<p>The paper <a href="http://hdl.handle.net/10355/2541" rel="nofollow">Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error</a> (J. Isaac Miller (2009)) seems to have what you are looking for. </p>

<blockquote>
  <p>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.</p>
</blockquote>

<p>Here  is the bit on testing for cointegration:</p>

<blockquote>
  <p>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.</p>
</blockquote>

CC BY-SA 3.0
2015-04-27T13:19:39.593Z
2015-04-27T13:19:39.593Z
BKay
<p>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?</p>

CC BY-SA 3.0
2015-02-22T22:00:42.350Z
I don't know if software questions are on topic here. This was discussed in a meta question: http://meta.economics.stackexchange.com/questions/78/are-software-questions-on-topic
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
CC BY-SA 3.0
2015-02-23T14:40:15.563Z
Stata's multiple imputation function (mi) might be a good place to start.
BKay
CC BY-SA 3.0
2015-04-27T13:36:30.807Z
@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
<econometrics><time-series>
Missing values in economic time series
Bimz
# Missing values in economic time series

(Asked by: username_0 on 2015-02-22)

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?

**Tags:** econometrics, time-series
> **Comments:**
> **username_1**: I don't know if software questions are on topic here. This was discussed in a meta question: http://meta.economics.stackexchange.com/questions/78/are-software-questions-on-topic 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.  
> **username_2**: Stata's multiple imputation function (mi) might be a good place to start.  
> **username_3**: @Majoko I think they would be better suited else where, but are still on-topic here. But let's move that discussion to meta.  

---

## 1 answers

### Answer by username_2 on 2015-04-27. Score: 3

The paper [Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error](http://hdl.handle.net/10355/2541) (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.


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