Endogenously Detecting Structural Breaks in a Time Series: Implementation in R

The most conventional approach to determine structural breaks in longitudinal data seems to be the Chow Test.

From Wikipedia,

The Chow test, proposed by econometrician Gregory Chow in 1960, is a test of whether the coefficients in two linear regressions on different data sets are equal. In econometrics, it is most commonly used in time series analysis to test for the presence of a structural break at a period which can be assumed to be known a priori (for instance, a major historical event such as a war). In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.

As shown in the figure below, regressions on the 2 sub-intervals seem to have greater explanatory power than a single regression over the data.

440px-chow_test_structural_break

For the data above, determining the sub-intervals is an easy task. However, things may not look that simple in reality. Conducting a Chow test for structural breaks leaves the data scientist at the mercy of his subjective gaze in choosing a null hypothesis for a break point in the data.

Instead of choosing the breakpoints in an exogenous manner, what if the data itself could learn where these breakpoints lie? Such an endogenous technique is what Bai and Perron came up with in a seminal paper published in 1998 that could detect multiple structural breaks in longitudinal data. A later paper in 2003 dealt with the testing for breaks empirically, using a dynamic programming algorithm based on the Bellman principle.

I will discuss a quick implementation of this technique in R.

Brief Outline:

Assuming you have a ts object (I don’t know whether this works with zoo, but it should) in R, called ts. Then implement the following:

An illustration 

I started with data on India’s rice crop productivity between 1950 (around Independence from British Colonial rule) and 2008. Here’s how it looks:

rice_productivity

You can download the excel and CSV files here and here respectively.

Here’s the way to go using R:

Voila, this is what you get:

02_rice_multiplebreaks

The dotted vertical lines indicated the break dates; the horizontal red lines indicate their confidence intervals.

This is a quick and dirty implementation. For a more detailed take, check out the documentation on the R package called strucchange.

Statistics: The Sexiest Job of the Decade

Anyone who’s got a formal education in economics knows who Hal Varian is. He’s most popularly known for his book Intermediate Economics. He’s also the Chief Economist at Google. He is known to have famously stated more or less, that statisticians and data analysts would be the sexiest jobs of the next decade.

That has come true, to a great extent, and we’ll be seeing more.

Great places to learn more about data science and statistical learning:
1] Statistical Learning (Stanford)
2] The Analytics Edge (MIT)

In a paper called ‘Big Data: New Tricks for Econometrics‘, Varian goes on to say that:

In fact, my standard advice to graduate students these days is “go to the computer science department and take a class in machine learning.” There have been very fruitful collaborations between computer scientists and statisticians in the last decade or so, and I expect collaborations between computer scientists and econometricians will also be productive in the future.

See Also: Slides on Machine Learning and Econometrics