Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 89
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Comparison between estimated and actual path
2.02-
2.00-
a,
m
1.98 Key
True path
- Long-term mean
Least Squares Estimated
1.96 Maximum Likelihood Estimated
9850 9900
time
FIGURE 5.30. Paths of length 126 for the trend-stationary OU process, gen-
erated from one realization of estimates from maximum likelihood and least
squares methods, with true parameter values a = 0.0002, = 0.02, A = 0.08
and a- =0.005True Value Method Estimate Bias Standard Error RMSE
MLE 0.00020047 0.00000047 0.00001548 0.00000000
a 0.00020000
LS 0.00020751 0.00000751 0.00015013 0.00000002
MLE 0.01572380 -0.00427620 0.15276549 0.02335558
b 0.02000000
LS -0.05404180 -0.07404180 1.48428565 2.20858609
MLE 0.11847379 0.03847379 0.05471677 0.00447416
A 0.08000000
LS 0.14065392 0.06065392 0.05857387 0.00710980
MLE 0.00505847 0.00005847 0.00033740 0.00000012
0 0.00500000
LS 0.00508214 0.00008214 0.00034027 0.00000012
TABLE 5.16. Performance of Maximum Likelihood and Least Squares meth-
ods for estimating the trend-stationary OU parameters, by 10,000 Monte Carlo
simulations, using a path of length 12689
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Tamakloe, Emmanuel Edem Kwaku. Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes, dissertation, December 2021; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1873709/m1/108/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .