Temporal Data Mining

282    ◾    Temporal Data Mining

7.4.4 Independent Component Analysis for Financial Time Series

In [Oja98], the authors discuss independent component analysis (ICA)

for nancial time series for two dierent purposes: (1) decomposition of

parallel nancial time series of weekly sales into basic factors and (2) time

series prediction by linear combinations of ICA component predictions.

e starting point is to convert a time series into a signal vector x(t) =

(x

1

(t), x

2

(t), … x

m

(t))

T

. en the ICA problem can be approached as

YWx=

(7.8)

where the goal is to nd the matrix W that makes the elements of Y sta-

tistically independent. e ith row of W, W

i

, can be found by maximizing

the kurtosis of Y

i

. Another way of describing the same problem is ...