Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos

This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns.Artificial neural networks, nonlinear dynamics, nonlinear time series, nonparametric regression, sieve estimation

Measuring business cycles by saving for a rainy day

We propose a simple saving-based measure of the cyclical component in GDP. The measure is motivated by the prediction that the representative consumer changes savings in response to temporary deviations of income from its stochastic trend, while satisfying a present-value budget constraint. To evaluate our procedure, we employ the bivariate error correction model of Cochrane (1994) to the member countries of the G-7 and Australia. Our estimates reveal, that to a close approximation, the stochastic trend component of GDP is consumption and the transitory component is the error correction term, which justifies the use of our saving-based measure.Business cycles ; Saving and investment ; Gross domestic product ; Consumer behavior

Testing for flexible nonlinear trends with an integrated or stationary noise component

This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu (2009a) and is based on a Feasible Generalized Least Squares procedure that uses a super-efficient estimator of the sum of the autoregressive coefficients α when α = 1. The resulting Wald test statistic asymptotically follows a chi-square distribution in both the I(0) and I(1) cases. To improve the finite sample properties of the test, we use a bias-corrected version of the OLS estimator of α proposed by Roy and Fuller (2001). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modelling the trend of global and hemispheric temperatures

Spurious Regressions in Technical Trading: Momentum or Contrarian?

This paper investigates the spurious effect in forecasting asset returns when signals from technical trading rules are used as predictors. Against economic intuition, the simulation result shows that, even if past information has non predictive power, buy or sell signals based on the difference between the short-period and long-period moving averages of past asset prices can be statistically significant when the forecast horizon is relatively long. The theory implies that both e momentumf and econtrarianf strategies can be falsely supported, while the probability of obtaining each result depends on the type of the test statistics employed. Several modifications to these test statistics are considered for the purpose of avoiding spurious regressions. They are applied to the stock market index and the foreign exchange rate in order to reconsider the predictive power of technical trading rules.Efficient market hypothesis, Nonstationary time series, Random walk, Technical analysis