“Chaos” in futures markets? A nonlinear dynamical analysis

Blank, Steven C.

doi:10.1002/fut.3990110606

Cited by 102 publications

(49 citation statements)

References 41 publications

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“…To search for the underlying generating processes in the futures markets of the S&P 500 index and soybeans, Blank (1991) estimated the CD and the LE and conducted the BDS test on the residuals of GARCH models since GARCH structures had been identified in these series. All the results were consistent with the existence of chaos.…”

Section: Previous Empirical Studiesmentioning

confidence: 99%

“…The estimates of the CD and the largest LE suggest that chaos is responsible for this remaining nonlinear dynamics in the wheat market. Except for the two problems discussed shortly about filters and the phase space, the research procedures of Blank (1991) and Cromwell and Labys (1993) are generally sound. Brorsen (1992, 1993) analyzed nonlinear dynamics of daily cash and futures prices for some agricultural commodities (corn, soybeans, wheat, etc.)…”

Section: Previous Empirical Studiesmentioning

confidence: 99%

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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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Section: Previous Empirical Studiesmentioning

confidence: 99%

Section: Previous Empirical Studiesmentioning

confidence: 99%

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

Wei¹,

Leuthold

1998

SSRN Journal

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“…Section 5 reports the results of summary statistics and univariate unit root tests applied to basis data, cointegration tests applied to a regression involving the spot price and the futures price, linearity tests applied to the basis data, and the estimation results from employing nonlinear models to characterize the basis of the S&P 500 and the FTSE 100 indices. In Section 6 Monte Carlo integration methods are used to calculate the half-lives implied by estimated nonlinear models for the basis, further examining how the nonlinear estimation results can improve the profession's understanding of the dynamics 2 The literature related to the present study is very large and includes, among others, Blank (1991), Brennan and Schwartz (1990), Chan (1992), Dwyer et al (1996), Figlewski (1984), Mougoue (1997a, 1997b), Gao and Wang (1999), Kawaller (1991), Kawaller, Koch, and Koch (1987), Klemkosky and Lee (1991), Lekkos and Milas (2001), Ramaswamy (1988), Miller, Muthuswamy, andWhaley (1994), Modest and Sundaresan (1983), Parhizgari and de Boyrie (1997), Sarno and Valente (2000), Stoll and Whaley (1990), Brorsen (1993, 1994), Yadav et al (1994). 3 See, e.g., Dumas (1994) and Sofianos (1993) on this point.…”

Section: Introductionmentioning

confidence: 99%

Mean reversion in stock index futures markets: A nonlinear analysis

Monoyios

Sarno

2002

Journal of Futures Markets

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Several stylized theoretical models of futures basis behavior under nonzero transactions costs predict nonlinear mean reversion of the futures basis towards its equilibrium value. Nonlinearly mean-reverting models are employed to characterize the basis of the S&P 500 and the FTSE 100 indices over the post-1987 crash period, capturing empirically these theoretical predictions and examining the view that the degree of mean reversion in the basis is a function of the size of the deviation from equilibrium. The estimated half lives of basis shocks, obtained using Monte Carlo integration methods, suggest that for smaller shocks to the basis level the basis displays substantial persistence, while for larger shocks the basis exhibits highly nonlinear mean reversion towards its equilibrium value.

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“…The main difficulty in using the proposed model in (1) is specifying the functional coefficients. We consider in this section, a special class of neural networks called Tangent Hyperbolic neural Networks THNN to identify the model in (1). The most important feature of the THNN is the smooth output which is due to the shape of the tangent hyperbolic functions.…”

Section: Neural Net Architecturementioning

confidence: 99%

“…Within the past decades, there has been a growing interest in applying nonlinear models to predict chaotic time series [1]. The major problem in these researches is the difficulty of distinguishing between deterministic chaos and purely random processes.…”

Section: Introductionmentioning

confidence: 99%

Neural Network For Modeling Nonlinear Time Series: A New Approach

Slim

Trabelsi

2003

Lecture Notes in Computer Science

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Abstract. Nonlinear modeling with neural networks offers a promising approach for studying the prediction of a chaotic time series. In this paper, we propose a neural net based on Extended Kalman Filter to examine the nonlinear dynamic proprieties of some financial time series in order to differentiate between low-dimensional chaos and stochastic behavior. Kalman filtering, because it can deal with varying unobservable states, provides an efficient framework to model these non-stationary exposures. A controlled simulation experiment is used to introduce the issues involved and to present the proposed approach. Measures of forecast accuracy are developed. The pertinence of this model is discussed from the Tunisian Stock Exchange database.

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“Chaos” in futures markets? A nonlinear dynamical analysis

Cited by 102 publications

References 41 publications

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

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

Mean reversion in stock index futures markets: A nonlinear analysis

Neural Network For Modeling Nonlinear Time Series: A New Approach

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