non-'linear, a.
"Not linear, in sense 3 of the adj.; involving terms of an equation that are not of the first degree; involving or possessing the property that the magnitude of an effect or output is not linearly related to that of the cause or input."
Oxford English Dictionary
Summary
Frank and Stengos (1989) examined the rates of return on gold and silver and found evidence of a nonlinear deterministic data generating process.
Hsieh (1989) investigates daily changes in five major foreign exchange rates and find no linear correlation, but evidence that indicates the presence of substantial nonlinearity in a multiplicative rather than additive form.
Scheinkman and LeBaron (1989) find evidence that indicates the presence of nonlinear dependence on weekly returns from the Center for Research in Security Prices (CRSP) value-weighted index.
Abhyankar, Copeland and Wong (1997) find nonlinear dependence in the world’s four most important stock-market indexes.
Brooks (1996) tests for non-linearity in 10 daily sterling exchange rates and finds irrefutable evidence of non-linearity in many of the series.
Abhyankar, Copeland and Wong (1995) test for the presence of nonlinear dependence in minute-by-minute real time returns on the UK FTSE-100 Index and find clear evidence of nonlinearity.
Barkoulas and Travlos (1998) test stock returns in the Athens Stock Exchange (Greece), an emerging capital market, the results of which suggest the presence of nonlinearities.
Ammermann and Patterson (2003) show that nonlinear serial dependencies play a significant role in the returns for a broad range of financial time series, including returns from six different stock market indices from across the world, as well as the stock returns for the vast majority of individual stocks trading on the Taiwan Stock Exchange.
Abstract: "After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected under a normal distribution. There are a number of possible explanations. A popular one is that the stock market is governed by chaotic dynamics. What exactly is chaos and how is it related to nonlinear dynamics? How does one detect chaos? Is there chaos in financial markets? Are there other explanations of the movements of financial prices other than chaos? The purpose of this paper is to explore these issues."
Abstract: "This paper gives an overview of joint work with Buz Brock, on evolutionary adaptive belief systems (ABS) for modelling financial markets. Recent work with Andrea Gaunersdorfer is also reviewed and some recent experimental work on expectation formation in financial markets is also discussed. Financial markets are viewed as evolutionary systems between different, competing trading strategies. Agents are boundedly rational in the sense that they tend to follow strategies that have performed well, according to realized profits or accumulated wealth, in the recent past. Simple technical trading rules may survive evolutionary competition in a heterogeneous world where prices and beliefs co-evolve over time. The evolutionary model explains stylized facts of real markets, such as fat tails and volatility clustering. Although the ABS is very simple, it is able to match the autocorrelation patterns of returns, squared returns and absolute returns of 40 years of S&P 500 data."
Abstract: "We present an analysis of the time behavior of the S&P 500 (Standard and Poors) New York stock exchange index before and after the October 1987 market crash and identify precursory patterns as well as aftershock signatures and characteristic oscillations of relaxation. Combined, they all suggest a picture of a kind of dynamical critical point, with characteristic log-periodic signatures, similar to what has been found recently for earthquakes. These observations are confirmed on other smaller crashes, and strengthen the view of the stockmarket as an example of a self-organizing cooperative system."
Abstract: "Linear and nonlinear Granger causality tests are used to examine the dynamic relation between daily Dow Jones stock returns and percentage changes in New York Stock Exchange trading volume. We find evidence of significant bidirectional nonlinear causality between returns and volume. We also examine whether the nonlinear causality from volume to returns can be explained by volume serving as a proxy for information flow in the stochastic process generating stock return variance as suggested by Clark's (1973) latent common-factor model. After controlling for volatility persistence in returns, we continue to find evidence of nonlinear causality from volume to returns."
Abstract: "This paper models the dynamics of adjustment to long-run purchasing power parity (PPP) over the post-Bretton Woods period in a nonlinear framework consistent with the presence of frictions in international trade. We estimate exponential smooth transition autoregressive (ESTAR) models of deviations from PPP, which are obtained using the Johansen cointegration method, for both consumer price index (CPI) and wholesale price index (WPI) based measures and a broad set of US trading partners. In several cases, we find clear evidence of a mean-reverting dynamic process for sizable deviations from PPP, with the equilibrium tendency varying nonlinearly with the magnitude of disequilibrium. Analysis of impulse response functions also supports a nonlinear dynamic structure, but convergence to long-run PPP in the post-Bretton Woods era is very slow."
