Kernel-Based Aggregating Learning System for Online Portfolio Optimization

Algorithm 1

Solving ARIMA model.

Input: Given parameters h, k, m, learning rate η, and initial matrix and initial vector .
(1)	for t = 1 to T do
(2)	Calculate price prediction by (9);
(3)	Receive and incur loss ;
(4)	Let gradient , update ;
(5)	Calculate the inverse matrix by Sherman–Morrision formula:
(6)	;
(7)	Update the coefficient vector , where is the projection in the norm induced by ;
(8)	end for
Output: The coefficient vector .