By Ming Zhang
Synthetic greater Order Neural Networks (HONNs) considerably switch the study method that's utilized in economics and enterprise components for nonlinear info simulation and prediction. With the real advances in HONNs, it turns into crucial to stay familiar with its advantages and enhancements. man made better Order Neural Networks for Economics and enterprise is the 1st booklet to supply sensible schooling and functions for the hundreds of thousands of pros operating in economics, accounting, finance and different company components on HONNs and the benefit in their utilization to acquire extra actual program effects. This resource presents major, informative developments within the topic and introduces the options of HONN team versions and adaptive HONNs.
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Extra info for Artificial Higher Order Neural Networks for Economics and Business
Since f k x = [sin (ak x x) / (ak k x)]k netk x = ak x x and f k x '(netk x ) = k[sin (ak x x) / (ak k x)]k -1 *[cos(ak x x) / (ak x x) - sin ( ak x x) / ( ak k x) 2 ] Then ak x (t + 1) = ak x (t ) - (∂E p / ∂ak x ) = ax x (t ) + (d - z ) f o '(net o )akj o * f h '(netkj h )akj hy b j y akj hx f k x '(netk x ) x = ax x (t ) + * ol * akj o * kj = ax x (t ) + * ol * akj o * kj hx * akj hx * f k x '(netk x ) * x hx * akj hx *[k[sin (ak x x) / (ak k x)]k -1 *[cos( ak x x) / (ak x x) - sin ( ak x x) / ( ak k x) 2 ]]* x = ax x (t ) + * ol * akj o * kj hx * akj hx * k x *x where : = (d - z ) ol kj hx x k = akj b j hy f o '(net o ) = 1 and y x (linear f '(netkj ) = 1 h and x h x (linear k -1 = f k '(netk ) = k[sin (ak x) / (ak x)] k neuron) neuron) x *[cos(ak x) / (ak x x) - sin ( ak x x) / ( ak k x) 2 ] Equation (37).
Comparison Using Japanese vs. Us Dollar Exchange Data comparison Using Us consumer Price Index 1992-2004 Data The monthly Japanese vs. US dollar exchange rate from November 1999 to December 2000 is shown in Table 5. The input Rt-2 uses exchange rates from November 1999 to October 2000. The input Rt-1 uses exchange rates from December 1999 to November 2000. The desired output Rt numbers are exchange rates from January 2000 to December 2000. UCSHONN simulator with Model 0 and Order 5 is used to simulate these data.
PHONN models are defined as follows: Model n z= ∑a k , j =0 where : and kj o 0: ( x) k ( y ) j (akj hx ) = (akj hy ) = 1 ak x = a j y = 1 (15) The learning formulae of the output layer weight for PHONN and all other HONN model is the same as the learning formula (6) of the output layer weight for HONN. Similarly, the learning formulae of the second hidden layer weight for Equation (16). Since f k x = (ak x x) k netk x = ak x x and f k x '(netk x ) = k (netk x ) k -1 = k (ak x x) k -1 Then ak x (t + 1) = ak x (t ) - (∂E p / ∂ak x ) = ax x (t ) + (d - z ) f o '(net o )akj o * f h '(netkj h )akj hy b j y akj hx f k x '(netk x ) x = ax x (t ) + * ol * akj o * kj = ax x (t ) + * ol * akj o * kj = ax x (t ) + * ol * akj o * kj hx * akj hx * f k x '(netk x ) * x hx * akj hx * k (ak x x) k -1 * x hx * akj hx * k x *x where : = (d - z ) ol kj hx x k = akj b j hy x and y f o '(net o ) = 1 f '(netkj ) = 1 h and x x k -1 = f k '(netk ) = k (netk ) h x = k ( ak x ) (linear (linear neuron) neuron) k -1 Artificial Higher Order Neural Network Nonlinear Models Equation (17).