# Missing values in economic time series

I am trying to run a time series analysis on some variables - GDP being my dependent variable, and my independent variables are oil revenues, government expenditure, exports and FDI inflows. My data contains missing values for some years for at least 3 variables. I have been able to ascertain that they are non-stationary. However, I am unable to perform the Johansen test of cointegration due to the missing variables in between the data set. How do I resolve this?

• I don't know if software questions are on topic here. This was discussed in a meta question: meta.economics.stackexchange.com/questions/78/… Nevertheless, it seems to me that a question about how to treat missing values is not economics per se, so I would advice you check the Stata help documentation, ask on stats.SE or on Statalist. – han-tyumi Feb 22 '15 at 22:00
• Stata's multiple imputation function (mi) might be a good place to start. – BKay Feb 23 '15 at 14:40
• @Majoko I think they would be better suited else where, but are still on-topic here. But let's move that discussion to meta. – FooBar Apr 27 '15 at 13:36

## 1 Answer

The paper Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error (J. Isaac Miller (2009)) seems to have what you are looking for.

We consider a cointegrating regression in which the integrated regressors are messy in the sense that they contain data that may be mismeasured, missing, observed at mixed frequencies, or have other irregularities that cause the econo- metrician to observe them with mildly nonstationary noise. Least squares esti- mation of the cointegrating vector is consistent. Existing prototypical variance- based estimation techniques, such as canonical cointegrating regression (CCR), are both consistent and asymptotically mixed normal. This result is robust to weakly dependent but possibly nonstationary disturbances.

Here is the bit on testing for cointegration:

In cases where cointegration between ($y_ t$) and ($x_t$) is not obvious or expected, 5 testing is desirable. The variance ratio test and multivariate trace statistic proposed by Phillips and Ouliaris (1990) rely on the estimation of the long-run variance of a different residual series. Specifically, ($y_ t, x'_t$ ) is regressed on one lag of itself, and the long-run variance of the residual series from that regression is estimated. This series is I(0) under the null, so we can expect that adding ($z^*_t$) – i.e., using ($y_ t, x^{'*}_t$) – would have a similar effect to adding ($z^*_t$) to the residual series below. Specifically, it would inflate the variance of both the numerator and denominator of these statistics, so that the limits would be preserved. Approaches using more robust variance ratio tests (Wright, 2000; Müller and Watson, 2008) hold more promise still.