Nonlinear Dependence in Gold and Silver Futures: Is it Chaos?

Resources Policy, 2018

The possible scarcity of copper (and the likely resulting pressure on prices) is an issue of concern, especially in the light of its importance for the ever growing networking industry. Also for that reason, copper is the nonferrous metal most traded in the markets. Therefore, assessing the nature of its price fluctuations is an important task. Several papers have been devoted to analysing the characteristics of the time series of copper prices, especially for the purpose of predicting its future behaviour. The field of approaches can be divided roughly equally between those adopting a stochastic model and those opting for a deterministic nonlinear (chaotic) model. Nevertheless, while papers employing the stochastic paradigm have completely ignored the presence of chaotic features, at the same time papers recognizing the chaotic paradigm have neglected the presence of noise.The purpose of this paper is to investigate copper price behaviour in the CMX, considering a very long time series and adopting estimation methods that provide the coexistence of stochastic and chaotic features. We find that: a) the presence of noise is very significant (amounting to more than a quarter of the average signal value), as well as the presence of chaotic features; b) intermittency is present, which may be indicative of a bubblerelated value that emerged without any fundamental cause.

This research aims to determine non-linear properties in the time-series of the London Gold price fixes. The study covers 45 years of daily data, which consists of the 10:30am price fix with 11,387 daily observations, and the 3:00pm price fix with 11,265 daily observations. The paper utilizes four tests of non-linearity and chaotic behavior, namely, the Brock, Dechert, and Scheinkman (BDS) test, which delineates a random series from deterministic chaos or from nonlinear stochastic series; rescaled range (RS) analysis, which identifies short-term and long term dependencies in time-series data; the correlation dimension (CD) analysis; which models complexity of data, and determines possible signs of chaos; and the Lyapunov exponent test, which serves as a robustness test and verifies the results of the CD analysis. These tests will be applied on the daily returns of the morning and afternoon London Gold price fixes, and generally finds evidence of chaotic properties in the gold price fixes. The a) BDS test indicates that the morning and afternoon gold fixes are not independent and identicallydistributed (i.i.d.) series, except for the filtered residuals from the generalized autoregressive conditional heteroscedasticity (GARCH) filter. The b) RS analysis shows that after scrambling the data, all Hurst exponents are above 0.5, and the morning fix is found to be more persistent than the afternoon fix. The c) CD analysis finds the presence of a high dimensional noisy chaotic structure. Lastly, d) Lyapunov exponent test concludes that the returns of the London gold price fixing are consistent with deterministic chaos.

Journal of Futures Markets, 1993

R (1985); Hall et al. (1988)l has found that the distribution of futures prices is not normal but leptokurtic. Specifically, the empirical distributions of daily price changes have more observations around the means and in the extreme tails than does a normal distribution. Leptokurtosis also appears in stock returns l and exchange rate changes l. Further, nonlinear dependence has been found in futures price changes ; l. Yet, empirical research on market anomalies has either ignored the non-normality and dependence or resorted to nonparametric tests which generally are less powerful than parametric tests.

Journal of Engineering Science and Technology Review

This paper applies non linear methods to analyze the weekly gold prices close index .The aim of the analysis is to quantitatively show if the corresponding time series is a deterministic chaotic one and its predictable. For this purpose the correlation and minimum embedding dimensions of the corresponding strange attractor are calculated. Also the maximum Lyapunov exponent is estimated.

Agricultural Economics, 2002

We conduct tests for the presence of low-dimensional chaotic structure in the futures prices of four important agricultural commodities. Though there is strong evidence of non-linear dependence, the evidence suggests that there is no long-lasting chaotic structure. The dimension estimates for the commodity futures series are generally much higher than would be for low dimension chaotic series. Our test results indicate that autoregressive conditional heteroskedasticity (ARCH)-type processes, with controls for seasonality and contract-maturity effects, explain much of the non-linearity in the data. We make a case that employing seasonally adjusted price series is important in obtaining robust results via some of the existing tests for chaotic structure. Finally, maximum likelihood methodologies, that are robust to the non-linear dynamics, lend strong support to the Samuelson hypothesis of maturity effects in futures price changes.

