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on Econometric Time Series |
| By: | Takero Ibuki; Shunsuke Higano; Sei Suzuki; Jun-ichi Inoue; Anirban Chakraborti |
| Abstract: | In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective behaviour of markets during a financial crisis through cross-correlations between typical Japanese daily stocks by making use of multi- dimensional scaling. We find that all the two-dimensional points (stocks) shrink into a single small region when a economic crisis takes place. By using the properties of cross-correlations in financial markets especially during a crisis, we next propose a theoretical framework to predict several time-series simultaneously. Our model system is basically described by a variant of the multi-layered Ising model with random fields as non-stationary time series. Hyper-parameters appearing in the probabilistic model are estimated by means of minimizing the 'cumulative error' in the past market history. The justification and validity of our approaches are numerically examined for several empirical data sets. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.1871&r=ets |
| By: | Raffaello Morales; T. Di Matteo; Tomaso Aste |
| Abstract: | We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.2411&r=ets |
| By: | R\'emy Chicheportiche |
| Abstract: | The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I propose two extensions of usual tests when dependence is present in the sample data and when observations have a fat-tailed distribution. The financial content of the thesis starts in Part II. I present there my studies regarding the "cross-sectional" dependences among the time series of daily stock returns, i.e. the instantaneous forces that link several stocks together and make them behave somewhat collectively rather than purely independently. A calibration of a new factor model is presented here, together with a comparison to measurements on real data. Finally, Part III investigates the temporal dependences of single time series, using the same tools and measures of correlation. I propose two contributions to the study of the origin and description of "volatility clustering": one is a generalization of the ARCH-like feedback construction where the returns are self-exciting, and the other one is a more original description of self-dependences in terms of copulas. The latter can be formulated model-free and is not specific to financial time series. In fact, I also show here how concepts like recurrences, records, aftershocks and waiting times, that characterize the dynamics in a time series can be written in the unifying framework of the copula. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.5073&r=ets |
| By: | Andreou, Elena; Werker, Bas J M |
| Abstract: | This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR-GARCH type residuals obtained through QMLE estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to residuals, and find that standard critical values often lead to conservative tests. For this result, we give simple sufficient conditions. Simulations show that our asymptotic approximations work well for a large number of AR-GARCH models and parameter values. We also show that the rank-based tests often, though not always, have superior power properties over the classical tests, even if they are conservative. We thereby provide a useful extension to the econometrician's toolkit. An empirical application illustrates the relevance of these tests to the AR-GARCH models for the weekly stock market return indices of some major and emerging countries. |
| Keywords: | conditional heteroskedasticity; linear and quadratic residual autocorrelation tests; model misspecification test; nonlinear time series; parameter constancy; residual symmetry tests |
| JEL: | C22 C32 C51 C52 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9583&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Shu-Ping Shi (Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple bubble phenomena within the same sample period. To meet this challenge the present paper develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup ADF test of Phillips, Wu and Yu (2011, PWY) and delivers a consistent date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identifies the well-known historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and a related CUSUM dating procedure locate far fewer episodes in the same sample range. |
| Keywords: | Date-stamping strategy, Flexible window, Generalized sup ADF test, Multiple bubbles, Rational bubble, Periodically collapsing bubbles, Sup ADF test |
| JEL: | C15 C22 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1914&r=ets |