# Using previous hour's value in time series data for inclusion in random forest

I have a training data set, which is something like the following:

hour   windspeed   pollution
0              5           8
1              6           9
2              3           1


I am using scipy's RandomForestRegressor to estimate pollution given windspeed, hour. It is doing "ok", with $r^2 = 0.7$ and $rmse = 35$. However, I would like to include the previous hours pollution values as additional predictors, as in:

hour   windspeed   pollution   pollution@t-1  polluion@t-2 ... pollution@t-n
0              5           8              NA           NA
1              6           9               8           NA
2              3           1               9           8


Eventually, I will be applying this to future weather conditions, estimating pollution, where pollution can only be known at time zero:

hour   windspeed  pollution  p@t-1  p@t-2  p@t-3  p@t-4    ...
1              5          ?     34     28     25     ...   ...
2              6          ?     NA     34     28      25   ...
3              3          ?     NA     NA     34      28   ...


How should I best go about including this in a Random Forest? Since RFs don't tolerate null values, how best to impute them? Since '0' is not appropriate (given that 0 is likely very far from the current value), I was thinking that perhaps NaNs could be filled with the nearest known value, as in:

hour   windspeed  pollution  p@t-1  p@t-2  p@t-3  p@t-4    ...
1              5          ?     34     28     25     ...   ...
2              6          ?     34     34     28      25   ...
3              3          ?     34     34     34      28   ...

• This post has a helpful, possibly duplicate answer. – Samuel Harrold Oct 4 '15 at 17:31