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filter is widely used in engineering for two main purposes: for combining mea-
surements of the same variables but from different sensors, and for combining
an inexact forecast of a system’s state with an inexact measurement of the
state. We use a Kalman filter to combine the neural network forecast with
the observed value at time t − k, where k depends on the horizon forecast
as defined above. The one-dimensional Kalman filter works by considering:
ˆy
i
= ˆy
i−1
+ K(y
i
− ˆy
i−1
) where σ
2
i
= (1 − K)σ
2
i−1
and K =
σ
2
i−1
σ
2
i−1
+σ
2
r
.
11.3 Similarity between Time-Series
Most of time-series analysis techniques (clustering, classification, novelt ...