We use a new statistical test based on the signal coherence function to detect subtle periodicities in the Chilean exchange rate. We resort to a unique intraday data set that allows us to capture persistent cyclical movements during the day that challenge the random walk hypothesis. We provide a microstructural explanation for the observed behavior, and also look at the day-of-the-week effect for the Chilean peso and find that the different days of the week indeed have different behavior patterns. This is an important result for investment allocation and risk assessment.

In this article, we show how tests of nonlinear serial dependence can be applied to high-frequency time series data that exhibit high volatility, strong mean reversion, and leptokurtotis. Portmanteau correlation, bicorrelation, and tricorrelation tests are used to detect nonlinear serial dependence in the data. Trimming is used to control for the presence of outliers in the data. The data that are employed are 161,786 half-hourly spot electricity price observations recorded over nearly a decade in the wholesale electricity market in New South Wales, Australia. Strong evidence of nonlinear serial dependence is found and its implications for time series modeling are discussed.

The purpose of this note is to analyze the capability of bandpass filters to extract a known periodicity. The specific bandpass filters considered are a conventional discrete Fourier transform (DFT) filter and the filter recently proposed by Iacobucci and Noullez. We employ simulation methods to investigate cycle extraction properties. We also examine the implications arising from the Gibbs effect in practical settings that typically confront applied macroeconomists

Democracy Defended. By Gerry Mackie. New York: Cambridge University Press, 2004. 483p. $85.00 cloth, $29.99 paper.

The main thesis in this book is that social choice theorists, and especially Bill Riker and his Rochester “school,” have cast a “long dark shadow over democratic politics” (the title of Chapter 1). Gerry Mackie then proceeds to dispel this dark shadow by an excessively argumentative interpretation of an impressive number of intellectual accomplishments in the study of social choice, public choice, and what is called in political science “formal theory.” His main attack is directed against the work of Riker, especially that author's work on disequilibrium in majority rule.

One usually assumes that the joint probability distribution is known or that agents will use Bayesian updating to estimate the true probabilities after a number of trials when the states of nature are finite in classical decision theory under uncertainty. If there are important states that have very low probabilities of occurrence, then each agent must make a subjective assessment of the probability distribution until a sufficient number of outcomes are observed in order to generate a precise estimate of the probability distribution. If one assumes that all agents know the states and their payoffs, the probability distribution is stationary, and they observe all outcomes that unfold over time, then it will take at least 10 times the mean time between occurrences of the lowest probability event in order to generate enough outcomes that all agents share the same objective knowledge of the distribution. The mean time of recurrence depends on both the probability distribution and the time unit used between recordings of the observations. If at least one state has a low probability of occurrence, then the time to convergence will exceed the period of stationarity of the process.

In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. We compare two statistical index numbers—the Divisia monetary aggregate and the simple-sum monetary aggregate—with the exact rational expectations monetary aggregate, using actual data. Because we are not using simulated data, we estimate the parameters of the Euler equations, and thereby of the nested monetary aggregator function, using the generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors.

Linear dynamical systems are widely used in many different fields from engineering to economics. One simple but important class of such systems is called the single-input transfer function model. Suppose that all variables of the system are sampled for a period using a fixed sample rate. The central issue of this paper is the determination of the smallest sampling rate that will yield a sample that will allow the investigator to identify the discrete-time representation of the system. A critical sampling rate exists that will identify the model. This rate, called the Nyquist rate, is twice the highest frequency component of the system. Sampling at a lower rate will result in an identification problem that is serious. The standard assumptions made about the model and the unobserved innovation errors in the model protect the investigators from the identification problem and resulting biases of undersampling. The critical assumption that is needed to identify an undersampled system is that at least one of the exogenous time series be white noise.

We introduce a frequency-domain test of time reversibility, the REVERSE test. It is based on the bispectrum. We analytically establish the asymptotic distribution of the test and also explore its finite-sample properties through Monte-Carlo simulation. Following other researchers who demonstrated that the problem of business-cycle asymmetry can be stated as whether macroeconomic fluctuations are time irreversible, we use the REVERSE test as a frequency-domain test of business-cycle asymmetry. Our empirical results show that time irreversibility is the rule rather than the exception for a representative set of macroeconomic time series for five OECD countries.