Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 84
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5.2.3. Long Path
5.2.3.1. Generating the Spread
We use the last 1260 points of the path presented in figure 5.25 in our study. A graph
of this path can be found in figure 5.26.9000
time
9500
10000
FIGURE 5.26. Discretized trend-stationary Ornstein-Uhlenbeck Process of
length 1260, with parameter values a = 0.0002, b = 0.02, A = 0.08 and
7- = 0.0055.2.3.2. Parameter Estimation
We now estimate the parameters of the model by maximum likelihood and least
squares methods. The result is shown in table 5.13. We notice that both methods estimate
the parameters a, A and - quite well, but do not perform well for b. We generate paths from
the estimates and compare them against the true path in figure 5.27. From this figure we
can see that the model is quite resistant to the error in estimating b.84
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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/m1/103/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .