1. A computer-implemented method for identifying local patterns in at least one time series data stream, the method comprising: generating multiple ordered levels of hierarchical approximation functions directly from at least one given time series data stream including at least one set of time series data, wherein the hierarchical approximation functions for each level of the multiple ordered levels is based upon creating a set of approximating functions; selecting a current window with a current window length from a set of varying window lengths, wherein the current window is selected for a current level of the multiple ordered levels; wherein generating multiple ordered levels of hierarchical approximation functions includes generating multiple increasing consecutive numerically ordered levels, wherein the current window is a portion of the set of time series data divided into consecutive sub-sequences, and wherein the current window length along with the hierarchical approximating functions reduces an approximation error between the current window and the set of time series data portion, calculating the approximation error between the current window and the set of time series data portion; basing the current window length on the approximation error calculated between the current window and the set of time series data portion; wherein the time series data stream is divided into non-overlapping consecutive subsequences, wherein the current window length for the current window is larger than a current window length for a previous window in the multiple ordered levels of hierarchical approximation functions, wherein the hierarchical approximation functions for each of level of the multiple ordered levels is further based upon creating a set of coefficients that summarize the set of time series data portion in the current window; reusing the set of approximating functions from the previous window; and reducing a power profile π (w) defined by a total squared error, via principal component analysis, wherein the total squared error is given by equation 
 Σ i=k+1 w σ i 2 w =(Σ t=1 m x t 2 −Σ i=1 k σ i 2 )/ w wherein k is an number of patterns chosen {1. .. k}, wherein the patterns are vectors equal to a window length w, where m is a multiple of the window size and wherein x t is the set of time series data portion, and wherein σ is a singular value for a given index I; and using a subspace tracking algorithm to approximate incrementally all of the following quantities: the window length w, singular values of a matrix σ, local patterns for window length w, local approximations for each window of length w, and k; storing the multiple ordered levels of hierarchical approximation functions into memory after being generated.