Evidence of chaos in commodity futures prices

DeCoster, Gregory P.; Labys, Walter C.; Mitchell, Douglas W.

doi:10.1002/fut.3990120305

Cited by 72 publications

(40 citation statements)

References 41 publications

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“…Similar problems of specificity and reliability (7,8) also baffle other approaches to chaos detection that rely on certain topological or information measures of attractors reconstructed from the data (9,10). The lack of a definitive test of chaos in experimental time series has thwarted the application of nonlinear dynamics theory (4,11) to a variety of physical (6,(12)(13)(14)(15), biomedical (16)(17)(18)(19)(20)(21)(22)(23)(24), and socioeconomic systems (25)(26)(27)(28)(29)(30) where chaos is thought to play a role. Overcoming these hurdles may open exciting possibilities for practical applications such as the improved forecasting of weather (31) and economic (30) patterns, novel strategies for diagnosis and control of pathological states in biomedicine (23,24,(32)(33)(34)(35) or the unmasking of chaotically encrypted electronic or optical communication signals (36)(37)(38)(39).…”

mentioning

confidence: 99%

Titration of chaos with added noise

Poon

Barahona

2001

Proc. Natl. Acad. Sci. U.S.A.

135

114

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Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple ''litmus test'' for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.

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confidence: 99%

Titration of chaos with added noise

Poon

Barahona

2001

Proc. Natl. Acad. Sci. U.S.A.

135

114

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“…The study concluded that evidence of chaos had been found, which implies that asset price changes can be predicted in a very short period but not in a long run. There is one common problem for both studies of Frank and Stengos (1989), andDeCoster et al (1992). According to the chaos theory as discussed later, the estimates of the CD for a chaotic system will saturate at a certain value as the embedding dimension rises.…”

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confidence: 99%

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

Wei¹,

Leuthold

1998

SSRN Journal

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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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“…are all rejected in original series, we choose the optimal ARMA model under BIC information criteria and t-test of auto-regression parameters to filter and eliminate the linear dependence of return series, and then test the residuals of ARMA model to decide whether nonlinear dependence existed in series. For London spot return series we choose ARMA(3,3) as linear model, for COMEX future return ARMA (3,3), and for Shanghai spot return MA(2)(see Table 5 for detailed results). After eliminating the linear dependence with optimal linear model, we test the residuals of the three return series respectively (see Table 6 for test results).…”

Section: Bds Test After Linear Model Filtrationmentioning

confidence: 99%

“…Frank and Stengos [4] estimated the correlation dimensions and Kolmogorov entropy of gold and silver spot prices, finding chaotic characteristics. DeCoster et al [3] calculated the correlation dimensions of the futures of sugar, silver, copper and coffee, in which evidence for the existence of chaos had been found. By calculating correlation integral and carrying out BDS test, Yang and Brorsen [15] [13] calculated the correlation dimensions d of Shanghai Composite Index using G-P algorithm, and Lyapunov exponent using Wolf method and reached a conclusion that chaos existed in Chinese stock market.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of International Gold Prices: Conditional Heteroskedasticity or Chaos?

Huang

Ban

2014

Journal of Systems Science and Information

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Taking the special nonlinear characteristics of the domestic and international gold price into account, this paper systematically analyzed its nonlinearity by the methods of BDS test, R/S analysis and improved largest Lyapunov exponent. We find three main results: (1) ARMA-GARCH model could adequately explain the linear and nonlinear dependence of gold price series; (2) long-memory does not exist anymore in price series explained by ARMA-GARCH model; (3) chaos phenomenon which is sensitive to the initial value does not exist either in the residuals of regression model. Therefore, we believe that the nonlinearity of gold price is mainly characterized in conditional heteroscedasticity rather than chaos.

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Evidence of chaos in commodity futures prices

Cited by 72 publications

References 41 publications

Titration of chaos with added noise

Titration of chaos with added noise

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

Nonlinear Dynamics of International Gold Prices: Conditional Heteroskedasticity or Chaos?

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