This study utilizes the Hinich portmanteau bicorrelation test in conjunction with the windowed testing procedure to examine the cross−temporal universality of non−linear dependencies in the returns series for Asian stock market indices. As a whole, the detected non−linear dependencies do not appear to be persistent or stable across time for all the stock markets. In particular, the underlying process is of a switching type, with the pure noise process from time to time switches to a non−linear dependent stochastic process for some unknown length of time, and then switches back to pure−noise. This provides a plausible explanation for the disappointing forecasting performance of many non−linear models, as these existing models do not take note of the episodic transient nature of the non−linear dependency structures.