Abstract: "Simple deterministic systems are capable of generating chaotic output that "mimics" the output of stochastic systems. For this reason, algorithms have been developed to distinguish between these two alternatives. These algorithms and related statistical tests are also useful in detecting the presence of nonlinear dependence in time series. In this article we apply these procedures to stock returns and find evidence that indicates the presence of nonlinear dependence on weekly returns from the Center for Research in Security Prices (CRSP) value-weighted index."
Abstract: "The purpose of this article is to investigate whether daily changes in five major foreign exchange rates contain any nonlinearities. Although the data contain no linear correlation, evidence indicates the presence of substantial nonlinearity in a multiplicative rather than additive form. Further examination reveals that a generalized autoregressive conditional heteroskedasticity (GARCH) model can explain a large part of the nonlinearities for all five exchange rates."
Abstract: "Growing evidence suggests that extraordinary average returns may be obtained by trading in options on
the S&P 500 Index, and that at least part of this abnormal performance may be attributed to the existence of
volatility and jump risk premia. This paper addresses the sufficiency of this explanation, asking whether
any set of priced risk factors is able to explain the expected returns of equity index options. To provide
an answer in as general as possible a setting, a flexible class of nonlinear factor models is estimated using
a large data set of daily returns on all S&P 500 Index futures options traded between 1986 and 2000.
The results show that while priced factors other than the return on the underlying security contribute
to these expected returns, factor-based models are insufficient to explain their magnitude. For a variety
of option classes, but particularly short-term out-of-the-money puts, the magnitude of the mispricing
remains large."
Abstract: "This review is a partial synthesis of the book ``Why stock market crash'' (Princeton University Press, January 2003), which presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are ``outliers'': they form a class of their own as can be seen from their statistical signatures. If large financial crashes are ``outliers'', they are special and thus require a special explanation, a specific model, a theory of their own. In addition, their special properties may perhaps be used for their prediction. The main mechanisms leading to positive feedbacks, i.e., self-reinforcement, such as imitative behavior and herding between investors are reviewed with many references provided to the relevant literature outside the confine of Physics. Positive feedbacks provide the fuel for the development of speculative bubbles, preparing the instability for a major crash. We demonstrate several detailed mathematical models of speculative bubbles and crashes. The most important message is the discovery of robust and universal signatures of the approach to crashes. These precursory patterns have been documented for essentially all crashes on developed as well as emergent stock markets, on currency markets, on company stocks, and so on. The concept of an ``anti-bubble'' is also summarized, with two forward predictions on the Japanese stock market starting in 1999 and on the USA stock market still running. We conclude by presenting our view of the organization of financial markets."
Methods for nonlinear impulse response analysis are introduced. The methods are based on conditional moment profiles defined for a stationary time series. Comparing conditional moment profiles to baseline profiles is the nonlinear analog of conventional impulse-response analysis. The bootstrap may be used for statistical inference. Profile bundles may be examined for evidence of damping or persistence. Application to bivariate NYSE price and volume series from 1928 to 1987 finds evidence of a heavily damped 'leverage effect' and a differential response of trading volume to 'common-knowledge' price shocks.
Abstract: "Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and non-chaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The 2000 observation case was large enough to support the use of asymptotic inference, and (3) the inclusion of a noisy chaotic case. But the computational burdens upon the participants in this competition were already pressing the limits that could reasonably be expected of those courageous enough to subject their tests to this professionally risky competition."
Abstract: "This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to estimate ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time-varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives."
GRANGER, C.W.J. and O. MORGENSTERN, 2001. Spectral analysis of New York stock market prices. Cambridge University Press New York, NY, USA. [Cited by 38] (7.86/year)
Abstract: "This paper examines the empirical relation between nominal exchange rates and macroeconomic fundamentals for five major OECD countries between 1974 and 1987. Five theoretical models of exchange rate determination are considered. Potential non-linearities are examined using a variety of parametric and nonparametric techniques. The authors find that the poor explanatory power of the models considered cannot be attributed to nonlinearities, arising from time-deformation or improper functional form."
