Regression Estimates, Maximum Likelihood, Ordinary Least Squares

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

[Oleg Komarov]

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

[Lu]

thank you so much for the tips! have a nice weekend :)

Answer 2

[bym]

Seems like a simple multiple linear regression. Is e_t a constant?

[Lu]

Hi proecsm,

I guess it is the error term :) do you have any ideas or suggestions of any kind of simple models I could use to run this regression?

Thank you so much for your help :)

[Lu]

but it is a constant though :)

[bym]

do you have sample data for r_t, spread_t,depth_t and liquidity?

[Lu]

yes I have sample data, do you have any suggestions? i would really appreciate it, because I don´t know what model to use and still keep it simple.

Thank you so much for your help :)

[bym]

can you share your sample data?

Answer 3

[S.Behzad Hassani]

go here:

http://stats.stackexchange.com/questions/74878/numerical-example-for-mle-for-linear-regression-model