Algorithm 1RCSNet training algorithm

Require:Input: Xall =(X¹, X²,⋯,XN) e RN×T, Parameters

Ensure:To predict final result sets yfinal=(y₁final , y₂final,⋯yNfinal), The target result is xtarget=(x₁target , x₂target,⋯xNtarget)

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whileInput series is not finished (i < N) do

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  linear_predict ← ARIMA(xi)

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  non_linear ← xtarget- linear_predict

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  ifnon_linear component exists then

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   Input ← non linear

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   hidden_state ← encoder (Input)

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   decode state ← decoder (hidden state)

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  To generate: non_linear_predict

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  end if

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 combine_prediction:

  linear_predict and non_linear_predict intermediate results to Fully connected layer to get yfinal series

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 To minimize the loss of Σ (yifmal – xitarget)

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 update Parameters to decrease the loss

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  i ← i + 1

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end while