Are there methods for automatically detecting features of a curve? I have a raw discrete data(curves). I need to find methods for detecting features of each curve. Some example features:
1) Stable growing
2) Fast growing
3) Stable falling
4) Fast falling
5) And so on
Here is good example of such curves type(russian):

How can i do it?
 A: The features that you are describing are mostly "edges" or discontinuities in the curves. I would suggest that you find local maxima of the first derivative and zero-crossings of the second derivative of each curve (after smoothing the signal to make sure noise doesn't affect your derivatives greatly). 
A: Most of this can be seen by initially plotting the data. As the curves show different types of features no one method will detect everything.  If you expect periodicity look at the periodogram or a smoothed version the spectral density.  Fisher's test will detect a significant period.  For linear time trends fit a linear function of time and test for a nonzero slope.
A: Perhaps use correlation analysis to be able to detect a feature in the curve?  Compute a target signal similar to the feature that you are searching for, and then use correlation analysis to find the location of the feature.  This is a well-known procedure in Digital Signal Processing (DSP).  I would highly recommend reading the DSP guide by Steven W. Smith at the first link below.  You appear to be interested in a matched filtering problem.
If the time series that you are working with is very long, you can split the signal up and run correlation analysis on each segment (see my comp.dsp post here).
DSP guide
Wikipedia
JOS
Matlab implementation
Secondary reference
