Econometrics II

We were occupied with algebraic properties of the ring of formal power series w.r.t. the lag operator as well as some analytic properties that emerge when given relevant properties of the sequences of coefficients. These along with the preparations in the previous lectures on the class of causal linear processes, allowed us to easily describe conditions for the existence and properties of ARMA models as linear processes with absolutely summable coefficients, their weak stationarity, regularity and short memory, and further conditions for their strict stationarity and ergodicity.

We were further occupied with the example of the ARMA(1,1) process by deriving the solution and the relevant properties which were shown to comply with the results of our general theorem.

You can find notes for the above here and here.

Exercise. Derive the solutions and the autocovariance function of the ARMA(1,2) process under the relevant UDC.