Long Agricultural Futures Prices: ARCH, Long Memory, or Chaos Processes

Abstract

Price series that are 21.5 years long for six agricultural futures markets, corn, soybeans, wheat, hogs, coffee and sugar, possess characteristics consistent with nonlinear dynamics. Three nonlinear models, ARCH, long memory and chaos, are able to produce these symptoms. Using daily, weekly and monthly data for the six markets, each of these models is tested against the martingale difference null, one-by-one. Standard ARCH tests suggest that all series might contain ARCH effects, but further diagnostics show that the series are not ARCH processes, failing to reject the null. A long-memory technique, the AFIMA model, fails to find long-memory structures in the data, except for sugar. This allows chaos analysis to be applied directly to the raw data. Carefully specifying phase space, and utilizing correlation dimension and Lyapunov exponent together, the remaining five price series are found to be chaotic processes. Long Agricultural Futures Prices: ARCH, Long Memory,or Chaos Processes? INTRODUCTIONIt is not uncommon that agricultural futures prices, like many other financial series: (1) are distributed nonnormally with the fat tails (Taylor 1986, Yang andBrorsen 1993), (2) possess autocorrelations that decay to zero very slowly, even for a very long time period (Taylor 1986), and (3) seem to have non-periodic cycles. Recently, three newly developed nonlinear models, i.e., autoregressive conditional heteroscedasticity (ARCH) process and its variants, long memory, and chaos, demonstrate good power to capture these characteristics. 1Often in agricultural futures markets, a large price change is followed by another large change, and a small change is followed by another small change. The volatility of markets is not constant over time. It also is observed that in futures trading the variance of prices will often increase as a contract gets closer to the maturity time. Commercial users trade more actively on those contracts which are nearby maturity due to more available information (Leuthold et al. 1989, p.10). This may suggest an ARCH process. A process with ARCH errors can be stationary with constant mean and finite and fixed variance, though its conditional variance is time dependent. Such processes often have fat tails in distributions and spikes in movements. Many empirical studies have found ARCH and its variants in financial markets.A long-memory structure is a process characterized by long-term dependence and nonperiodic cycles (Fang et al. 1994). 2 The ARCH model considers that the nonlinear structure 1 From now on, "an ARCH model" refers to the autoregressive conditional heteroscedasticity process and its variants. "ARCH" will be used in a broad sense.2 See Beran (1994, p. 42) for a formal definition.2 of a given series comes from the time-dependent conditional variance. In a long-memory process, the nonlinearity is the result of accumulated long-term dependence. Though these two models argue irregular price movements are an endogenous phenomenon of a market, they are stochastic models.In contras...

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