MIDAS Regression is Now in EViews

The acronym, "MIDAS", stands for several things. In the econometrics literature it refers to "Mixed-Data Sampling" regression analysis. The term was coined by Eric Ghysels a few years ago in relation to some of the novel work that he, his students, and colleagues have undertaken. See Ghysels et al. (2004).

Briefly, a MIDAS regression model allows us to "explain" a (time-series) variable that's measured at some frequency, as a function of current and lagged values of a variable that's measured at a higher frequency. So, for instance, we can have a dependent variable that's quarterly, and a regressor that's measured at a monthly, or daily, frequency.

There can be more than one high-frequency regressor. Of course, we can also include other regressors that are measured at the low (say, quarterly) frequency, as well as lagged values of the dependent variable itself. So, a MIDAS regression model is a very general type of autoregressive-distributed lag model, in which high-frequency data are used to help in the prediction of a low-frequency variable.

There's also another nice twist.......

The Econometrics of Temporal Aggregation - VI - Tests of Linear Restrictions

This post is one of several related posts. The previous ones can be found here, here, here, here and here. These posts are based on Giles (2014).

Many of the statistical tests that we perform routinely in econometrics can be affected by the level of aggregation of the data. Here, Let's focus on time-series data, and with temporal aggregation. I'm going to show you some preliminary results from work that I have in progress with Ryan Godwin. These results relate to one particular test, but work covers a variety of testing problems.

I'm not supplying the EViews program code that was used to obtain the results below - at least, not for the moment. That's because the results that I'm reporting are based on work in progress. Sorry!

As in the earlier posts, let's suppose that the aggregation is over "m" high-frequency periods. A lower case symbol will represent a high-frequency observation on a variable of interest; and an upper-case symbol will denote the aggregated series.

So,

               Y_t = y_t + y_{t - 1} + ......+ y_{t - m + 1} .

If we're aggregating monthly (flow) data to quarterly data, then m = 3. In the case of aggregation from quarterly to annual data, m = 4, etc.

Now, let's investigate how such aggregation affects the performance of standard tests of linear restrictions on the coefficients of an OLS regression model. The simplest example would be a t-test of the hypothesis that one of the coefficients is zero. Another example would be the F-test of the hypothesis that all of the "slope" coefficients in such a regression model are zero.

Consider the following simple Monte Carlo experiment, based on 20,000 replications.

The Econometrics of Temporal Aggregation V - Testing for Normality

This post is one of a sequence of posts, the earlier members of which can be found here, here, here, and here. These posts are based on Giles (2014).

Some of the standard tests that we perform in econometrics can be affected by the level of aggregation of the data. Here, I'm concerned only with time-series data, and with temporal aggregation. I'm going to show you some preliminary results from work that I have in progress with Ryan Godwin. Although these results relate to just one test, our work covers a range of testing problems.

I'm not supplying the EViews program code that was used to obtain the results below - at least, not for now. That's because what I'm reporting is based on work in progress. Sorry!

As in the earlier posts, let's suppose that the aggregation is over "m" high-frequency periods. A lower case symbol will represent a high-frequency observation on a variable of interest; and an upper-case symbol will denote the aggregated series.

So,

               Y_t = y_t + y_{t - 1} + ......+ y_{t - m + 1} .

If we're aggregating monthly (flow) data to quarterly data, then m = 3. In the case of aggregation from quarterly to annual data, m = 4, etc.

Now, let's investigate how such aggregation affects the performance of the well-known Jarque-Bera (1987) (J-B) test for the normality of the errors in a regression model. I've discussed some of the limitations of this test in an earlier post, and you might find it helpful to look at that post (and this one) at this point. However, the J-B test is very widely used by econometricians, and it warrants some further consideration.

Consider the following small Monte Carlo experiment.

October Reading

October already!

