A nation's economy is a complex nonlinear dynamical system with links to other national economies. Classical macroeconomic models typically incorporate linear approximations to the nonlinear world and add simple dynamics to capture adjustments over time. Most of these simplifications offer little insight into the nonlinear structure of economic relationships that exist. Nor do they provide useful predictions beyond the short-term predictions of the autoregressive linear models from which they are derived.

This paper employs the rolling bicorrelation test to measure the degree of nonlinear departures from a random walk for aggregate stock price indices of fifty countries over the sample period 1995–2005. We find that stock markets in economies with low per capita GDP in general experience more frequent price deviations than those in the high-income group. This clustering effect is not due to market liquidity or other structural characteristics, but instead can be explained by cross-country variation in the degree of private property rights protection. Our conjecture is that weak protection deters the participation of informed arbitrageurs, leaving those markets dominated by sentiment-prone noise traders whose correlated trading causes stock prices in emerging markets to deviate from the random walk benchmarks for persistent periods of time.

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.

Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

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.

This paper investigates the possible formation of informational cascades by traders in a random sample of 8,000 NYSE stock-days experiencing extreme price changes during 1998–2001. Our cascade measure is designed to detect informational cascades in high-frequency stock market prices. First, we find evidence of cascades on approximately 12% of the days when the NYSE experiences, on average, large price increases. This percentage increases to about 20% on days experiencing large price decreases, on average. Second, we find evidence that the interarrival times of trades in those stocks exhibiting significant informational cascades are generated by a nonlinear stochastic process. Third, the evidence supporting cascades is largely confined to smaller stocks and to stocks followed by fewer security analysts. Last, the occurrence of cascades appears to correlate with the incorporation of fundamental information into security prices.

Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1, 1) processes. Here we test this specification using new model evaluation technology developed by Ashley and Patterson that examines the ability of the estimated model to reproduce features of particular interest: various aspects of nonlinear serial dependence, in the present instance. Using daily returns to the CRSP equally weighted stock index, we find that the GARCH(1, 1) specification cannot be rejected; thus, this model appears to be reasonably adequate in terms of reproducing the kinds of nonlinear serial dependence addressed by the battery of nonlinearity tests used here.