# Calculating and Plotting MSE - PowerPoint PPT Presentation

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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

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

• 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

• 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

Case (1:30):

Case (2:31):

### 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

• 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