Abstract
Abstract We propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations in QAR. This new modelling perspective is appealing for investigating the presence of bubbles in economic and financial time series, and is an alternative to approximate maximum likelihood methods. We illustrate our analysis using hyperinflation episodes of Latin American countries.
Highlights
We propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR)
The aggregate sum of rescaled absolute residuals (SRAR) is a measure based on the whole dynamics of the underlying process, which is not dominated by the conditional mean information any more
To adapt to heavy tailed distributions, we generalize the quantile autoregression theory for regularly varying distributions. This confirms the validity of quantile autoregressions in analysing heavy tailed time series, such as explosive or bubble-type dynamics
Summary
Mixed causal and noncausal time series models have been recently used in order (i) to obtain a stationary solution to explosive autoregressive processes, (ii) to improve forecast accuracy, (iii) to model expectation mechanisms implied by economic theory, (iv) to interpret non-fundamental shocks resulting from the asymmetric information between economic agents and econometricians, (v) to generate non-linear features from simple linear models with non-Gaussian disturbances, (vi) to test for time reversibility. The aggregate SRAR is a measure based on the whole dynamics of the underlying process, which is not dominated by the conditional mean information any more This characteristic of the aggregate SRAR criterion makes it robust in model selection even for some general situations such as with asymmetric distributed innovations. Another remark on this paper is that our method is restricted to the model framework of purely causal or noncausal autoregressions without other explanatory variables, thereby this method can be used to questions like asset pricing of exchange rate where current exchange rate is associated with future exchange rates.
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