title: Python pandas time series interpolation datetime data
body: <p>From <a href="https://stackoverflow.com/questions/30530001/python-pandas-time-series-interpolation-and-regularization">this question</a> I know how to interpolate time series with given timestamps. I am wondering how to interpolate timestamps with given values such as the following example to get the estimated <code>NaT</code> value.</p>
  
  <pre><code>interval            datetime             
  0.782296 2012-11-19 12:40:10
  0.795469                 NaT
  0.821426 2012-11-19 12:35:10
  0.834957                 NaT
  0.864383 2012-11-19 12:30:10
  0.906240 2012-11-19 12:25:10
  </code></pre>
  
  <p>P.S. I have tried to use <code>df['datetime'].interpolate()</code> directly but failed. </p>