英文文献：Testing for rational bubbles in a co-explosive vector autoregression-在共爆向量自回归中测试理性泡沫
英文文献作者：Tom Engsted,Bent Nielsen
英文文献摘要：
We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The analysis for the no-bubble case is done within the traditional Johansen model for I(1) variables, while the bubble model is analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000.

我们推导了一个标准股票市场模型对股票价格和股息的二元向量自回归所隐含的参数限制，并展示了如何使用似然比检验来检验这些限制。这一限制意味着股票收益是不可预测的，对无泡沫模型和有理性泡沫模型都是如此。在这两种情况下，我们展示了如何通过标准的卡方推理来测试这些限制。对于无气泡情况的分析是在I(1)变量的传统Johansen模型中进行的，而气泡模型则使用共爆框架进行分析。该方法使用1872-2000年期间的美国股票价格和股息来说明。