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Box Jenkins, ADF and KPSS tests on a time series

Data Science Asked by Jorge Paredes on July 28, 2021

this is my first question

I have the growth from Ecuadors GDP from 2000 to 2025 (Annually) and I have to predict Ecuadors GDP growth from 2026 to 2030 taking into account:

  1. Ecuadors GDP Growth
  2. Ecuadors Oil revenue
  3. US GDP Growth.

I tried to follow Box-Jenkins methodology, so I did some Augmented Dickey Fuller tests and KPSS tests.

(where ecu_ts is Ecuadors GDP Growth)

I put my code and results here:(i use R)

adf_drift0<-ur.df(ecu_ts, type="drift", lags=5, selectlags="AIC")
#test statistic: -2.5454 | Critical Value (5%): tau2=-2.94 | Therefore I don't reject H0


adf_trend0<-ur.df(ecu_ts, type="trend", lags=5, selectlags="AIC")
#test statistic: -2.8878 | Critical Value (5%): tau3=-3.50 | Therefore I don't reject H0


adf_none0<-ur.df(ecu_ts, type="none", lags=5, selectlags="AIC")
#test statistic: -2.1466 | Critical Value (5%): tau1=-1.95 | Therefore I reject H0

And KPSS:

kpss_trend0<-ur.kpss(ecu_ts, type="tau", lags="long", use.lag=NULL)
#test statistic: 0.1232 | Critical Value (5%): 0.146 | Therefore I don't reject H0

kpss_cons0<-ur.kpss(ecu_ts, type="mu", lags="long", use.lag=NULL)
#test statistic: 0.2758 | Critical Value (5%): 0.463 | Therefore I don't reject H0

What should I do? Should I differentiate the series once more? (d=1) to reject H0 in the ADF test and don’t reject H0 in the KPSS test?

The series looks like this: (Let me know if you need the data set)
enter image description here

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