INFERENCE IN MILDLY EXPLOSIVE AUTOREGRESSIONS UNDER UNCONDITIONAL HETEROSKEDASTICITY
研究了在无条件异方差条件下，如何为温和爆炸自回归模型中的爆炸参数构建渐近有效的置信区间，并提出了依赖野自助法来改进小样本推断，对资产泡沫检测有实用价值。
Mildly explosive autoregressions have been extensively employed in recent theoretical and applied econometric work to model the phenomenon of asset market bubbles. An important issue in this context concerns the construction of confidence intervals for the autoregressive parameter that represents the degree of explosiveness. Existing studies rely on intervals that are justified only under conditional homoskedasticity/heteroskedasticity. This paper studies the problem of constructing asymptotically valid confidence intervals in a mildly explosive autoregression where the innovations are allowed to be unconditionally heteroskedastic. The assumed variance process is general and can accommodate both deterministic and stochastic volatility specifications commonly adopted in the literature. Within this framework, we show that the standard heteroskedasticity- and autocorrelation-consistent estimate of the long-run variance converges in distribution to a nonstandard random variable that depends on nuisance parameters. Notwithstanding this result, the corresponding t -statistic is shown to still possess a standard normal limit distribution. To improve the quality of inference in small samples, we propose a dependent wild bootstrap- t procedure and establish its asymptotic validity under relatively weak conditions. Monte Carlo simulations demonstrate that our recommended approach performs favorably in finite samples relative to existing methods across a wide range of volatility specifications. Applications to international stock price indices and U.S. house prices illustrate the relevance of the advocated method in practice.