Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 70
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Comparison between estimated and actual path
Key
- True path
- - Long-term mean
- Least Squares Estimated
- Maximum Likelihood Estimated9880
9920
time
9960
10000
FIGURE 5.17. Spreads of length 126 each, generated from one realization of
parameter estimates from maximum likelihood and least squares methods,
using ln(Qt) and ln(P)TABLE 5.10.
Parameter estimates by Maximum Likelihood and Least Squares
methods the 126 steps OU process, by Monte Carlo simulations
70
2.4-
0 2.0
1.6True Value Method Estimate Bias Standard Error RMSE
MLE 0.29927062 -0.00072938 0.05609920 0.00314765
r 0.30000000
LS 0.29571629 -0.00428371 0.04870552 0.00239058
MLE 1.54209289 0.04209289 0.51689144 0.26894857
1.50000000
LS 1.43436118 -0.06563882 1.46113841 2.13923392
MLE 0.08370286 0.03370286 0.05781343 0.00447828
A 0.05000000
LS 0.10151337 0.05151337 0.04976264 0.00512995
MLE 0.01303405 0.00003405 0.00088106 0.00000078
- 0.01300000
LS 0.01321786 0.00021786 0.00092366 0.00000090
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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/m1/89/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .