Fig 1.
The flowchart of the proposed deep learning framework for financial time series.
D(j) is the detailed signal at the j-level. S(J) is the coarsest signal at level J. I(t) and O(t) denote the denoised feature and the one-step-ahead output at time step t, respectively. N is the number of delays of LSTM.
Fig 2.
The flowchart of the single layer autoencoder.
The model learns a hidden feature a(x) from input x by reconstructing it on x'. Here,W1 and W2 are the weight of t he hidden layer and the reconstruction layer, respectively. b1 and b2 are the bias of the hidden layer and the reconstruction layer, respectively.
Fig 3.
Instance of a stacked autoencoders with 5 layers that is trained by 4 autoencoders.
Fig 4.
A recurrent neural network and the unfolding architecture.
U, V and W are the weights of the hidden layer, the output layer and the hidden state, respectively.xt and ot are the input vector and output result at time t, respectively.
Fig 5.
The architecture of an LSTM memory cell.
Fig 6.
The repeating module in an LSTM.
Here,xt and ht are the input vector and output result to the memory cell at time t, respectively. ht is the value of the memory cell. it, ft and ot are values of the input gate, the forget gate and the output gate at time t, respectively. are values of the the candidate state of the memory cell at time t.
Table 1.
Description of the input variables.
Fig 7.
Continuous dataset arrangement for training, validating and testing during the whole sample period.
Table 2.
Time interval of the six prediction years.
Fig 8.
Displays the actual data and the predicted data from the four models for each stock index in Year 1 from 2010.10.01 to 2011.09.30.
Table 3.
Predictive accuracy in developing markets.
Table 4.
Predictive accuracy in relatively developed markets.
Table 5.
Predictive accuracy in developed markets.
Table 6.
Profitability performance of each model.