Hello Researchers,

I'm currently doing my research on time series modelling for predicting solar irradiation using ARMA models. The simple steps I followed to develop the ARMA model is:

1. To ensure that the 20 year data I used is stationary: First, checked the Auto correlation function (ACF) and Partial auto correlation function (PACF). Found that ACF is declining and follows a shape of periodic sinusoidal wave cycle. PACF too got declined. Thus concluded data is stationary. 

2. Found the p,q order using AIC/BIC criterion.

3. Used long RA and Non linear least square estimation method to estimate the value of coefficients.

Question:  

When I compare the actual and predicted values of solar irradiation within this 20 year, the values are similar and perfectly fitted. (Please see the figure attached) But when I try to predict the 21th year, the prediction is totally wrong and can't see any correlation in actual and predicted values. !!

Let's say, t is the time given to the algorithm for predicting particular time period solar irradiation. So my question is, do I need to give t= (8760*20) + 1 to the algorithm to find the solar irradiation of 1st day of 21 th year.? Or can I use the values predicted within 20 years as the solar irradiation for 21st year? Because I am thinking that the Gaussian white noises and coefficient value added may accommodate the variation in the irradiation in next year. It's just a random thought!!

Kindly please enlighten me to sought out this issue. Thanks!