Further Analysis Of Nonlinear Wave Patterns
Singular Spectrum Analysis: Part II
by Sergiy Drogobetskii
Here's another look at applying singular spectrum analysis to the foreign exchange markets.
IN my last article, I discussed some of the variables that make up single spectrum analysis (SSA), an analytical method that has been applied to various branches of scientific study. It has proved useful for compressing information, smoothing initial data and, in certain cases, predicting time series data prices. Last time, I showed how SSA could be applied to forex market prices. This time, I will continue in that direction and show how you can apply SSA to forecast prices.
In reconstructing the initial time series, one important consequence of the singular value decomposition (SVD) of a trajectory matrix (built from the time series of prices) is that it is possible to completely reconstruct the decomposed initial trajectory matrix by using empirical orthogonal functions (EOFS) contained in the right matrix V:
It's not necessary to use all EOFS from matrix V to reconstruct the trajectory matrix. Only l corresponds to the leading singular values. By using l EOFS, you can reconstruct the trajectory matrix using formula (1) and replace m with l. The initial matrix will contain n rows and m columns.
According to formula (1), a reconstructed matrix is the sum of separate matrixes reconstructed by some specific EOF. Each reconstructed matrix represents an elementary pattern of behavior (EPB) in a multidimensional space, so you need to reduce them back to a one-dimensional space. If you look at the result of the trajectory matrix, you'll see that it's a matrix with constant elements on skew diagonals - that is, the second element in the first column of trajectory matrix is equal to the first element in the second column, and so on. ...Continued in the November issue of Technical Analysis of STOCKS & COMMODITIES.
Excerpted from an article originally published in the November 2005 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2005, Technical Analysis, Inc.
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