I have shared the main data d2015.txt, includes 5 columns. The first column is the ytyt the time series observation. The 2nd to the 4th column is the covariates/aggressors and the fifth column is the mean of the three covariates. The main file shared in my google drive.
I used this code to fit an ARIMA model in which "ur" is univariate time series of observation and the "gt" is a multivariate covariates dataset with 3 columns:
> fit2 = auto.arima(ur,xreg=gt) the output is:
Series: ur Regression with ARIMA(1,1,0) errors Coefficients: ar1 drift Apply office resume 0.5109 -0.1562 0.0098 0.0001 -5e-04 s.e. 0.1141 0.0277 0.0013 0.0017 9e-04 sigma^2 estimated as 0.01239: log likelihood=50.62 AIC=-89.24 AICc=-87.71 BIC=-76.48 Training set error measures: ME RMSE MAE MPE MAPE MASE ACF1 Training set 0.002114705 0.10588 0.08902272 0.04035552 0.5226742 0.497244 -0.06112877
My first question is: how to formulate this ARIMA into mathematical writing?
YtYt= ???
I used pred2 = forecast(fit2,h=1, xreg=gt)to forecast the next month, but it predicts for more months!!! Why? Can you correct me, please?
The ARIMA (1,1,0) with drift is
$y_t=X_t β+ϵ_t$, where X_t contains your regressors at time t, and
ϵ_t∼ARIMA(1,1,0) with drift, ϵ_t∼ARIMA(1,1,0) with drift,
or
(ϵ_t−ϵ_t−1)=γ_t+ϕ(ϵ_t−1−ϵ_t−2)+η_t.
γ is estimated by the drift parameter and ϕ by the ar1 one.
- Badges
- Science topic
- Similar topics
- Organizational Psychology
- Training