This paper uses nonlinear error correction models to study yield movements in the US Treasury Bill Market. Nonlinear error correction arises because portfolio adjustment is an `on-off' process, which occurs only when disequilibrium in the bill market is large enough to induce investors to incur the transaction costs associated with buying/selling bills. This, together with heterogeneity of transaction costs, implies that the strength of aggregate error correction depends on both the distribution of costs and the extent of disequilibrium in the market. Smooth transition models are used to describe an aggregate adjustment process which is strong when the market is distant from equilibrium, but becomes weaker as the market approaches equilibrium. Linearity tests indicate that the types of nonlinearities that would be induced by transactions costs are statistically significant, and estimated models which incororate these nonlinearities outperform their linear counterparts, both in sample and out of sample.
Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This includes, for example, the square root law that has been proposed based on market microstructure theory. In analogy to the linear model, a 'characteristic time' for optimal trading is defined, which now depends on the initial portfolio size and decreases as execution proceeds. A model is also considered in which uncertainty of the realized price is increased by demanding rapid execution; it is shown that optimal trajectories are described by a 'critical portfolio size' above which this effect is dominant and below which it may be neglected.
Abstract: "In this paper we provide a review of the literature with respect to the efficient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that have arisen about the available tests and results, and raise the issue of whether dynamical systems theory is practical in finance."
"Most of the empirical tests that we discussed so far are designed to detect ‘linear’ structure in financial data — that is, linear predictability is the focus. However, as Campbell, et al. (1997, pp. 467) argue ‘…many aspects of economic behavior may not be linear. Experimental evidence and casual introspection suggest that investors’ attitudes towards risk and expected return are nonlinear. The terms of many financial contracts such as options and other derivative securities are nonlinear. And the strategic interactions among market participants, the process by which information is incorporated into security prices, and the dynamics of economy-wide fluctuations are all inherently nonlinear. Therefore, a natural frontier for financial econometrics is the modeling of nonlinear phenomena’."
Abstract: "Inspired by the linear predictability and nonlinearity found in the finance literature, this article examines the nonlinear predictability of the excess returns. The relationship between the excess returns and the predicting variables is recursively modeled by a neural-network model, which is capable of performing flexible nonlinear functional approximation. The nonlinear neural-network model is found to have better in-sample fit and out-of-sample forecasts compared to its linear counterpart. Moreover, the switching portfolio based on the recursive neural-network forecasts generates higher profits with lower risks than both the buy-and-hold market portfolio and the switching portfolio based on linear recursive forecasts."
Abstract: "This article tests for nonlinear dependence and chaos in real-time returns on the world's four most important stock-market indexes. Both the Brock-Dechert-Scheinkman and the Lee. White, and Granger neural-network-based tests indicate persistent nonlinear structure in the series. Estimates of the Lyapunov exponents using the Nychka, Ellner, Gallant, and McCaffrey neural-net method and the Zeng, Pielke, and Eyckholt nearest-neighbor algorithm confirm the presence of nonlinear dependence in the returns on all indexes but provide no evidence of low-dimensional chaotic processes. Given the sensitivity of the results to the estimation parameters, we conclude that the data are dominated by a stochastic component."
MCMANUS, B., 2001. Nonlinear Pricing in an Oligopoly Market: The Case of Specialty Coffee. Olin school of Business, Washington University, St. Louis, …. [Cited by 19] (4.18/year)
Abstract: "Firms that practice second-degree price discrimination may intentionally distort product characteristics away from their efficient levels (e.g., the small version of a product is “too small.”) This paper offers the first empirical study of this product design issue. Using data from a specialty coffee market, I estimate a structural utility model that allows for consumer screening under vertical preference heterogeneity. Comparisons of cost data and the estimated benefits from changing product characteristics suggest that some of the central predictions of nonlinear pricing theory are realized in the observed market. Product design distortions are relatively large for drinks that are not the most profitable but over which the firms hold market power. The estimated distortions decrease toward zero for the products with the highest price-cost margins; this result provides empirical support for the “no distortion at the top” prediction from theory."
In this paper we investigate the profitability of a simple technical trading rule based on Artificial Neural Networks (ANNs). Our results, based on applying this investment strategy to the General Index of the Madrid Stock Market, suggest that, in absence of trading costs, the technical trading rule is always superior to a buy-and-hold strategy for both ‘‘bear’’ market and ‘‘stable’’ market episodes. On the other hand, we find that the buy-and-hold strategy generates higher returns than the trading rule based on ANN only for a ‘‘bull’’ market subperiod.
