Volume 5, Issue 2

This paper presents the asymptotic and finite sample properties of the efficient method of moments and indirect inference, when applied to estimating stationary ARMA models. Issues such as identification, model selection, and testing are also discussed. The properties of these estimators are compared to those of maximum likelihood using Monte Carlo experiments for both invertible and noninvertible ARMA models.

Simulations are used to check the probability of detecting a time-varying equilibrium correction by applying the existing tests of no cointegration and parameter constancy. Smooth-transition regressions are chosen to describe the nonlinearity, and the Johansen cointegration test and the Lin and Ter¨asvirta parameter constancy test are applied. It turns out that both tests perform well separately, but the joint power is quite low. The most notable result of this study is the high power when dealing with unrestricted cointegration, that is, when no cointegrating vector is estimated and the cointegrated variables freely enter the model in levels. The power of the parameter constancy test for the unrestricted cointegration is close to the power when the cointegrating vector is assumed to be known.

We examine the intraday and interday dynamics of both the level of and changes in the FTSE (Financial Times-Stock Exchange) 100 index futures mispricing. Like numerous previous studies we find significant evidence of mean reversion and hence predictability in mispricing changes measured over high (minute-by-minute) and low (daily) frequencies. Contrary to other studies we show explicitly that for high-frequency data, this predictability is due not to microstructure effects but to arbitrage activity. Using a threshold autoregressive model that is consistent with arbitrage behavior, we show that such models imply first-order autocorrelation in mispricing changes similar in magnitude to that actually observed. For low-frequency data, we show that predictability is driven neither by arbitrage activity nor by microstructure effects. Rather, it is a statistical illusion that is the result of overdifferencing a trend-stationary series.