Add trend line to pandas
<p>I have time-series data, as followed:</p>

<pre><code>                  emplvl
date                    
2003-01-01  10955.000000
2003-04-01  11090.333333
2003-07-01  11157.000000
2003-10-01  11335.666667
2004-01-01  11045.000000
2004-04-01  11175.666667
2004-07-01  11135.666667
2004-10-01  11480.333333
2005-01-01  11441.000000
2005-04-01  11531.000000
2005-07-01  11320.000000
2005-10-01  11516.666667
2006-01-01  11291.000000
2006-04-01  11223.000000
2006-07-01  11230.000000
2006-10-01  11293.000000
2007-01-01  11126.666667
2007-04-01  11383.666667
2007-07-01  11535.666667
2007-10-01  11567.333333
2008-01-01  11226.666667
2008-04-01  11342.000000
2008-07-01  11201.666667
2008-10-01  11321.000000
2009-01-01  11082.333333
2009-04-01  11099.000000
2009-07-01  10905.666667
</code></pre>

<p><a href="https://i.stack.imgur.com/i28tJ.png" rel="noreferrer"><img src="https://i.stack.imgur.com/i28tJ.png" alt="time series graph"></a></p>

<p>I would like to add, in the most simple way, a linear trend (with intercept) onto this graph. Also, I would like to compute this trend only conditional on data before, say, 2006.</p>

<p>I've found some answers here, but they all include <code>statsmodels</code>. First of all, these answers might be not up to date: <code>pandas</code> improved, and now itself includes an OLS component. Second, <code>statsmodels</code> appears to estimate an individual fixed-effect for each time period, instead of a linear trend. I suppose I could recalculate a running-quarter variable, but there most be a more comfortable way of doing this?</p>

<pre><code>                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 emplvl   R-squared:                       1.000
Model:                            OLS   Adj. R-squared:                    nan
Method:                 Least Squares   F-statistic:                     0.000
Date:                tor, 14 apr 2016   Prob (F-statistic):                nan
Time:                        17:17:43   Log-Likelihood:                 929.85
No. Observations:                  40   AIC:                            -1780.
Df Residuals:                       0   BIC:                            -1712.
Df Model:                          39                                         
Covariance Type:            nonrobust                                         
============================================================================================================
                                               coef    std err          t      P&gt;|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------------------------------------
Intercept                                 1.095e+04        inf          0        nan           nan       nan
date[T.Timestamp('2003-04-01 00:00:00')]   135.3333        inf          0        nan           nan       nan
date[T.Timestamp('2003-07-01 00:00:00')]   202.0000        inf          0        nan           nan       nan
date[T.Timestamp('2003-10-01 00:00:00')]   380.6667        inf          0        nan           nan       nan
date[T.Timestamp('2004-01-01 00:00:00')]    90.0000        inf          0        nan           nan       nan
date[T.Timestamp('2004-04-01 00:00:00')]   220.6667        inf          0        nan           nan       nan
</code></pre>

<p>How do I, in the simplest way possible, estimate this trend and add the predicted values as a column to my data frame?</p>