3. (ACF, PACF, and forecasting) Consider the time series data in the file sunspot. dot. It consists of n = 285 observations of the number of sunspots, from 1700 to 1984. This is a quantity that is believed to affect our weather patterns. This time series has been studied by many authors, including Yule (Philosophical Transactions of the Royal Society of London, Series A, 1927) and Brillinger and Rosenblatt (Spectral Analysis of Time Series, B. Harris (Ed), pp 153188, Wiley, 1967). We will study the square root of the data (this transformation ensures that the variance is roughly constant). That is, for the series Zl, . . . , Zn from the file sunspotdot, rst compute the series X t = x/Zt, work with the series {X t} in what follows. (a) Compute the sample ACF and the sample PACF for this series. (b) By considering the sample ACF and sample PACF, decide which of the following would be appropriate for this data: AR(1),AR(2), MA(1) or MA (2). Use the data to estimate the parameters of the model that you choose