Simulating Critical Values for Some Test Statistics

This post comes at the request of Francesca, in a comment on an earlier post on Monte Carlo simulation.

The request was for some examples of how we can compute finite-sample critical values for different test statistics.  What this really means is that we want to simulate particular "quantiles" (points on the X-axis) for the distribution of the statistic.

Let's see what we can do about this. First, some background information.

Last Week's Reading

There are some great econometrics papers out there, just waiting to be read. I need more hours in the day!

Some of the papers I enjoyed reading last week were:

• Barsoum, F. and S. Stankiewicz, 2013. Forecasting GDP growth using mixed-frequency models with switching regimes. Department of Economics, University of Konstanz, Working Paper 2013-10.
• Castle, J. L., M. P. Clements, and D. F. Hendry, 2013. Forecasting by factors, by variables, by both or neither? Journal of Econometrics, in press.
• Chiu, C. W., B. Eraker, A. T. Foerster, T. B. Kim, and H. D. Seoane, 2012. Estimating VAR's sampled at mixed or irregular spaced frequencies: A Bayesian approach. Federal Reserve Bank of Kansas City, Research Working Paper 11-11 (revised, December 2012).
• Dufour, J-M. and J. Wilde, 2013. Weak identification in probit models with endogenous covariates.
• Lim, H. K., J. Song, and B. C. Jung, 2013. Score tests for zero-inflation and overdispersion in two-level count data. Computational Statistics and Data Analysis, 61, 67-82.
• Millimet, D. L. and I. K. McDonough, 2013. Dynamic panel data models with irregular spacing: With applications to early childhood development. IZA Discussion Paper 7359.
• Pesaran, H. H., A. Pick, and M. Pranovich, 2013. Optimal forecasts in the presence of structural breaks. Journal of Econometrics, in press.

© 2013, David E. Giles

Vintage Years in Econometrics - The 1930's

We all know that when it comes to wine-making, some years yield better wine than others. If you like to sip a little wine while looking at pictures, then The Wine Advocate's "Vintage Chart" may appeal to you. (It's just a pity that they don't acknowledge the fact that there's more than one wine-producing region in New Zealand!)

That got me thinking about vintage years for econometrics. Funny how the mind works, sometimes, isn't it?

So, this post is for you budding students of econometrics. Our future lies with you, but it's not a bad thing to know something about our past!

Snowfall

Yesterday I had a short post reminding EViews users that their package (versions 7 or 8) will access all of the cores on a multi-core machine. I've been playing around with parallel processing in R on my desktop machine at work over the last few days. It's something I've been meaning to do for a while, and it proved to be well worth the time.

Before I share my results with you, let me make a couple of comments. 

Multi-Core Processing With EViews

If you're using a "multi-core" computer for your econometrics work, you want to be able to take advantage of those extra cores - at least when it's efficient to do so. Some tasks, such as Monte Carlo or bootstrap simulations, lend themselves well to multi-processing. However, not all tasks will benefit - more on this in another, more detailed post..

EViews 7 and EViews 8 incorporate automatic sensing and use of the number of CPU "cores" your machine has. Unlike some other packages, which shall remain nameless, you don't have to purchase a different version of the package to get this facility.

There's just one caveat: in the "Help" file for EViews 8 you'll find the following statement:

"This is guaranteed to work with Intel processors, and, to our knowledge, should work with other brands of processors as well."

Unless you've tinkered with the global settings for you installation of EViews, you'll be getting the full benefit of your machine's processing power when using this package. However, you can check this as follows:

1. Start EViews (7 or 8).
2. Choose the "Options" tab at the top of the main window.
3. Choose: "General options", "Advanced system options".
4. Then, in the "Multi-processor/multi-core use" drop-down, make sure that the setting is either "Auto" (the EViews default), or is the number of cores you want to assign.

Any change that you make to this setting will take effect once you re-start EViews.

© 2013, David E. Giles

International Year of Statistics

Yes, 2013 is the International Year of Statistics. The major professional statistics bodies, and statistical agencies around the world are celebrating the role that statistics (the discipline) and statistics (the data) play in our everyday lives. Academic statisticians, and those of us who work in related disciplines are in on the act too.

Statistics 2013 have been working hard, and creatively, to promote the importance of statistics. They've organized all sorts of celebrations, activities, and competitions.

You can check out the Statisics 2013 logos, in all of the accredited languages, on their website, and I like their statcloud:

You can sign up for the Statistics 2013 newsletter, here.

© 2013, David E. Giles

What's in a Title?

I'm not one of those people who go in for "cute" titles for my research papers. Some people obviously do. However, they probably spend way too much of their valuable time conjuring up snappy titles in the hope that they'll come up with something that will attract people's attention.

Ultimately, it's the content of the paper that's going to matter - at least, I like to think that's true! So, most of my published papers have titles that describe what the research is about - but those titles aren't going to win any awards for creativity. I mean, really, titles such as:

A saddlepoint approximation to the distribution function of the Anderson-Darling test statistic.

Exact asymptotic goodness-of-fit testing for discrete circular data, with applications.

Bias reduction for the maximum likelihood estimator of the parameters in the half-logistic distribution.

Do you see what I mean? (Assuming you're still awake, that is.)

Actually Computing the Sample Variance!

I always enjoy the posts from John Cook on his The Endeavour blog. John's a knowledgable guy and there's a lot on his blog that's of interest to econometricians. Take a look for yourself!

Back in 2008, John had a post that's relevant to something I've been blogging about recently. It also reminded me of some important issues associated with computation - issues that we used to worry about a great deal in the bad old days of "hand calculations", and computers with short word-lengths and very limited memory

One thing that needs to be stressed to students is that the algebraic formulae that they learn about are not necessarily expressed in the form that's most appropriate computationally. By "appropriate", I'm referring to both computational accuracy and computational speed. There are actually lots and lots of examples that illustrate the point that I want to make. However, let's just consider the "simple problem" of computing the variance of a sample of data.

Minimum MSE Estimation of a Regression Model

Students of econometrics encounter the Gauss-Markhov Theorem (GMT) at a fairly early stage - even if they don't see a formal proof to begin with. This theorem deals with a particular property of the OLS estimator of the coefficient vector, β, in the following linear regression model:

                        y = Xβ + ε  ;  ε ~ [0 , σ² I_n] ,

where X is (n x k), non-random, and of rank k.

The GMT states that among all linear estimators of β that are also unbiased estimators, the OLS estimator of β is most efficient. That is, OLS is the BLU estimator for β.

EViews Tutorials

If you're a student who is just learning to use the EViews econometrics package, the tutorials that IHS (the supplier of EViews) has made available should be very helpful. You'll find them here.

There are 13 tutorials at this time, ranging from "EViews basics" to "Forecasting".

"The tutorials are split into self-contained sessions, although we recommend that new users of EViews work their way through the tutorials one by one.

Each tutorial is accompanied by data files so that you may follow the tutorials in your own copy of EViews. The data files are available in the Supporting Files side bar of each tutorial. Each tutorial is available in Microsoft Powerpoint® format, along with the data files, bundled together in a Zip file, in the Download Package area of of the side bar of each tutorial. 

You should note that the tutorials are written based on EViews 8, however the vast majority of material covered in them is applicable to earlier versions of EViews too."

Certainly, these tutorial won't tell you everything you'll want to know,  but they're a good start.

© 2013, David E. Giles