Progress Report

This blog post is concerned with the milestones achieved and some upcoming features in statsmodels

NONLINEAR MODELS

The model implemented is

y = f(x,θ) + e

where the y is one dimensional endogenous data matrix, f is the nonlinear function, x is exogenous data  matrix, θ is parameter matrix and 'e' is the noise in data. 

Estimation

The estimation of parameters is done using the 'leastq' method from scipy.optimize which minimizes the sum of squares of residuals. We subclass the model class 'NonlinearLS' and provide the 'expr' function which calculates 'f' in the above expression using the parameter values and exogenous data provided to it. It is encouraged that the user provides the analytical derivative of the given function by defining 'jacobian' function in the similar way as 'expr'.

Testing
For testing purposes we used the 'Misra1a' model from NIST data. Details regarding this given in previous post. In summary, we obtained satisfactory results as compared to 'Gretl' which uses the same minpack module used by scipy.

Miscellaneous Features

• Parameters calculated at each iteration by the algorithm can be viewed using view_iter() method
• Prediction table with confidence intervals for each predicted value of endogenous data using prediction_table(alpha) method

Example
A complete example can be viewed here https://github.com/divyanshubandil/statsmodels/commit/db2e388232303323cc9bb36e0fe9f682892993ba

ROBUST NONLINEAR MODELS
I have been working on the M-estimation of nonlinear models for some time now. The best research paper I found having all the tests, computational algorithm and simulation data is here. http://www.tandfonline.com/doi/abs/10.1080/03610920802074836
Recently, I have been able to implement the algorithm in my first commit regarding this topic here https://github.com/divyanshubandil/statsmodels/commit/1745e02b45ebe3f83a8e0d55f477fcef33621d6f
Now I am working with testing this model for the 'Numerical example' given in the paper.