What Proportion of Time is a particular Market inefficient?...Analysing market efficiency when equity prices follow Threshold Autoregressions

We assume that log equity prices follow multi-state threshold autoregressions and generalize existing results for threshold autoregressive models, presented in Knight and Satchell (2012) for the existence of a stationary process and the conditions necessary for the existence of a mean and a variance; we also present formulae for these moments. Using a simulation study we explore what these results entail with respect to the impact they can have on tests for detecting bubbles or market efficiency. We find that bubbles are easier to detect in processes where a stationary distribution does not exist. Furthermore, we explore how threshold autoregressive models with i.i.d trigger variables may enable us to identify how often asset markets are inefficient. We find, unsurprisingly, that the fraction of time spent in an efficient state depends upon the full specification of the model; the notion of how efficient a market is, in this context at least, a model-dependent concept. However, our methodology allows us to compare efficiency across different asset markets.