the stock is 1 dollar try to predict the evolution of the stock value over one year (365 days) first by using a linear least square fit and secondly by using a quadratic least square fit. Which of the two predictions will be more accurate? Why? What will the final value of the stock be at the end of the year?

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document