Analyzing the time sequence of classes of solar days leads us to think that the solar radiation days would be governed by e Hidden Markov Model with some underlying unobservable mechanism of solar radiation. Under this consideration, we have first established HMM (X_t,Y_t) for solar radiation sequences. The Markov chain X_t is homogeneous and is not observed directly, instead we observe the scalar process Y_t. Then, the problem of estimating the parameters for HMM is discussed. New exact filters for obtaining Maximum Likelihood parameter estimates are dirived from the Expectation Maximization (EM) algotithm.