Abstract: "We consider two ways of distinguishing deterministic time-series from stochastic white noise; the Grassberger-Procaccia correlation exponent test and the Brock, Dechert, Scheinkman (or BDS) test. Using simulated data to test the power of these tests, the correlation exponent test can distinguish white noise from chaos. It cannot distinguish white noise from chaos mixed with a small amount of white noise. With i.i.d. as the null, the BDS correctly rejects the null when the data are deterministic chaos. Although the BDS test may also reject the null even when the data are stochastic, it may be useful in distinguishing between linear and nonlinear stochastic processes."
Abstract: "In this paper we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng, 1993) and the Glosten, Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations such as the 1987 stock market crash and that the GJR model cannot be recommended for forecasting."
This paper considers nonlinear aspects of testing capital market integration and real interest rate equalization. In contrast to standard linear regression tests, we consider two nonlinear approaches to evaluating the relationship between international real interest rates. The ¯rst considers threshold autoregression (TAR) models. Results con¯rm the presence of nonlinearities in equilibrating responses to deviations from parity. Larger shocks evoke faster adjustments. A second segment of the analysis considers more °exible nonlinear modeling techniques. In particular, nonparametric regression tests are used to evaluate real interest rate relationships. This evaluation also suggests that important nonlinearities may characterize real interest rate linkages and thus that standard tests which assume linear relationships may produce misleading inferences. We consider a more °exible nonparametric version of the TAR models and ¯nd further support for the implications of the threshold models, though in several cases, more complex patterns of adjustment are implied.
Abstract: "A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire post Bretton-Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH effects clearly demonstrated in a large number of papers, but with the tests for non-linearity which are currently available being unable to classify any additional non-linear structure."
Abstract: "This paper tests for the presence of nonlinear dependence and chaos in real-time returns on the U.K. FTSE-100 Index using a six-month sample of about 60,000 observations. Since there is clear evidence of nonlinearity, the authors follow other researchers in this field by applying the same tests to the residuals from a GARCH process fitted to the data in order to find out whether or not the nonlinearity can be explained by this type of model. In the event, their results suggest that GARCH can explain some but not all of the observed nonlinear dependence."
Abstract: "Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (April 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a new and powerful detection tool of speculative bubbles and herding behavior."
ABHYANKAR, A., 1998. Linear and nonlinear Granger causality: Evidence from the UK stock index futures market. Journal of Futures Markets. [Cited by 18] (2.38/year)
[CONCLUSIONS:]The study contributes to the literature on lead-lag relationships between the index futures and the cash markets in several ways. First, it provides evidence that the FT-SE 100 index futures tend to lead the cash index by about 5-15 minutes, confirming a similar pattern seen in the U.S., German, and Japanese stock index futures markets. Second, it also suggests that the linear lead-lag relationship persists even after the return series are adjusted for persistence in volatility. Finally, the results imply, in sharp contrast to the linear tests, that if nonlinear effects are accounted for, neither market leads or lags the other. The strong evidence for nonlinear causality provides support for models of index arbitrage which seek to include transaction cost thresholds to model the activities of index arbitrageurs. An issue for future research could be to see if the strong nonlinear causal effects are robust to changes in market conditions, e.g., in periods of high and low volume and volatility and during periods of "good" and "bad" news.
Abstract: "This paper investigates the existence of a deterministic nonlinear structure in the stock returns of the Athens Stock Exchange (Greece), an emerging capital market. The analysis utilizes the concepts of correlation dimension and Kolmogorov entropy, and it also includes a forecasting experiment. Application of the BDS statistical test to raw and filtered returns series suggests the presence of nonlinearities. The findings provide very weak, at best, evidence in support of a nonlinear deterministic data generating process."
Abstract: "Recent empirical evidence suggests that stock market returns are predictable from a variety of financial and macroeconomic variables. However, with two exceptions this predictability is based upon a linear functional form. This paper extends this research by considering whether a nonlinear relationship exists between stock market returns and these conditioning variables, and whether this nonlinearity can be exploited for forecast improvements. General nonlinearities are examined using a nonparametric regression technique, which suggest possible threshold behaviour. This leads to estimation of a smooth-transition threshold type model, with the results indicating an improved in-sample performance and marginally superior out-of-sample forecast results."
