I have a column of a Pandas DataFrame that is fractional day of year (DOY). This column appears as:

```
               DOY
0       200.749967
1       200.791667
2       200.833367
3       200.874967
4       200.916667
5       200.958367
6       200.999967
7       201.041667
       ...    
3491    627.166667
3492    627.333367
3493    627.499967
3494    627.666667
3495    627.833367
3496    627.999967
3497    628.166667
3498    628.333367
Name: DOY, Length: 3499, dtype: float64

```

The starting year is 2011, however the DOY data continues with increasing values through 2012 without resetting to zero on the new year.

How do I convert this to a Pandas DatetimeIndex with format 'YYYY-MM-DD HH:MM:SS'?