Calculating and plotting mse
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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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Calculating and plotting mse

Calculating and Plotting MSE

Angela Ryu

Economics 201FS

Honors Junior Workshop: Finance

Duke University

March 24, 2010


Example

Example

  • XOM (Y) vs. WMT (X)

  • Number of days: 1093 days

  • Sampling interval: 5 minutes

  • Beta Calculation days: 30 days


Preparation 1 setup

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


Preparation 2 calculate beta

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


Preparation 2 calculate beta1

Preparation (2) – Calculate Beta

Case (1:30):

Case (2:31):


Preparation 3 calculate mse

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


Preparation 4 change intervals plot for each sampling interval

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


Wmt y vs xom x 5 min

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


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