Abstract: "This article examines the relationship between returns and trading volume for three petroleum futures contracts. Using daily data on futures prices and trading volume, the study first tests for linear causality between returns and volume. The results of this linear causality test show that futures returns and volume have no predictive power for one another. However, because the distribution of the returns and volume series provides some evidence of nonlinear dependence, the study formally tests for and finds evidence of significant nonlinearities in the returns and volume for the three petroleum futures contracts. The returns and volume series are then filtered for linear dependence through the use of a VAR process. A nonparametric test statistic based on the correlation integral reveals significant bidirectional nonlinear causal relationships between the filtered returns and volume series. Using a third-order moment test, this study finds that the nonlinear dependence in the futures returns and volume series arises from the variance, rather than the mean, of the process. Consequently, the filtered returns and volume series are adjusted for conditional heteroscedasticity. The study then examines the GARCHfiltered returns and volume series and finds that, even after adjusting for volatility effects, there is still strong evidence of bidirectional nonlinear Granger causality and concludes that the nonlinear process may influence both the mean and variance of futures returns and volume. The finding of strong nonlinear causal relationships between petroleum futures returns and trading volume implies that knowledge of current trading volume improves the ability to forecast futures prices. Thus, the results of this study should be useful to regulators, practitioners, and futures markets participants whose success hinges crucially on the ability to forecast futures price movements."
Abstract: "The random-walk (white-noise) model and the harmonic model are two polar models in linear systems. A model in between is color chaos, which generates irregular oscillations with a narrow frequency (color) band. Time-frequency analysis is introduced for evolutionary time-series analysis. The deterministic component from noisy data can be recovered by a time-variant filter in Gabor space. The characteristic frequency is calculated from the Wigner decomposed distribution series. It is found that about 70 percent of fluctuations in Standard & Poor stock price indexes, such as the FSPCOM and FSDXP monthly series, detrended by the Hodrick-Prescott (HP) filter, can be explained by deterministic color chaos. The characteristic period of persistent cycles is around three to four years. Their correlation dimension is about 2.5. The existence of persistent chaotic cycles reveals a new perspective of market resilience and new sources of economic uncertainties. The nonlinear pattern in the stock market may not be wiped out by market competition under nonequilibrium situations with trend evolution and frequency shifts. The color-chaos model of stock-market movements may establish a potential link between business-cycle theory and asset-pricing theory."
Abstract: "The predictability of rates of return on gold and silver are examined. Econometric tests do not reject the martingale hypothesis for either asset. This failure to reject is shown to be misleading. Correlation dimension estimates indicate a structure not captured by ARCH. The correlation dimension is between 6 and 7 while the Kolmogorov entropy is about 0.2 for both assets. The evidence is consistent with a nonlinear deterministic data generating process underlying the rates of return. The evidence is certainly not sufficient to rule out the possibility of some degree of randomness being present."
\citeasnoun{FrankStengos89} examined the rates of return on gold and silver and found evidence of a nonlinear deterministic data generating process.
Abstract: "In this paper, linear and nonlinear Granger causality tests are used to examine the dynamic relationship between daily Korean stock returns and trading volume. We find evidence of significant bidirectional linear and nonlinear causality between these two series. ARCH-type models are used to examine whether the nonlinear causal relations can be explained by stock returns and volume serving as proxies for information flow in the stochastic process generating volume and stock returns respectively."
Abstract: "Both academic and applied researchers studying financial markets and other economic series have become interested in the topic of chaotic dynamics. The possibility of chaos in financial markets opens important questions for both economic theorists as well as financial market participants. This paper will clarify the empirical evidence for chaos in financial markets and macroeconomic series emphasizing what exactly is known about these time series in terms of forecastability and chaos. We also compare these two concepts from a financial market perspective contrasting the objectives of the practitioner with those of the economic researchers. Finally, we will speculate on the impact of chaos and nonlinear modelling on future economic research."
"The results often find strong evidence for nonlinear dependence, but no convincing evidence for chaotic dynamics."
