I consider the problem of (multiclass) classification based on time series of variable length $T$, that is, to find a function
$$f(X_T) = y \in [1..K]\\
\text{for } X_T = (x_1, \dots, x_T)\\
\text{with } x_t \in \mathbb{R}^d ~,$$
via a global representation of the time serie by a set of selected features $v_i$ of fixed size $D$ independent of $T$,
$$\phi(X_T) = v_1, \dots, v_D \in \mathbb{R}~,$$
and then use standard classification methods on this feature set.
I'm not interested in forecasting, i.e. predicting $x_{T+1}$.
For example, we may analyse the way a person walks to predict the gender of the person.
What are the standard features that I may take into account ?
In example, we can obviously use the mean and variance of the serie (or higher order moments) and also look into the frequency domain, like the energy contained in some interval of the Discrete Fourier Transform of the serie (or Discrete Wavelet Transform).
Best Answer
Simple statistical features
Time serie analysis related features
Frequency domain related features
See Morchen03 for a study of energy preserving features on DFT and DWT