We establish a link between liquidity in a limit order book market and the existence of a unique stationary distribution of transactions prices. The main implication of the model, that illiquidity can lead to the lack of existence of a unique distribution, is investigated using a newly developed...

We propose a set of algorithms for testing the ergodicity of empirical time series, without reliance on a specific parametric framework. It is shown that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes, and maximal power against non-ergodic...