Accounting for outliers and calendar effects in surrogate simulations of stock return sequences

Surrogate Data Analysis (SDA) is a statistical hypothesis testing framework for the determination of weak chaos in time series dynamics. Existing SDA procedures do not account properly for the rich structures observed in stock return sequences, attributed to the presence of heteroscedasticity, seasonal effects and outliers. In this paper we suggest a modification of the SDA framework, based on the robust estimation of location and scale parameters of mean-stationary time series and a probabilistic framework which deals with outliers. A demonstration on the NASDAQ Composite index daily returns shows that the proposed approach produces surrogates that faithfully reproduce the structure of the original series while being manifestations of linear-random dynamics.Comment: 21 pages, 7 figure

Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant

Intertrade duration of equities is an important financial measure characterizing the trading activities, which is defined as the waiting time between successive trades of an equity. Using the ultrahigh-frequency data of a liquid Chinese stock and its associated warrant, we perform a comparative investigation of the statistical properties of their intertrade duration time series. The distributions of the two equities can be better described by the shifted power-law form than the Weibull and their scaled distributions do not collapse onto a single curve. Although the intertrade durations of the two equities have very different magnitude, their intraday patterns exhibit very similar shapes. Both detrended fluctuation analysis (DFA) and detrending moving average analysis (DMA) show that the 1-min intertrade duration time series of the two equities are strongly correlated. In addition, both multifractal detrended fluctuation analysis (MFDFA) and multifractal detrending moving average analysis (MFDMA) unveil that the 1-min intertrade durations possess multifractal nature. However, the difference between the two singularity spectra of the two equities obtained from the MFDMA is much smaller than that from the MFDFA.Comment: 10 latex pages, 4 figure

Multivariate cumulants in outlier detection for financial data analysis

There are many research papers yielding the financial data models, where returns are tied either to the fundamental analysis or to the individual, often irrational, behaviour of investors. In the second case the bubble followed by the crisis is possible on the market. Such bubble or crisis is reflected by the cross-correlated extreme positive or negative returns of many assets. Such returns are modelled by the copula with the meaningful tail dependencies. The typical model of such cross-correlation provides the t-Student copula. The author demonstrates that the mutual information tied to this copula can be measured by the 4th order multivariate cumulants. Tested on the artificial data, the 4th order multivariate cumulant approach was used successfully for the financial crisis detection. For this end the author introduces the outliers detection algorithm. In addition this algorithm displays the potential application for the crisis prediction, where the cross-correlated extreme events may appear before the crisis in the analogy to the auto-correlated ones measured by the Hurst Exponent

Chaotic price dynamics of agricultural commodities

Traditionally, commodity prices have been analyzed and modeled in the context of linear generating processes. The purpose of this dissertation is to address the adequacy of this work through examination of the critical assumption of independence in the residual process of linearly specified models. As an alternative, a test procedure is developed and utilized to demonstrate the appropriateness of applying generalized conditional heteroscedastic time series models (GARCH) to agricultural commodity prices. In addition, a distinction is made between testing for independence and testing for chaos in commodity prices. The price series of interest derive from the major international agricultural commodity markets, sampled monthly over the period 1960--1994. The results of the present analysis suggest that for bananas, beef, coffee, soybeans, wool and wheat seasonally adjusted growth rates, ARCH-GARCH models account for some of the non-linear dependence in these commodity price series. As an alternative to the ARCH-GARCH models, several neural network models were estimated and in some cases outperformed the ARCH family of models in terms of forecast ability. This further demonstrated the nonlinearity present in these time series. Although, further examination is needed, all prices were found to be non-linearly dependent. It was determined by use of different statistical measures for testing for deterministic chaos that wheat prices may be an example of such behavior. Therefore, their may be something to be gained in terms of short-run forecast accuracy by using semi-parametric modeling approaches as applied to wheat prices

Critical Market Crashes

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.Comment: Latex 89 pages and 38 figures, in press in Physics Report

Hybrid group anomaly detection for sequence data: application to trajectory data analytics

Many research areas depend on group anomaly detection. The use of group anomaly detection can maintain and provide security and privacy to the data involved. This research attempts to solve the deficiency of the existing literature in outlier detection thus a novel hybrid framework to identify group anomaly detection from sequence data is proposed in this paper. It proposes two approaches for efficiently solving this problem: i) Hybrid Data Mining-based algorithm, consists of three main phases: first, the clustering algorithm is applied to derive the micro-clusters. Second, the kNN algorithm is applied to each micro-cluster to calculate the candidates of the group's outliers. Third, a pattern mining framework gets applied to the candidates of the group's outliers as a pruning strategy, to generate the groups of outliers, and ii) a GPU-based approach is presented, which benefits from the massively GPU computing to boost the runtime of the hybrid data mining-based algorithm. Extensive experiments were conducted to show the advantages of different sequence databases of our proposed model. Results clearly show the efficiency of a GPU direction when directly compared to a sequential approach by reaching a speedup of 451. In addition, both approaches outperform the baseline methods for group detection.acceptedVersio