Suggestions to my thesis?

[Englund]

I'm writing a thesis for a masters degree in statistics soon, and I would like some input and suggestions on what to write about.

For my bachelor thesis I predicted a multinomial logistic model and used it for predicting outcomes of football (soccer) games, and estimated the expected return when using this model. This gave me insights into the multinomial logit model as well as a lot of programming experience. So this might be a subject to write about again.

I am also very interested in estimation under non-response. The Heckman two-step estimator, the Särndal & Lundström estimator and GREG two-phase estimation are interesting topics, for example.

Another interesting topic would be to conduct a simulation study and examine the properties of the estimated parameters using different methods of estimating them. Usually we estimate parameters of a model by choosing parameter estimates which minimizes the squared distances. An interesting topic is how well methods like minimization of MAD and/or the absolute values of the cubed distances (and maybe some other methods of estimating the parameters) performs. But I guess this have been studied extensively already, and simulation studies feels so 1980.

Please suggest topics if you have any ideas

 

[Englund]

In the last paragraph I am talking about linear regression.

 

[noetsi]

My input is talk a lot to your committee And when others disagree with them, do what your committee says and ignore everyone else. Based on my own painful experience....

Doing something you are interested in which is not overly difficult (in terms of the math or the availability of the data) is always a plus. You can solve the Schroeder equations after you graduate, do something reasonable on your master's thesis. Doing something that will interest people you want to get a job from later is a big plus. Make sure your committe know the method you use (personally I think there is a danger in picking a topic they have written on, but that is purely a guess).

 

[Englund]

Bump. Any other ideas, anyone? It is about two months untill I'll begin working on my thesis, so it's no hurry. But it would be nice to not decide upon a subject in the last minute = )

 

[Englund]

Bump, I thought I could tell everyone who's interested what I'm writing for my thesis.

When we have multivariate time series we're sometimes interested in whether they are cointegrated or not. It exists several tests for this, but the most widely used one is Johansens trace and max tests. See Johansen (1991) for a thorough introduction. Unfortunately, these tests are sensitive to breaks in the variance and also to GARCH-effects aswell. The actual alfa-level seem to be greater than the nominal levels in the presence of breaks and/or GARCH. What I am doing in my thesis is investigating the actual sizes and power of these tests under certain conditions, as well as proposing a couple of new tests that are (hopefully) robust.

The tests that I am going to use are based on bootstrap techniques, such as regular nonparametric bootstrap, Sieve bootstrap and Wild bootstrap. As an appetizer I'll below display estimated actual size of the Johansen trace test and the test based on Wild bootstrap when there are GARCH-effects in the series.

Nominal level: 0.05
Estimated actual size Johansen test (t=480, N=1000): 0.115
Estimated actual size Wild bootstrap test (t=480, N=50, bootstrap samples=200): 0.0467

Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59, 1551-1580.