• Chauvel, C. and J. O'Quigley, 2014. Tests for comparing estimated survival functions. Biometrika, 101, 535-552. 
• Choi, I., 2014. Unit root tests for dependent and heterogeneous micropanels. Discussion Paper No. 2014-04, Research Institute for Market Economy, Sogang University.
• Cho, J. S. and H. White, 2014. Testing the equality of two positive-definite matrices with application to in formation matrix testing. Discussion Paper, School of Economics,Yonsei University.
• Hansen, B. E., 2013. Model averaging, asymptotic risk, and regressor groups. Quantitative Economics, in press.
• Miller, J. I., 2014. Simple robust tests for the specification of high-frequency predictors of a low-frequency series. Mimeo., Department of Economics, University of Missouri.
• Owen, A. B. and P. A. Roediger, 2014. The sign of the logistic regression coefficient. American Statistician, in press.
• Westfall, P. H., 2014. Kurtosis as peakedness, 1905-2014. R.I.P.. American Statistician, 68, 191-195.

© 2014, David E. Giles

The Econometrics of Temporal Aggregation - IV - Cointegration

My previous post on aggregating time series data over time dealt with some of the consequences for unit roots. The next logical thing to consider is the effect of such aggregation on cointegration, and on testing for its presence.

As in the earlier discussion, we'll consider the situation where the aggregation is over "m" high-frequency periods. A lower case symbol will represent a high-frequency observation on a variable of interest; and an upper-case symbol will denote the aggregated series. So,

           Y_t = y_t + y_{t - 1} + ......+ y_{t - m + 1} .

If we're aggregating quarterly (flow) data to annual data, then m = 4. In the case of aggregation from monthly to quarterly data, m = 3, and so on.

We know, from my earlier post, that if y_t is integrated of order one (i.e.,  I(1)), then so is Y_t.

Suppose that we also have a second temporally aggregated series:

           X_t = x_t + x_{t - 1} + ......+ x_{t - m + 1} .

Again, if x_t is I(1) then X_t is also I(1). There is the possibility that x_t and y_t are cointegrated. If they are, is the same true for the aggregated series, X_t and Y_t?

The Econometrics of Temporal Aggregation - III - Unit Roots

In two previous posts, I've talked a bit about the effect that aggregating time series data can have on some standard econometric results. The first of those posts was about a talk that I gave last month at the 2014 Conference of the New Zealand Association of Economists. That talk was on the general topic of "The Econometrics of Temporal Aggregation". The second post looked more specifically of the consequences of such aggregation on the results of testing for Granger causality.

Here, I'll provide some information about the impact of temporal aggregation on the existence of, and testing for, unit roots in time-series data.

The Econometrics of Temporal Aggregation - II - Causality Testing

In my recent post about my presentation at the recent conference of the N.Z. Association of Economists, I promised some follow-up posts of a more specific nature. I thought I'd begin with some brief comments about the effects of temporal aggregation on Granger causality.

By temporal aggregation, I'm referring to the situation where the economic activity takes place at some frequency (say daily), but our time-series data are recorded at only a lower frequency (say monthly). My use of the word "aggregation' tells you that we're "adding up" the data over time - so, at least implicitly, I'm thinking about flow data.

How does this sort of aggregation impact on Granger causality?

The Econometrics of Temporal Aggregation - I

Yesterday, I gave the A. W. H. Phillips Memorial Lecture at the 55^th Conference of the New Zealand Association of Economists. The conference was held at Auckland University of Technology in New Zealand, and it was a great success.

More on the conference itself in a subsequent post.

Meantime, you can find the slides for (a slightly extended version of) my address here, and an extended bibliography for the talk here.

In some posts that will follow I'll elaborate on some of the main messages that should be drawn from what I had to say at the conference.

© 2014, David E. Giles

New Zealand Association of Economists Conference

In a couple of days' time I'll be heading off to New Zealand to participate in the 55th Annual Conference of the N.Z. Association of Economists. I'll be one of the keynote speakers, and I'm honoured to be presenting the A. W. H. Phillips Memorial Lecture.

That's "Bill" Phillips of The Phillips Curve fame - a very interesting and immensely talented New Zealander about whom I've posted previously, here and here.

My talk is titled, "The Econometrics of Temporal Aggregation: 1956-2014". The link to Bill Phillips is through his seminal work on continuous-time econometrics, and the lessons it has for econometric modelling when our data have been aggregated over time.

You can guess that I'll be posting on this topic in more detail in the near future. As soon as I've given my address, I'll make the slides available through this blog.

© 2014, David E. Giles