MATLAB: Regression Estimates, Maximum Likelihood, Ordinary Least Squares

Question

Hi everyone!

I´m trying to estimate the following model:

r_t=a0+a1*spread_t+a2*depth_t+a3*liquidity+e_t

It is supposed to be really simple (nothing complicated) and I don´t have much knowledge in econometrics, so I don´t really know what model to use. At first I thought I should use Ordinary Least Squares, but then I thought using Maximum Likelihood Estimation because it is supposed to be more efficient. However, I don´t know if this is right. The data set is high frequency data, so I don´t know if that has an impact on the model to choose.

I would really appreciate any help 🙂 or suggestions of what kind of model can I use.

Have a nice weekend!

Lourdes

Answer 1

When the errors are distributed normally then OLS (easiest) = MLE (numerical solution)

• http://en.wikipedia.org/wiki/Ordinary_least_squares
• http://en.wikipedia.org/wiki/Maximum_likelihood

When the variance of the errors change from observation to observation (over time in your case) you have:

• http://en.wikipedia.org/wiki/Heteroskedasticity

If the change is autocorrelated then you have to use arch models:

• http://en.wikipedia.org/wiki/ARCH

Which mean at least two courses in undergrad econometrics (OLS and Time Series). A good start could be Introductory econometrics by Wooldridge.

This link could be very useful and easy to understand:

• http://econ.lse.ac.uk/ie/ieppt/series2/

Said that you could find a least squares solution to a system by simply doing:

x = A\b (OLS)

Good luck