7 ARIMA Models + ADL and Box-Jenkins Methodology

Considering a single time series \(Y_t\), the interest is in determining the relationship between \(Y_t\) and its past.

Literature

• HW: The Box-Jenkins (ARIMA) Methodology

• ADL: [https://www.econometrics-with-r.org/14-5-apatadlm.html

• Additional on ADL: http://faculty.washington.edu/ezivot/econ584/stck_watson_var.pdf

  • Note, just the intuitions behind are important, not the over-technical details or derivations.

go ARIMA or ADL or VAR??

ARIMA does univariate assessment (only one variable) –> \(ARIMA_{(p,d,q)}\)

ADL does multivariate assessment while also doing AR on the dependent variable, hence we are able to assess effects from another lagged variables. Note, this only takes on one other variable –> \(ADL_{(p)}\)

So, what to do if we have more variables we want to include? Then we do VAR (Vector AuroRegressive mdoel) with

With VAR, we are able to see relationship between several variables, and do forecast for each of the variables with p order lags, both from the other variables and also the variable itself –> \(VAR_{(p)}\)