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Calculating and Plotting MSE

Calculating and Plotting MSE. Angela Ryu Economics 201FS Honors Junior Workshop: Finance Duke University March 24, 2010. Example. XOM (Y) vs. WMT (X) Number of days: 1093 days Sampling interval: 5 minutes Beta Calculation days: 30 days. Preparation (1) - Setup.

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Calculating and Plotting MSE

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  1. Calculating and Plotting MSE Angela Ryu Economics 201FS Honors Junior Workshop: Finance Duke University March 24, 2010

  2. Example • XOM (Y) vs. WMT (X) • Number of days: 1093 days • Sampling interval: 5 minutes • Beta Calculation days: 30 days

  3. Preparation (1) - Setup • Get WMT, XOM log returns and denote Px, Py respectively. • Sample P by 5 minutes: 76 data for each day • Take out the overnight returns • Size (Px) = Size (Py) = 76 * 1093

  4. Preparation (2) – Calculate Beta • Days – (1:30), (2:31), (3:32), … , (1064:1093) • Case (1:30): • Take first 76 * 30 data (1 to 76*30) from Px and Py and denote X1:30 and Y1:30 . • Calculate with (where Y = βX) • Take the mean and denote β1:30 • Case (2:31): • Exclude the day 1 data (1 to 76) and add data on the day 31 (76*30+1 to 76*31). Get β2:31 • Repeat to get β3:32, …, β1063:1092 Note: all betas are scalar

  5. Preparation (2) – Calculate Beta Case (1:30): Case (2:31):

  6. Preparation (3) – Calculate MSE • Calculate SE for each beta. • SE31 = (Y31 - β1:30 * X31 )2 • SE32 = (Y32 – β2:31 * X32 )2 … • SE1093= (Y1093 – β1063:1092 * X1093 )2 Note: SEi is a vector of size 76 for all i = 31, … 1093 • Take the average to get MSE30 • MSE30 = avg [avg(SE1:30 ), …, avg(SE1064:1093)] ()2  Square each term in vector

  7. Preparation (4) – change intervals & plot for each sampling interval • Sampling intervals: change from 1 min to 20 mins in prep. (1) • Beta Calculation intervals: change from 1 day to 50 days in prep (2) • Plot for each sampling interval • X axis: Beta Cal. Interval days (from 1 to 50) • Y axis: the value of MSE • In total, we get 20 plots

  8. WMT(Y) vs. XOM(X) (5 min)

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