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* Advanced Applied Econometrics
* Jakub Muck 
* Exercise 19

* importing data
clear all 
use "http://e-web.sgh.waw.pl/jmuck/AAE/Datasets/USPhillipsCurve.dta"

* data preparation 
sort year quarter 
gen t=_n
tsset t
gen cpi=ln(CPI)
gen infl=d.cpi 

* (i) Stationarity 
tsline infl 
dfuller infl, lags(1) regress

* (ii) AR(1) model 
reg infl L.infl 
* serial correlation 
estat bgodfrey, lags(1/4) 
* half-life 
nlcom(half_lif:ln(.5)/ln(_b[L.infl]))
* IRF => available only for the ML estimates 
arima infl, ar(1)
irf create ar1, set(myirf) replace step(20)
irf graph irf 

* (iii) AR(2) model 
reg infl L(1/2).infl 
* serial correlation 
estat bgodfrey, lags(1/4) 
* IRF => available only for the ML estimates 
arima infl, ar(1/2)
irf create ar2, set(myirf) replace step(20)
irf graph irf 


* (iv) AR(3) and AR(4)  model 
reg infl L(1/3).infl 
* serial correlation 
estat bgodfrey, lags(1/4) 
* IRF => available only for the ML estimates 
arima infl, ar(1/3)
irf create ar3, set(myirf) replace step(20)
irf graph irf 

reg infl L(1/4).infl 
* serial correlation 
estat bgodfrey, lags(1/4) 
* IRF => available only for the ML estimates 
arima infl, ar(1/4)
irf create ar4, set(myirf) replace step(20)
irf graph irf