[Neural Forecasting] Delayed time series predictions with neural networks .

Dear Colleagues,

I would like to report here a strange behaviour that I have observed when
trying to use feedforward neural networks to predict financial time series.

The procedure I have adopted is to present to the network the samples [x(t)
x(t-1) x(t-2) x(t-3) ... x(t-N+1)] and train it to give x(t+1) in the
output. The problem is that, although the training and validation sets
behave well, the test set presents a "delay" in the output, that is, the
answer to the input [x(t) x(t-1) x(t-2) x(t-3) ... x(t-N+1)]  is x(t)
instead of x(t+1).

I suspect that it is due the noisy behaviour of such series.

This phenomenon also happens when I use Recurrent Networks, such Elman ones,
instead of simple feedforward (with backpropagation training algorithm).

The only thing that has been able to attenuate (without solving) this
problem was the following: do not allow the training set to contain
overlapping samples between consecutive input patterns, that is, the network
is trained with the following set:

[x(t) x(t-1) x(t-2) x(t-3) ... x(t-N+1)]  --> x(t+1)
[x(t+N) x(t+N-1) x(t+N-2) x(t+N-3) ... x(t+1)] --> x(t+N+1)
[x(t+2N) x(t+2N-1) x(t+2N-2) x(t+2N-3) ... x(t+N+1)] --> x(t+2N+1)
and so on...

Thi disadvantage here is that I have to train N independent networks to
reconstruct the final predicted series.

Does anyone know what may be really hapenning?

Any help would be fully appreciated!

Please do not hesitate to ask me more details of the problem.

Best wishes,

Augusto Dantas.

Graduate Student at Federal University of Rio de Janeiro/Brazil

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