Feature Selection, Machine learning and Time Series analysis, for large financial timeseries
Your model should be based on what your data represents.  If you want meaningful results, you should get some idea of what your data is representing before trying to answer this question.  

For instance, you could use your ind# columns to predict the values of your ind#${_j}$ rows, then use the ind#${_j}$s to predict the val${_j}$.  But this would only make sense if there is a predictive relationship between the ind#${_j}$s.  And you would definite want to have some idea of what that relationship might be in order to choose an appropriate algorithm for each particular column. 

Furthermore, the same would apply for $j_{th}$ row val${_j}$ prediction.  At the very least you would want to  make an educated guess about the relationship between your ind#${_j}$s and your val${_j}$ column so that an appropriate algorithm could be chosen.  

As another example, you may be able to use the previous row as a predictor for the next value in the time series. i.e. ind#${_{j-1}}$s  => val${_j}$.  But again, this only makes sense if you are able to make reasonable assumptions about the relationship of the data, because you ultimately need to choose the algorithm you use to make the predictions.