Model identification for infinite variance autoregressive processes

Mixed causal-noncausal models

“…In this section, we outline the estimation strategy of mixed causal-noncausal models as specified in Section 2, with the small modification that these models are augmented with an intercept α. If the error process ε t possesses a density f ε (ε t ; λ), with λ being a vector collecting distributional parameters (e.g., scale parameters, degrees of freedom), the associated approximate likelihood function 5 is given by…”

“…The limiting distribution of these parameters could also be considered in the infinite variance setting. Findings in Davis et al (1992) and Andrews and Davis (2013) however show that a closed form solution for these distributions does not exist (and hence is intractible in practice). One could overcome this problem by means of bootstrapping and simulation-based methods.…”

“…4 Interestingly, information This simulation study has also been performed for different values of φ 1 and ϕ 1 and yielded similar results. 5 There is, however, one major difference visible. For this reason, we report the results for the case where φ 1 = ϕ 1 = 0.3 in Table 3.3.…”

“…Results are available upon request. 5 Simulation results are available upon request. Table 3.3: Frequency (in percentages) with which model is selected (X-11 seasonal adjustment), φ 1 = ϕ 1 = 0.3…”

“…When k = 1, ω 1 = 1 2 π, f (ω 1 ) = 5 5 16 /2π and when k = 2, ω 2 = π, f (ω 2 ) = 10 9 16 /2π. Hence, the spectrum of the deterministic part shows spikes at the frequences 1 2 π and π, but equals zero otherwise.…”