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The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

Many investors have been disappointed with the practical results of portfolio insurance programs, which attempt to achieve option‐like results through dynamic hedging. This article takes the simplest form of dynamic hedging, constant proportion portfolio insurance (CPPI), as a model for developing a more optimal approach. The author uses Monte Carlo simulation to model the multi‐period median growth in discretionary wealth. In addition, he constructs leverage policies that mitigate the practical drawbacks to dynamic hedging. The article also shows that self‐imposed ex ante borrowing constraints (not the ex post constraint imposed by a margin call) can, under certain conditions, improve the performance of dynamic hedging with respect to median terminal wealth.

The Laplace-type estimator (LTE) is a simulation-based alternative to the classical extremum estimator that has gained popularity in applied research. We show that even though the estimator has desirable asymptotic properties, in small samples the point estimate provided by LTE may not necessarily converge to the extremum of the sample objective function. Furthermore, we suggest a simple test to verify if the estimator converges. We illustrate these results by estimating a prototype dynamic stochastic general equilibrium model widely used in macroeconomics research.

An optimal maintenance program for electrical power system components should be based on their reliability. Since, for components characterized by high reliability and cost such as HV circuit breakers, available statistical data are in limited number, a physical model for their ageing is opportune. In the paper a Predictive Maintenance Program (PMP), for determining when a HV circuit‐breaker should be rebuilt, is formalized; it is based upon an adequate stochastic model of electrical wear associated with breaking operations due to system faults. In the model, both fault times and amplitudes are described by means of random variables, in order to deduce a reliability function used as input data for a Bayesian discriminant analysis which dynamically estimates, also in the presence of observation errors, the state of the component, determining the optimal times to perform a maintenance action.

Knocks the final few nails into the coffin which contains the remains of the notion that the theory and practice of control charting depend on assumptions of normality. The subject’s creator, Dr Walter Shewhart, denied this as long ago as 1939! His most famous student, Dr W. Edwards Deming, denied it repeatedly thereafter. There appear to be two most crucial arguments as to why the “orthodox” statistician claims that normality is necessary. One is to enable probability interpretations of control limits. The other is to justify the conversion factors which are in common use in control‐chart calculations. The truth is that, even under normality, the usual probability interpretations are meaningless in practice and that, in the latter case, the behaviour of the conventional conversion factors is not at all dependent on normality but is in fact very similar over a wide range of differently‐shaped probability distributions.

In this study, the performance of ordinal GA-based trading strategies is evaluated under six classes of time series model, namely, the linear ARMA model, the bilinear model, the ARCH model, the GARCH model, the threshold model and the chaotic model. The performance criteria employed are the winning probability, accumulated returns, Sharpe ratio and luck coefficient. Asymptotic test statistics for these criteria are derived. The hypothesis as to the superiority of GA over a benchmark, say, buy-and-hold, can then be tested using Monte Carlo simulation. From this rigorously-established evaluation process, we find that simple genetic algorithms can work very well in linear stochastic environments, and that they also work very well in nonlinear deterministic (chaotic) environments. However, they may perform much worse in pure nonlinear stochastic cases. These results shed light on the superior performance of GA when it is applied to the two tick-by-tick time series of foreign exchange rates: EUR/USD and USD/JPY.