Abstract: "This paper employs a neural network (NN) to study the nonlinear predictability of exchange rates for four currencies at the 1-, 6- and 12-month forecast horizons. We find that our neural network model with market fundamentals cannot beat the random walk (RW) in out-of-sample forecast accuracy, although it occasionally shows a limited market-timing ability. The neural network model without monetary fundamentals forecasts somewhat better for the British pound and the Canadian dollar. The model also exhibits some market-timing ability for the Deutsche mark at the 6- and 12-month horizons, and for the Canadian dollar at the 1-month horizon. In general, the model performs more poorly when it becomes more complex or when the forecast horizon lengthens. Our overall results are more on the negative side and suggest that neither nonlinearity nor market fundamentals appear to be very important in improving exchange rate forecast for the chosen horizons."
Abstract: "This paper studies a variety of world financial market indices to determine how widespread the phenomenon of nonlinear serial dependency is, and then, by studying a relatively financially isolated market, the Taiwan Stock Exchange of the 1980s, examines more closely the extent to which nonlinearity appears to be an inherent feature of financial trading behavior. Nonlinearity is found to be a cross-sectionally universal phenomenon, existing within all the markets studied and within the vast majority of individual stocks traded on the Taiwan Stock Exchange. However, closer examination of the nonlinearity via a windowed testing procedure reveals that such dependencies do not appear to be cross-temporally universal; rather, the data seem to be characterized by relatively few brief episodes of extremely strong dependencies that are followed by longer stretches of relatively quiet behavior. Thus, the modeling of the extant nonlinearity appears to be problematic at best."
We develop a simple model with technical and fundamental traders to explain the cyclical motion ofcommodity prices. The crucial element of our model is a nonlinear market impact of technical traders: Estimation ofour STAR-GARCH model using monthly US corn price data reveals that technical traders increasingly enter the market as booms or slumps enlarge. One reason may be that they only gradually learn about the emergence ofpersistent price trends. The behavior oftrend-extrapolating speculators obviously enforces mispricings and thus contributes to cyclical motion as observed in actual commodity markets.
This article presents some evidence for the presence of a causal relationship between price and volume in the crude oil futures market. The results of linear causality testing reveal the presence of causality running from volume to price but not vice versa. While the results of testing for nonlinear causality are inconsistent, most of the evidence shows that causality runs in both directions. In general, there is evidence for the sequential information arrival hypothesis and the noise trading model, but not for market efficiency. There is also some evidence for the presence of a maturity or a liquidity effect. Finally, there is some variation in the results, depending on the sample period.
The proposed stock market prediction system is comprised of two preprocessing components, two specialized neural networks, and a decision rule base. First, the preprocessing components determine the most relevant features for stock market prediction, remove the noise, and separate the remaining patterns into two disjoint sets. Next, the two neural networks predict the market's rate of return, with one network trained to recognize positive and the other negative returns. Finally, the decision rule base takes both return predictions and determines a buy/sell recommendation. Daily and monthly experiments are conducted and performance measured by computing the annual rate of return and the return per trade. Comparison of the results achieved by the dual neural network system to that of the single neural network shows that the dual neural network system gives much larger returns with fewer trades. In addition, dual NN experiments with the appropriately selected filtering and decision thresh...
Recent empirical evidence suggests that stock market returns are predictable from a variety of financial and macroeconomic variables. However, with two exceptions this predictability is based upon a linear functional form. This paper extends this research by considering whether a nonlinear relationship exists between stock market returns and these conditioning variables, and whether this nonlinearity can be exploited for forecast improvements. General nonlinearities are examined using a nonparametric regression technique, which suggest possible threshold behaviour. This leads to estimation of a smooth-transition threshold type model, with the results indicating an improved insample performance and marginally superior out-of-sample forecast results.
[Summary and conclusion]Tests measuring the in-sample goodness of fit support the nonlinear model over the linear model, similarly the results for the out-of-sample forecasting performance select the nonlinear model over the linear alternative, although the forecasting gain is marginal.
[...]
Results suggest that the nonlinear models outperform the linear model both in-sample and out-of-sample, although the forecast gain is marginal, it thus remains an avenue for further research to see if alternative nonlinear forms can provide a better forecasting performance.
