Luck versus skill over time: time-varying performance in the cross-section of mutual fund returns.

This paper considers the estimation of the parameters of general systems of stochastic differential-difference equations in which the lag parameters themselves are treated as unknown and are not restricted to be integers and therefore form part of the parameter vector to be estimated+ The asymptotic properties of an infeasible frequency domain maximum likelihood estimator are established in addition to those of a feasible version based on truncating an infinite series that arises in the computation of the spectral density function of the observed discrete time series+ Precise conditions that the truncation parameter must satisfy for the asymptotic results to hold are provided+ We are grateful to Gordon Kemp, Andrew Harvey, the Editor, and two anonymous referees for helpful comments on an earlier version of this paper+ Any remaining errors are the sole responsibility of the authors+ The first author thanks the Economic and Social Research Council for financial support under grant number R00429434216, and the second author thanks the Leverhulme Trust for financial support in the form of a Philip Leverhulme

This paper considers statistics based on spectral regression estimators for testing for seasonal unit roots in a time series. An advantage of the frequency domain approach is that it enables serial correlation to be treated nonparametrically, thereby facilitating an explicit focus on the frequencies at which unit roots are of interest. The limiting distributions of the proposed test statistics are derived and their size and power properties are explored in simulation experiments.

It is undoubtedly desirable that econometric models capture the dynamic behavior, like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, for instance, the cyclical growth models of Bergstrom (1966); the economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976); unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997); and differential-difference equations of Chambers and McGarry (2002). This paper considers continuous time cyclical trends, which complement the trend-plus-cycle models in the unobserved components literature but could also be incorporated into Bergstrom type systems of differential equations, as were stochastic trends in Bergstrom (1997).

This paper uses a macroeconomic model of investment behaviour to identify cyclical activity in UK investment. Various cycles are detected and their lengths are estimated. As a new contribution to the business cycle literature, we estimate the gestation lags inherent in investment projects (arising from capital adjustment, buildings construction etc.) that are considered central to the creation of fluctuations in economic activity. We find multiple and statistically significant cycles in our investment series, including a 3.1-year Kitchin cycle, a 9.6-year Juglar cycle and a 22.2-year Kuznets swing, driven by gestation lags of 1.1 years, 2.4 years and 12 years respectively.