Arbitrage bounds and the time series properties of the discount on UK closed-end mutual funds

In a dataset of weekly observations over the period since 1990, the discount on UK closed-end mutual funds is shown to be nonstationary, but reverting to a nonzero long run mean. Although the long run discount could be explained by factors like management expenses etc., its short run fluctuations are harder to reconcile with an arbitrage-free equilibrium. In time series terms, there is evidence of long memory in discounts consistent with a bounded random walk. This conclusion is supported by explicit nonlinearity tests, and by results which suggest the behaviour of the discount is perhaps best represented by one of the class of Smooth-Transition Autoregressive (STAR) models.