Linear Vector Autoregression (VAR) models provide a useful starting point for analysing multivariate relationships between economic variables. They are frequently used for empirical macroeconomic modelling, policy analysis and forecasting. However, linear VAR systems fail to capture non-linear dynamics such as regime switching and asymmetric responses to shocks, suggested by the recent theoretical developments in macroeconomic research. In addition, an increasing body of empirical evidence suggests that the linear conditional expectations implied by standard VAR models do not always accord with the observed facts. For example, a significant number of empirical studies document asymmetries in the effects of monetary policy on output growth. This paper employs a more general nonlinear VAR methodology to re-examine previous findings that credit market conditions contribute to economic fluctuations as a propagator of shocks. Unlike linear projections it allows for nonlinear dynamics and asymmetric effects of shocks. We estimate a threshold vector autoregression (TVAR), in which the system's dynamics change back and forth between credit constrained and unconstrained regimes. Using generalised impulse response functions (GIRF) generated from the estimated nonlinear model, we examine the real effects of monetary policy. We find evidence of asymmetry in the effects of monetary policy in the credit constrained and unconstrained regimes as well as different output effects of monetary contractions and expansions.
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500 stock index within this framework by direct analysis and by simulation. We find that the power-law tails of the distributions, and the index’s anomalously diffusing dynamics, are very accurately described by this approach. Our results show good agreement between market data, Fokker-Planck dynamics, and simulation. Thus the combination of the Tsallis non-extensive entropy and the nonlinear Fokker-Planck equation unites in a very natural way the power-law tails of the distributions and their superdiffusive dynamics.
Abstract: "The purpose of this article is to characterize linear and nonlinear serial dependence in daily futures price changes. The daily prices of four futures are included in this study: (i) S&P 500; (ii) Japanese yen; (iii) Deutsche mark; and (iv) Eurodollar. Our major empirical findings are: (i) Based on the results of nonlinearity tests (that is, the BDS, the Q2, and the TAR-F tests), we found all futures price changes contain nonlinearity in the series; (ii) a GARCH model can explain the source of nonlinearity for three out of four series; (iii) a threshold autoregressive model and autoregressive volatility model can adequately represent nonlinear dynamics of S&P 500 series; and (iv) deterministic chaos is not evident in the scaled residuals from the nonlinear time series models. Hence we favor a statistical time series approach to represent the data-generating mechanism of futures price changes."
Volume 19, Issue 3, Pages 325 - 351
Journal of Futures Markets, Volume 17, Issue 1 , Pages 75 - 99
[Conclusion]This article tests for linear and nonlinear dependence in three petroleum futures returns and finds evidence of both types of dependence in all cases. The evidence against market efficiency based on tests for linear dependence, however, is not supported by the data after the presence of nonlinear dependence has been accounted for.
[...]
The third-order moment test suggests that the evidence for nonlinearity in the time series arises solely from the variance of the process. This provides some evidence against a nonlinear process for any risk premium. However, the standardized residuals from the GARCH estimates still exhibit substantial nonlinearities, a finding that is consistent with Hsieh’s (1991) contention that the third-order moment test may not be robust to heavy-tailed data. Thus, the evidence against nonlinear factors influencing both the mean and variance cannot be rejected.
The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' ``speculative'' or ``capital gain realizing'' attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basins of attraction.
ANDREOU, A.S., G. PAVLIDES and A. KARYTINOS, 2000. Nonlinear Time-Series Analysis of the Greek Exchange-Rate Market. International Journal of Bifurcation and Chaos. [Cited by 7] (1.26/year)
Using concepts from the theory of chaos and nonlinear dynamical systems, a time-series analysis is performed on four major currencies against the Greek Drachma. The R/S analysis provided evidence for fractality due to noisy chaos in only two of the data series, while the BDS test showed that all four systems exhibit nonlinearity. Correlation dimension and related tests, as well as Lyapunov exponents, gave consistent results, which did not rule out the possibility of deterministic chaos for the two possibly fractal series, rejecting though the occurrence of a simple low-dimensional attractor, while the other two series seemed to have followed a behavior close to that of a random signal. SVD analysis, used to filter away noise, strongly supported the above findings and provided reliable evidence for the existence of an underlying system with a limited number of degrees-of-freedom only for those series found to exhibit fractality, while it revealed a noise domination over the remaining two. These results were further confirmed through a forecasting attempt using artificial neural networks.
