Algorithm 1 AdaBoost-LSTM

Input:  The labeled target time series sequence, T, of size n${\displaystyle T=(x_1,x_2,\dots ,x_n)}$, the maximum number of iterations, N and a base learning algorithm, Learner LSTM. Set the initial weight vector: $W_j^t=1/\phantom{1n}n$. Output:  Strong learner $y_f\left(x\right)$ is equal to the $LST{M}_t$ prediction result $y_t\left(x\right)$ and its corresponding ${\beta }_t$ generated by weight collection.  1:Call learner $LST{M}_t$ with the training set, T, according to the distribution, $W_j^t$, to train and give the hypothesis, $y_t:x\to \mathbb{R}$.  2: Calculate the adjusted error for every sample: $$D_t=\underset{j=1}{\overset{n}{max}}|y_j-LST{M}_k\left(x_j^{}\right)|$$ $$e_j^t=\frac{{\left(y_j-LST{M}_N\left(x_j\right)\right)}^2}{{\left(D_t\right)}^2}$$  3: Calculate the adjusted error of the $LST{M}_t$ model: $${\epsilon }_t={\sum }_{j=1}^n{e}_j^t{w}_j^t$$ if ${\epsilon }_t\ge 0.5$, stop and set $N=t-1$.  4:Let ${\beta }_t={\epsilon }_t/(1-{\epsilon }_t)$. Update the weight vector: $w_j^{t+1}=w_j^t{\beta }_t^{1-e_j^t}/Z_t$. ($Z_t$ is a normalizing constant.)  5:Loop step 1 to 4. Reserve all models: $LST{M}_1,\dots LST{M}_t,\dots LST{M}_N$.