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Comparing MSE: Optimal Sampling Frequency and Beta Interval. Angela Ryu Economics 201FS Honors Junior Workshop: Finance Duke University March 31, 2010. Data & Variables. SPY TGT, XOM, WMT (3 stocks) Aug 20 2004 – Jan 7 2009 (1093 days) Sampling frequency (SF) : 1 – 20 min.
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Comparing MSE: Optimal Sampling Frequency and Beta Interval Angela Ryu Economics 201FS Honors Junior Workshop: Finance Duke University March 31, 2010
Data & Variables • SPY • TGT, XOM, WMT (3 stocks) • Aug 20 2004 – Jan 7 2009 (1093 days) • Sampling frequency (SF): 1 – 20 min. • Beta calculation days (BI): 1 – 50 days
Recap • So far, we have observed MSE varying over BI for a given sampling frequency. • Similar trends were observed among 9 different stocks: relative drop in MSE around 5 – 15 Beta interval days • Remaining questions: (1) (1 stock) For a stock, how do the levels of MSE vary among different sampling frequencies? (2) (2+ stocks) Are the results from different stocks comparable? If so, how? (3) Can we empirically find an “optimal” beta interval days for a given sampling frequency?
(1) Comparing MSE (1 stock) • Method: plot a stock’s MSEs of different frequency. *The higher the sampling frequency, the higher the MSE!
Results from (1) • As we have less data in low frequencies, it intuitively makes sense to have higher MSE. • Despite the sudden drop starting at (approx.) 5 days, the increase in MSE due to lower sampling frequency dominates • The lowest point of 10 min. MSE is still strictly higher than the highest point of 9 min. MSE, etc.
(2) Comparing MSE (2+ Stocks) • Method: For a given sampling frequency, compare percentage changes of MSE w.r.t. MSE1 (= MSE with Beta Interval Day = 1) • i.e. plot MSE / MSE1,where MSE = [MSE1 MSE2 … MSE50]
SPY vs. TGT, WMT, XOM (15 min) *In percentage terms, change in MSE of different stocks w.r.t. BI is similar to each other.
(3) “Optimal” Beta Interval • Method: For different stocks, plot Beta interval where MSE is minimum vs. Sampling Frequency. • For each sampling frequency, there exist a Beta interval day with minimum MSE. • X-axis: Sampling frequency (1 – 20 min) • Y-axis: Beta interval days (1 – 50 days) with min. MSE • Linear regression
BI with MinMSE vs. SF TGT WMT XOM ALL
Linear Regression: over divided SI Replaced the outlier data of day 7 Mean: 4.625 Mean: 13.3333 *For WMT, if approximately 5 or 13 days of data is used to calculate Beta, MSE is minimized.
Further Steps • Try regression on different stocks • Hypothesis on optimal Beta interval:e.g. H0: “BI with MinMSE lies in [4, 14]” • Relevant theses?