Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1308.1616

Complexity, Chaos, and the Duffing-Oscillator Model: An Analysis of Inventory Fluctuations in Markets

Varsha S. Kulkarni
View original source ↗Read source document ↗Export metadata ↓

Abstract

Apparently random financial fluctuations often exhibit varying levels of complexity, chaos. Given limited data, predictability of such time series becomes hard to infer. While efficient methods of Lyapunov exponent computation are devised, knowledge about the process driving the dynamics greatly facilitates the complexity analysis. This paper shows that quarterly inventory changes of wheat in the global market, during 1974-2012, follow a nonlinear deterministic process. Lyapunov exponents of these fluctuations are computed using sliding time windows each of length 131 quarters. Weakly chaotic behavior alternates with non-chaotic behavior over the entire period of analysis. More importantly, in this paper, a cubic dependence of price changes on inventory changes leads to establishment of deterministic Duffing-Oscillator-Model(DOM) as a suitable candidate for examining inventory fluctuations of wheat. DOM represents the interaction of commodity production cycle with an external intervention in the market. Parameters obtained for shifting time zones by fitting the Fourier estimated time signals to DOM are able to generate responses that reproduce the true chaotic nature exhibited by the empirical signal at that time. Endowing the parameters with suitable meanings, one may infer that temporary changes in speculation reflect the pattern of inventory volatility that drives the transitions between chaotic and non-chaotic behavior.

Explore related subjects

q-fin.GNphysics.data-an

Keep this discovery

BibTeXRIS

Varsha S. Kulkarni. 2013-07-24. Complexity, Chaos, and the Duffing-Oscillator Model: An Analysis of Inventory Fluctuations in Markets. https://arxiv.org/abs/1308.1616

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

AI for AI: Optimizing Additional Infrastructure Build-out to Power Artificial Intelligence Data Centers

The twenty-first century's transformative technology, artificial intelligence, is increasingly constrained by the twentieth century's transformative technology, the electricity grid. Rapid growth in electricity demand from data centers is leading to higher electricity prices, without a compensating supply-side response. We develop a framework linking data-center load growth, available generation capacity, and market-clearing prices to understand this phenomenon. We first analyze a deterministic model to show how differing estimates of demand and supply growth rates affect prices. We then model the expansion of new data centers and their associated electricity demand, together with build-outs of new electricity supply, as stochastic processes,resulting in probabilistic distributions of supply, demand, and prices rather than a single forecast. Finally, we formulate generation expansion as a stochastic control problem in which a revenue-maximizing investor dynamically chooses the intensity of supply-side investments. The analysis highlights a central challenge of the data-center build-out: even when rapid demand growth increases the need for new generation, the uncertainties related to load forecasts, development execution risks, and value cannibalization from overbuilding capacity may weaken incentives to invest at the pace required to keep electricity prices stable.

q-fin.GN↗
arXiv2026

Measuring DeFi Risk

Decentralized finance (DeFi) lending has grown from nonexistent in 2017 to nearly 40 billion US Dollars in deposited funds in May 2022. Using cryptocurrency as collateral, the platforms match speculative margin trading with yield-seeking depositors lending coins pegged to the dollar (stable coins). Depositors receive claims guaranteed by a basket of collateral, akin to new stable coins. We develop a framework requiring only knowledge of aggregate deposits and borrowings to measure overall system risks to lenders and borrowers. Using evidence from major protocols, the measures identify an increase in system fragility beyond prudent levels around mid 2021, with a potential loss of peg for extreme variations in coin prices. Overall, the model offers an easily implementable aggregate risk metric capturing the perspectives of synthetic investors and offers early warning signals as the industry is moving from deposits guaranteed by collateral to fiat money.

q-fin.GN↗
arXiv2026

Historical Reflections on Interest Rates and the Emergence of the Yield Curve

This text grew out of a historical introduction initially written for a study of interest rates in cryptocurrency markets. The difficulty of defining a term structure for a currency without a conventional bond market led naturally to a more fundamental question: under what historical conditions does a yield curve become observable at all? Credit existed long before modern money, and interest-bearing loans are documented as early as ancient Mesopotamia. For much of history, the surviving evidence lacks the institutional features that facilitate reliable comparisons of interest rates by maturity: standardised debt instruments, sufficiently homogeneous borrowers, regular issuance over a range of maturities, observable market prices, and liquid secondary markets. We trace the gradual emergence of these conditions from ancient Mesopotamia, Greece, and Rome, through medieval and early modern Europe, to the development of modern sovereign debt markets in the nineteenth and twentieth centuries.

q-fin.GN↗