How to combine time-series based features with different frequencies I have 3 features which I want to use in my classifier. They are all time-series data-based. However, they are all at different frequencies and there have different matrix dimensions. I was wondering if someone could give me some pointers on how to combine these three features?
Appreciate your help.
 A: As suggested by @ChuckKillerDoll, you could find aggregate / derive features from your current measures, but chances are you will lose information by doing so. Another way to go about it, is to create three separate models and train a model for each of the frequency information matrices individually. These produce output scores $S_1,S_2,S_3$, you can then combine these in a new ensemble model. The easiest way to combine them is in a linear model:
$$S = a_1 S_1 + a_2 S_2 + a_3 S_3$$
Here $S$ is the final output score and you still need to learn the weights $a_i$ on a validation set. You could of course, plug the scores into more complicated models ... The main disadvantage of this technique is that you lose some of the covariance information.
A: I would try an state-space model. The simplest possible form would be:
\begin{eqnarray}
\begin{pmatrix} \theta_{1t} \\ \theta_{2t} \\ \theta_{3t}
\end{pmatrix} &=& \begin{pmatrix} I & 0 & 0 \\ 0 & I & 0 \\ 0 & 0 & I \end{pmatrix}
\begin{pmatrix}\theta_{1,t-1} \\ \theta_{2,t-1} \\ \theta_{3,t-1}
\end{pmatrix} + \begin{pmatrix} \eta_{1t} \\ \eta_{2t} \\ \eta_{3t}
\end{pmatrix} \\
\begin{pmatrix}Y_{1t} \\ Y_{2t} \\ Y_{3t}
\end{pmatrix} &=& \begin{pmatrix} I & 0 & 0 \\ 0 & I & 0 \\ 0 & 0 & I \end{pmatrix}\begin{pmatrix} \theta_{1t} \\ \theta_{2t} \\ \theta_{3t}
\end{pmatrix} + \begin{pmatrix} \epsilon_{1t} \\ \epsilon_{2t} \\ \epsilon_{3t}
\end{pmatrix}
\end{eqnarray}
where all the $Y_{it}$, $\theta_{it}$ etc. are to be understood as vectors of the same dimensions of your three time series. 
You can fit such model --a multivariate random walk plus noise-- even if not all the $Y$'s are observed at all times, and estimate the state vector at all possible $t$'s. This removes the problem of the different frequencies of the three time series.
If the situation warrants, you might also fit a different model. For instance, if there is some redundancy among the components of $Y_{it}$ you might want to use $\theta_{it}$ with $dim(\theta_{it}) < dim(Y_{it})$, and fit what would be essentially a dynamic factor analysis model.
A: IMHO, your problem is related to "feature engineering".
Dealing with financial market time series, I use to create one new column (feature) for each set of parameters of each indicator.
For example a simple moving average (SMA) is defined by the set = {LookbackPeriod,Frequency,ShortPeriod,LongPeriod} and each combination of these elements forms a new feature/attribute.
The instances of your Y values (classes) can be trained separately (in your classifier) for each frequency, like Return(t+period) where period == days, weeks, ...
If you want something more general you are trying to predict using "first-order rule learning"
