Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 96
xviii, 147 pages : illustrations (some color)View a full description of this dissertation.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
5.2.5.3. Parameter Estimation
We estimate the parameters rj, a, b, A and - by maximum likelihood method based on
equation 68 and also by the method of least squares using the system of equations obtained
earlier in the section. A comparison of the outputs is presented in table 5.18. We observe
from the table that the parameters are quite well estimated by both methods except for b
for the least squares method, and A is also slightly off. Based on these parameter values, we
reproduce the trend-stationary OU process and plot them in figure 5.37. We see that again
the maximum likelihood estimates are better than the least squares estimates. However these
estimate for b in the least squares method is not good enough for the purpose of estimating
optimal thresholds since the drift level plays a major role in the level of the thresholds.TABLE 5.18.
Parameter estimation for the trend-stationary OU process repre-
senting the spread between lnPt and lnQt, by maximum likelihood and method
of least squares.96
True Value Method Estimate Bias Standard Error RMSE
MLE 0.28905200 -0.01094800 0.00240500 0.00012564
r 0.30000000
LS 0.30552645 0.00552645
MLE 0.00021070 0.00001070 0.00000018 0.00000000
a 0.00020000
LS 0.00015396 -0.00004604
MLE 0.80031100 0.00031100 0.02068100 0.00042780
b 0.80000000
LS 1.06789968 0.36789968
MLE 0.08562200 0.00562200 0.01212300 0.00017857
A 0.08000000
LS 0.09469577 0.01469577
MLE 0.00508800 0.00008800 0.00010600 0.00000002
o- 0.00500000
LS 0.00509058 0.00009058
Upcoming Pages
Here’s what’s next.
Search Inside
This dissertation can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Dissertation.
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/m1/115/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .