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Estimation of the yield curve using nonlinear least squares minimization: The last part of this assignment asks you to construct the Nelson Siegel yield curve from observed bond prices, by minimizing the mean squared error.
Unfortunately, the minimization problem, although mathematically simple, is computationally quite complex. We have studied several different methods for finding the roots of an equation that were easy to implement (e.g., the bisection method and the secant method). Finding roots of higher dimensional equations, however, is a whole different story and the same applies to function optimization (which the error minimization problem is an example of). Since the Nelson-Siegel yield curve depends on five parameters, we may therefore expect to work quite hard to implement a solver for this problem.
Fortunately - and this is often the case - this is a standard problem, which clever people have already solved. We can therefore use a predefined library that solves the minimization problem, using the so-called Levenberg-Marquardt nonlinear least squares solver.
The STL details are described in many places online (see the CS377 webpage for some links), and there's a very quick introduction in Section A.14. Here are just a few additional no
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Armed with your function from above, we can do some interesting things. For instance, any pixel where the offsets are both zero is a pit (lower than all surrounding points) .
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