A Neural Learning Approach for a Data-Driven Nonlinear Error Correction Model

Algorithm 1

Learning algorithm for nonlinear ECM neural network.

(1)	Cointegration test of time series: Verify the cointegration of gold price and US dollar index , by two-step cointegration test method described in 2.1.
(2)	Data standardization: The sequence of and , their first-order lag term and long-term equilibrium state deviation degree is standardized by equation (43).
(3)	Initialize: All network weight parameters and network bias parameters take the random number between , all error signals are initialized to 0, and the learning step is . let to (The number of training epochs of hybrid neural network.)
(4)	Let to (Number of observations), and calculate the network output according to equations (9)–(15).
(5)	To Calculate the error according to equation (20) and update total error:
(6)	To update network weight parameters and network bias parameters and error signals according to equations (24)–(42).
(7)	To calculate network output and compare and
(8)	Let
(9)	Repeat Step 5–8, until
(10)	, if , let learning step be
	Repeat Step 4–9, until , or when the stop condition is met to obtain the desired error.