10. We have observed 110 anual values of the CPI, z,. Complete the spaces in order to explain the rational behind the following steps. Hand written plz (a) Firstly, we took logs and obtaines w₁ = log(z,), in order to obtain a series which is in (b) Then, we took the first differences x₁ = (1-B)w, trying to obtain a process. (c) Then, we subtracted the sample mean = 0.7 to these x,, in order to obtain a process with (d) Finally, we adjusted an AR(2) to the series (x,-0.7), which is equivalent to assume that w, is an ARIMA(_,_,__). (e) In order to verify whether the residuals are Ljung-Box test. 15 we performed the (f) We have obtained Q = n(n+2)Σ (109−k)¯¹² = 11.243<23.362 = x².05(13), where n = (g) This means we haven't rejected Ho: P₁ = P2 = ... = P15=. (h) That means we concluded that the model AR(2) is for the residuals. for the data (x,-0.7).