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on Econometric Time Series |
| By: | Francisco (F.) Blasques (VU Amsterdam, The Netherlands; Tinbergen Institute, The Netherlands); Marc Nientker (VU Amsterdam, The Netherlands) |
| Abstract: | This article generalises the results of Sadi and Zakoian (2006) to a considerably larger class of nonlinear ARCH models with discontinuities, leverage effects and robust news impact curves. We propose a new method of proof for the existence of a strictly stationary and phi-mixing solution. Moreover, we show that any path converges to this solution. The proof relies on stochastic recurrence equation theory and builds on the work of Bougerol (1993) and Straumann (2005). The assumptions that we need for this approach are less restrictive than those imposed in Sadi and Zakoian (2006) and typically found in Markov chain theory, as they require very little from the distribution of the underlying process. Furthermore, they can be stated in a general setting for random functions on a separable Banach space as is done in Straumann and Mikosch (2006). Finally, we state sufficient conditions for the existence of moments. |
| Keywords: | Ergodicity; GARCH-type models; mixing; nonlinear time series; stationarity,stochastic recurrence equations; threshold models |
| JEL: | C50 C51 C58 |
| Date: | 2017–08–02 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20170072&r=ets |
| By: | Hecq, Alain; Issler, João Victor; Telg, Sean |
| Abstract: | The mixed autoregressive causal-noncausal model (MAR) has been proposed to estimate economic relationships involving explosive roots in their autoregressive part, as they have stationary forward solutions. In previous work, possible exogenous variables in economic relationships are substituted into the error term to ensure the univariate MAR structure of the variable of interest. To allow for the impact of exogenous fundamental variables directly, we instead consider a MARX representation which allows for the inclusion of strictly exogenous regressors. We develop the asymptotic distribution of the MARX parameters. We assume a Student's t-likelihood to derive closed form solutions of the corresponding standard errors. By means of Monte Carlo simulations, we evaluate the accuracy of MARX model selection based on information criteria. We investigate the influence of the U.S. exchange rate and the U.S. industrial production index on several commodity prices. |
| Keywords: | Mixed causal-noncausal process, non-Gaussian errors, identification, rational expectation models, commodity prices |
| JEL: | C22 E31 E37 |
| Date: | 2017–08–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:80767&r=ets |