Model selection in threshold models (Q2784959)

The author considers self-exciting threshold autoregressive (SETAR) and Markov-switching models with two regimes. In the SETAR model, the time series is described by the equation NEWLINE\[NEWLINEy_t=\phi_{j,0}+\phi_{j,1} y_{t-1}+\dots+\phi_{j,p}y_{t-p}+\sigma_j\varepsilon_t,NEWLINE\]NEWLINE where \(\varepsilon_j\) are i.i.d. Gaussian, and \(j\) is the number of the regimes. The process is in the regime \(j\) at time \(t\) if \(r_{j-1}\leq y_{t-d}\leq r_j\), \(d\) being an integer-valued delay parameter, and \(r_k\) are fixed thresholds. For two regimes, in SETAR models only one threshold \(r_1=r\) is needed. The parameter \(d\) is assumed known. For a fixed autoregression order \(p\) the other parameters can be estimated by the least squares technique. The problem is to estimate \(p\).NEWLINENEWLINENEWLINEThe author considers general information criteria for this purpose (including a generalized information criterion and an information complexity criterion) and derives consistency results for the obtained estimators. Small sample properties of the estimators are studied via Monte Carlo simulations.