AMBROSE, B.W., E. ANCEL and M.D. GRIFFITHS, 1992. … Real Estate Investment Trust Returns: The Search for Evidence of Market Segmentation and Nonlinear …. Real Estate Economics. [Cited by 16] (1.18/year)
Abstract: "Statistical techniques have been developed that use estimated bispectrum values to test whether a sample of a time series is consistent with the hypothesis that the observations are generated by a linear process. The magnitude of the test statistics indicates the amount of divergence between the observations and the linear model hypothesis. It is important to investigate such a divergence, since the usual linear model coefficients can be shown to be biased in the face of nonlinear time series structure. The tests presented here can thus be considered diagnostic as well as confirmatory. These tests are applied to a variety of real series previously modeled with linear models. The results indicate nonlinear models may yield better results, because many of the series analyzed appear to have considerable nonlinear lagged interactions."
HINICH, M.J. and D. PATTERSON, 1989. Evidence of nonlinearity in the trade-by-trade stock market return generating process. In: Barnett, W.A., Geweke, J., Shell, K. (Eds.), Economic Complexity: Chaos,
Bubbles, and Nonlinearity. Cambridge University Press, Cambridge, UK. [Cited by 16] (0.95/year)
GEOFFREY, G., et al., 1994. Nonlinear dependence in Finnish stock returns. European journal of operational research. [Cited by 8] (0.68/year)
PAPAIOANNOU, G. and A. KARYTINOS, 1995. Nonlinear time series analysis of the stock exchange: The case of an emerging market. International Journal of Bifurcation and Chaos. [Cited by 7] (0.66/year)
The extent to which daily return data from the Athens' Stock Exchange Index exhibits non-linear and chaotic characteristics is investigated by employing multiple tests from both the Economics' and the Natural Sciences' fields. The BDS test and Rescale Range (R/S) analysis provide evidence for non-linearity and fractality due to noisy chaos, respectively, while methods of chaotic dynamics, like correlation dimension and related tests, as well as, Lyapunov exponents, give consistent results, which do not rule out the possibility of deterministic chaos. The occurrence of a simple low-dimensional attractor, is not supported. However, noise filtered data by the use of SVD analysis and FIR filters, gives reliable evidence for the existence of an underlying dynamical system with a limited number of degrees-of-freedom.
[useful for chaos also]
XU-SONG, X. and C. YAN-BIN, 2001. Empirical Study on Nonlinearity in China Stock Market [J]. Quantitative and Technical Economics. [Cited by 3] (0.62/year)
Journal of Business and Economics Statistics, 15, 1-14.
This paper tests for the presence of nonlinear dependence and chaos in real-time returns on four of the world's major stock market indices: the FTSE-100, the S&P 500, the Nikkei 225 and the DAX. Our results suggest that GARCH-type models can explain some but not all of the observed nonlinear dependence. The neural network-based test for nonlinearity introduced by Lee, White and Granger (1993) provides conclusive evidence of a persistent nonlinear structure in the series. We also estimate Lyapunov exponents in order to test directly for chaos using both the Nychka, Ellner, Gallant, McCaffrey (1992) and the Zeng, Pielke and Eyckholt (1992) methods. We find that none of the series seem to be characterised by a low-dimensional chaotic process. Instead, the Lyapunov exponent estimates appear to be extremely sensitive to the parameter values used in estimation, a fact which in itself may be an indication that the data are dominated by a stochastic component.
MIRANDA, M., 1998. Numerical Solution Strategies for the Nonlinear Rational Expectations Commodity Market Model. Computational Economics. [Cited by 3] (0.40/year)
CHATEAUNEUF, A., R. KAST and A. LAPIED, 1994. Market Preferences Revealed by Prices: Nonlinear Pricing in Slack Markets. Models and Experiments in Risk and Rationality. [Cited by 4] (0.35/year)
SENGUPTA, J.K. and R.E. SFEIR, 1998. Nonlinear dynamics in foreign exchange markets. International journal of systems science. [Cited by 2] (0.26/year)
POSHAKWALE, S. and D. WOOD, 1998. Conditional variance and nonlinearity in the Polish emerging market. Emerging Capital Markets: Financial and Investment Issues. [Cited by 2] (0.26/year)
ABHYANKAR, A. and L.S. COLELAND, 1994. Nonlinear Dynamics in Real Time Equity Market Indices. Worshop Paper. [Cited by 3] (0.26/year)
NATTER, M., 1994. Nonlinear Market Reaction and Stochastic Price Management in a Multiproduct Enterprise: A …. [Cited by 1] (0.09/year)