Day-Ahead Crude Oil Price Forecasting Using a Novel Morphological Component Analysis Based Model

Algorithm 2

Iterative thresholding algorithm for MCA.

𝐼_max← number of iterations

𝜆⁽⁰⁾← the initial threshold

𝑦⁽⁰⁾←0.

𝜆_min← lower bound

while  𝜆^(𝑡)>𝜆_min  do

 𝑟(𝑡)=𝑟_PT(𝑡)+𝑟_TF(𝑡)  {Compute the residual}

 𝛼^(𝑡)=𝜙_𝜆^(𝑡)(𝜉⁻¹(𝑟^(𝑡)))  {Thresholding}

 𝑦^(𝑡)=𝜉𝛼^(𝑡)  {Reconstruction}

 𝜆^(𝑡+1)← Decreased threshold {𝜆^(𝑡+1)<𝜆^(𝑡) following a given strategy}

end while