Tests for structural breaks in time-series data

Let's see it work

We want to know whether there is a greater increase in malaria cases than would otherwise be predicted. Suppose we have data on a country where the number of cases varies over time and that variation is in general explained by the population of Anopheles mosquitoes. The model is

. regress malaria anopheles, vce(robust)

To determine whether and when there is a structural break in our data, we type

. tsset month

. estat sbsingle



   
 
   
 1 
   
 
   
 2 
   
 
   
 3 
   
 
   
 4 
   
 
   
 5 
 
..................................................    50

Test for a structural break: Unknown break date
Full sample:    2005m1 thru 2014m12
Trimmed sample: 2006m7 thru  2013m7
Estimated break date: 2013m4

H0: No structural break

                        Number of obs = 120


             Test    Statistic      p-value

    Supremum Wald   40966.4180       0.0000

Exogenous variables: anopheles
Coefficients included in test: anopheles _cons

The test rejects the null hypothesis of no structural break and detects a break in the fourth month of 2013.

We can also perform a test for more than one structural break if we have ex-ante information about when the breaks might be. It's artificial, but let's use these same data and test for a structural break, pretending that we suspect there might be one on 2013m1, which is close to 2013m4.

. estat sbknown, break(tm(2013m1))

Wald test for a structural break: Known break date
Sample:  2005m1 thru 2014m12
Break date:  2013m1

H0: No structural break

Number of obs =      120
      chi2(2) = 209.0560
  Prob > chi2 =   0.0000

Exogenous variables: anopheles
Coefficients included in test: anopheles _cons

The test rejects the null hypothesis of no structural break.