Resources Policy, 2001

Many financial time series exhibit irregular behaviour. Economic theory suggests that this irregular behaviour might be due to the existence of nonlinear dependence in the markets. Thus, economic time series are governed by nonlinear dynamics. The purpose of this paper is to investigate price behaviour in the London Metal Exchange market. Thus, this study will test the two most attractive nonlinear models-long memory and chaos-on six metal commodities to ascertain which model is consistent with the observed metal price nonlinear dynamics. Application of long memory and chaos analysis provides new approaches for assessing the behaviour of metal prices. We identified, in tin, a case of chaos. Our empirical results in the case of aluminium support the long memory hypothesis. A short memory model explains the underlying processes of the nickel and lead returns series, while zinc returns reflect an anti-persistent process. To our knowledge, this is one of the first attempts to apply long memory and chaos analysis in the evaluation of the behaviour of metal prices.

This research finds evidence of noisy chaotic properties in the returns of four Dow Jones indices, based on three tests of non-linearity and chaos. The study uses an average of 24,815 data points to correctly simulate chaos in financial time-series. The data consists of the Dow Jones Industrial Average (29,229 observations); Dow Jones Transportation Average (29,121 observations); Dow Jones Utility Average (21,150 observations) and the Dow Jones Composite Average (19,906 observations). The a) Brock, Dechert, and Scheinkman (BDS) test indicates that most of the Dow Jones indices are not iid series, except for the filtered residuals from the GARCH of the Dow Jones Utility Average. The b) rescaled range analysis shows that after scrambling the data, all Hurst exponents are above 0.5, and a trend-reinforcing property, which helps in the conclusion of having a chaotic process. Lastly, the c) correlation dimension analysis complements the initial findings and concludes the presence of a high dimensional noisy chaotic structure in the four Dow Jones indices.

International Business & Economics Research Journal (IBER), 2010

Employing the daily bilateral exchange rate of the dollar against the Canadian dollar, the Swiss franc and the Japanese yen, we conduct a battery of tests for the presence of low-dimension chaos. The three stationary series are subjected to Correlation Dimension tests, BDS tests, and tests for entropy. While we find strong evidence of nonlinear dependence in the data, the evidence is not consistent with chaos. Our test results indicate that GARCH-type processes explain the nonlinearities in the data. We also show that employing seasonally adjusted index series enhances the robustness of results via the existing tests for chaotic structure.

The structure of the relationship between oil prices, gold price, silver price and copper price are not only important for economists but also for policymakers since it contributes to the policy debate on the link between variables and co-movement of the variables. In this paper, the relationship between oil prices and the price of gold and silver was analysed by BDS test, non-linear ARDL approach and two non-linear Granger causality methods for 1973:1-2012:11 period in Turkey. This study complements previous empirical papers. However, it differs from the existing literature with simultaneous use of nonlinear ARDL and two non-linear causality model: Hiemstra and Jones (1994) non-linear causality and augmented granger causality developed by this paper. The main findings of this paper are: (a) the gold price level showed positive asymmetric response to changes in the oil price in the short-and long-run. The gold price probably possesses some market power and it is a means of store of value. Because of the exception of gold, there is a substantial sluggishness in the adaption to changes in demand. In the long run the exception of gold lags and adjustment costs should play a smaller part; b) there is a unique long-term relationship between oil prices and the prices of gold, silver and cooper; and (c) there is a unidirectional Granger causality between oil price and precious metal price.

This research finds evidence of noisy chaotic properties in the returns of four Dow Jones indices, based on three tests of non-linearity and chaos. The study uses an average of 24,815 data points to correctly simulate chaos in financial time-series. The data consists of the Dow Jones Industrial Average (29,229 observations); Dow Jones Transportation Average (29,121 observations); Dow Jones Utility Average (21,150 observations) and the Dow Jones Composite Average (19,906 observations). The a) Brock, Dechert, and Scheinkman (BDS) test indicates that most of the Dow Jones indices are not iid series, except for the filtered residuals from the GARCH of the Dow Jones Utility Average. The b) rescaled range analysis shows that after scrambling the data, all Hurst exponents are above 0.5, and a trend-reinforcing property, which helps in the conclusion of having a chaotic process. Lastly, the c) correlation dimension analysis complements the initial findings and concludes the presence of a high dimensional noisy chaotic structure in the four Dow Jones indices.