1. Find the parameters of the following MA process using Innovations estimator. The MA process is of second order, with O1=0.5 and O2=0.2. Generate the data without noise, then find the parameters. Subsequently, add noise.
2. The patterns of the Problem below are used to identify the order of the ARIMA process. Develop an ANN to pick the best order given this information.
Problem:-
Find the ACF and the PACF for various assumed ARIMA(1,0,0), ARIMA(0,0,1), ARIMA(1,0,1), ARIMA(2,0,0), ARIMA(0,0,2), and ARIMA(2,0,2). Note that the patterns of exponential decay are present in the ACF, the PACF, or both.
3. Compare the algorithms for curve fitting a Fourier (Hartley) series and the fast transforms.