Algorithm 1 Training of TD-LSTM networks

Input:

historical observations:$\left\{X_1,\dots ,X_{n-1}\right\}$;

target at time t: $X_t$;

lengths of closeness, period, trend: $l_c,l_p$;

period: p;

Output:

TD-LSTM model $\mathcal{M}$;

//construct training instance

1: $\mathcal{D}\leftarrow ⌀$;

2: for all available time interval $t(1\le t\le n-1)$ do

3: $S_c=[X_{t-l_c},X_{t-(l_c-1)},\dots ,X_{t-1}]$;

4: $S_p=[X_{t-l_p·p},X_{t-(l_p-1)·p},\dots ,X_{t-p}]$;

5: put a training instance ($\left\{S_c,S_p\right\}$) into $\mathcal{D}$;

6: end for

// train model

7: initialize parameter $\theta$;

8: repeat

9: randomly select a batch of instances from $\mathcal{D}$;

10:   find $\theta$ by optimization algorithm;

11: until the objective is minimized

12: output the optimized TD-LSTM model $\mathcal{M}$;