Abstract
The operation of order estimation of a Markov chain to represent the observation chain is an important problem in realistic applications. One method of order estimation depending on intelligence technicality is represented by artificial neural networks . in this research we design an artificial neural network which is the backpropagation error (BPE) .
This research treated realistic problem in Markov chain order estimation to the weather state of raining months in Nineveh Governorate ( clearly, cloudy, rainy) , and a special algorithm has been prepared for training the network .We suggest another neural network for backpropagation error which is forecasting the weather state , which is designed depending on the past network after modify it.