This research examines the relationship between dinar deposits and U.S. dollar payments at the Central Bank of Iraq using monthly data for the period 2016–2025. The ARDL model, the GRU neural network, and a hybrid ARDL–GRU model are applied. The results show that dollar payments are stationary at level, while dinar deposits become stationary after first differencing, with a significant positive long-run cointegrating relationship. The linear ARDL model has limited ability to capture sudden shocks, whereas the hybrid ARDL–GRU model achieves superior forecasting performance both in-sample and out-of-sample. The findings confirm the Central Bank of Iraq’s efficiency in managing domestic and foreign liquidity and maintaining market stab

Because of the experience of the mixture problem of high correlation and the existence of linear MultiCollinearity between the explanatory variables, because of the constraint of the unit and the interactions between them in the model, which increases the existence of links between the explanatory variables and this is illustrated by the variance inflation vector (VIF), L-Pseudo component to reduce the bond between the components of the mixture.

    To estimate the parameters of the mixture model, we used in our research the use of methods that increase bias and reduce variance, such as the Ridge Regression Method and the Least Absolute Shrinkage and Selection Operator (LASSO) method a

The aim of this paper is to estimate a nonlinear regression function of the Export of the crude oil Saudi (in Million Barrels) as a function of the number of discovered fields.

 Through studying the behavior of the data we show that its behavior was not followed a linear pattern or can put it in a known form so far there was no possibility to see a general trend resulting from such exports.

We use different nonlinear estimators to estimate a regression function, Local linear estimator, Semi-parametric as well as an artificial neural network estimator (ANN).

The results proved that the (ANN) estimator is the best nonlinear estimator am