Friday, March 25, 2016

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.......

Typically, some "extra" values for the high-frequency variable(s) will be available after the most recent sample value of the low-frequency dependent variable has been observed. In this case, these "extra" observations can be used as well, so we have the potential for what's usually termed "now-casting" in the forecasting literature.

The hope is that incorporating this extra high-frequency information will improve the forecasting performance of the model.

As you can imagine, MIDAS regression is just great if you want to forecast a low-frequency variable such as GDP, and you want to incorporate high-frequency financial data.

There have been numerous important empirical applications of MIDAS models. Some interesting examples include those of Ghysels et al. (2005, 2006, 2007), Alper et al. (2008), Clements  and Galvão (2008, 2009),  Ghysels and Wright (2009), and Penev et al. (2014). There's also an excellent survey paper of MIDAS and related techniques by Foroni and Marcellino (2013).

Originally, if you wanted to use MIDAS regression, you could use the Matlab toolbox that Eric made available.

More recently an R package, midasr, was created by Virmantas Kvedaras and Vaidotas Zemlys (see their site and the user's guide). This certainly widened the audience for MIDAS regression. However, if you were an applied econometrician or student who didn't want to get into a lot of coding, your options were limited.

Fast-forward to a couple of weeks ago, and the release of EViews 9.5.

EViews now includes MIDAS regression as a standard option. That's really cool!

This will be a huge help to a lot of applied researchers, and it definitely puts EViews ahead of the action.

The EViews team provide a nice MIDAS demonstration - it's based on a St. Louis Federal Reserve Bank paper by  Armesto et al. (2010). I usually pass on a copy of that paper to any of my grad. students who express an interest in MIDAS models, as it's very clearly written.

You'll recall that at the start of this post I mentioned that the acronym "MIDAS" has several meanings. For instance there are MIDAS user-packages for Stata out there. However, they deal with something called "meta-analysis of diagnostic accuracy studies". And that's got nothing to do with our MIDAS!

References

Alper, C. E., S. Fendoglu, & B. Saltoglu, 2008.  Forecasting stock market volatilities using MIDAS regressions: An application to the emerging markets. Mimeo.

Armesto, M. T., K. M. Engemann, & M. T. Owyang, 2010. Forecasting with mixed frequencies. Federal Reserve Bank of St. Louis, Review, 92, 521-536.

Clements, M. P. & A. B. Galvão, 2008. Macroeconomic forecasting with mixed-frequency data: Forecasting output growth in the United States. Journal of Business and Economic Statistics, 26, 546-554.

Clements, M. P., & A. B. Galvão, 2009. Forecasting US output growth using leading indicators: An appraisal using MIDAS models. Journal of Applied Econometrics, 24, 1057-1217.

Foroni, C., and M. Marcellino, 2013. A survey of econometric methods for mixed frequency data. Working Paper 2013/06, Norges Bank.

Ghysels, E., P. Santa-Clara, & R. Valkanov, 2004. The MIDAS touch: Mixed data sampling regression models. Working paper.

Ghysels, E., P. Santa-Clara, & R. Valkanov, 2005. There is a risk-return trade-off after all. Journal of Financial Economics, 76, 509-548.

Ghysels, E., P. Santa-Clara, & R. Valkanov, 2006. Predicting volatility: Getting the most out of return data sampled at different frequencies. Journal of Econometrics, 131, 59-95.

Ghysels, E., A. Sinko, & R. Valkanov, 2007. MIDAS regressions: Further results and new directions. Econometric Reviews, 26, 53-90.

Ghysels, E. & J. H. Wright, 2009. Forecasting professional forecasters. Journal of Business and Economic Statistics, 27, 504-516.

Penev, S., D. Leonte, Z. Lazarov, & R. A. Mann, 2014. Applications of MIDAS regression in analysing trends in water quality. Journal of Hydrology, 511, 151-159.

Tay, A. S., 2006. Mixing frequencies: Stock returns as a predictor of real output growth. Economics and Statistics Working Paper No. 34-2006, Singapore Management University.