Beware of Tests for Nonlinear Granger Causality

Standard tests for Granger causality (or, more correctly, Granger non-causality) are conducted under the assumption that we live in a linear world.

I've discussed some of the issues associated with applying such tests in the presence of possibly integrated/cointegrated time-series data previously, here and here.

But can we justify limiting our attention to a linear environment?

Summertime!

It's been a quiet week at the lake - specifically, no internet access! And hence no posts.

I haven't been able to respond to comments and requests either, so please accept my apology for that.

Yes, I know I should be better organized!

Hodrick-Prescott Filter Paper

A while back I posted (here, here, and here) about constructing confidence bands to go with the Hodrick-Prescott filter. Subsequently, I wrote up the material more formally, and that paper is to appear in Applied Economics Letters.

You can find the final version of the paper here.

Hat-tip to my colleague, Graham Voss, for encouraging me to write up the material properly.

Reference

Giles, D. E., 2012. Constructing confidence bands for the Hodrick-Prescott filter. Forthcoming in Applied Economics Letters.

© 2012, David E. Giles

Cleaning up Your Data Files

A recent post on The Data Monkey blog describes a really neat (and free) text editor, called Hex Editor Neo.

If you have large, messy, data files that need cleaning, this looks like the editor for you!

© 2012, David E. Giles

Where Have All the Data Gone?

Perhaps the title of this post shoud be "Why are all the Data Going?". This time it's Statistics Canada's SLID that's slip, sliding away. Or more correctly, effectively it slid away last month!

More Comments on the Use of the LPM

Alfredo drew my attention to Steve Pische's reply to a question raised by Mark Schaffer in the Mostly Harmless Econometrics blog. The post was titled, Probit Better than LPM? The question related to my own  posts (here, here, and here, in reverse order) on this blog concerning the choice between OLS (the Linear Probability Model - LPM) or the Logit/Probit models for binary data.

Thanks, Alfredo, as this isn't a blog I follow. 

Alfredo asked: "Would you care to respond? I feel like this is truly an exchange from which a lot of people can learn".

Concentrating, or Profiling, the Likelihood Function

We call it "concentrating", they (the statisticians) call it "profiling" - the likelihood function, that is.

Different language - same thing.

So what's this all about, anyway?

Decline and Fall of the Power Curve

When we think of the power curve associated with some statistical test, we usually envisage a curve that looks something like (half or all of) an inverted Normal density. That is, the curve rises smoothly and monotonically from a height equal to the significance level of the test (say 1% or 5%), until eventually it reaches its maximum height of 100%.

The latter value reflects the fact that power is a probability.

But is this picture that invariably comes to mind - and that we see reproduced in all elementary econometrics and statistics texts - really the full story?

Actually - no!

"Data is", or "Data are"?

I guess I'm a pedant traditionalist when it comes to the word "data": one "datum", several pieces of "data", etc.

As with many matters relating to the use of language, though, this one isn't open and shut, by any means.

And so a few days ago we saw The Wall Street Journal, The Economist, and The Guardian grappling with this issue once again.

However, I'm going to stick with my guns, dust off my slide-rule, and also continue to use the "Oxford comma"!

© 2012, David E. Giles

Local vs. Global Approximations

Approximating unknown (continuously differentiable) functions by using a Taylor (MacLaurin) series expansion is common-place in econometrics. However, do you ever pause to recall that such approximations are only locally valid - that is, valid only in a neighbourhood of the (possibly vector) point about which the approximation is made?

Unlike some other types of approximations - such as Fourier approximations - they are not globally valid.

Does this matter? Is it something we should be concerning ourselves with?

Mark Thoma in "The Browser"

It was nice to see this interview with Mark Thoma in The Browser today.

Enjoy!

© 2012, David E. Giles

The Milliken-Graybill Theorem

Let's think about a standard result from regression analysis that we're totally familiar with. Suppose that we have a linear OLS regression model with non-random regressors, and normally distributed errors that are serially independent and homoskedastic. Then, the usual F-test statistic, for testing the validity of a set of linear restrictions on the model's parameters, is exactly  F-distributed in finite samples, if the null hypothesis is true.

In fact, the F-test is Uniformly Most Powerful Invariant (UMPI) in this situation. That's why we use it! If the null hypothesis is false, then this test statistic follows a non-central F-distribution.

It's less well-known that all of these results still hold if the assumed normality of the errors is dropped in favour of an assumption that the errors follow any distribution in the so-called "elliptically symmetric" family of distributions. On this point, see my earlier post here.

What if I were now to say that some of the regressors are actually random, rather than non-random? Is the F-test statistic still exactly F-distributed (under the null hypothesis)?

The Role of Statistics in the Higgs Boson Discovery

With the scientific world abuzz today over the (possible) confirmation of the existence of the Higgs Boson, this post from David Smith on the SmartData Collective is a must-read for anyone with an interest in statistics.

© 2012, David E. Giles