The BDS test of independence

2021 ◽  
Vol 21 (2) ◽  
pp. 279-294
Author(s):  
Christopher F. Baum ◽  
Stan Hurn ◽  
Kenneth Lindsay
Keyword(s):  
Time Series ◽  
Paper Test ◽  
Test Of Independence ◽  
Working Paper ◽  
Bds Test

In this article, we describe and implement the Brock, Dechert, and Scheinkman (1987, Working paper) test of independence of the elements of a time series.

Is there Chaos on the German Labor Market? / Ist der deutsche Arbeitsmarkt chaotisch?

1999 ◽  
Vol 218 (5-6) ◽  
Author(s):  
Michael Neugart
Keyword(s):  
Time Series ◽  
Labor Market ◽  
Chaotic Dynamics ◽  
Alternative Hypothesis ◽  
The Past ◽  
Labor Market Dynamics ◽  
Linear And Nonlinear ◽  
Bds Test ◽  
Linear And Nonlinear Systems

SummaryEvidence on the role of chaotic and nonlinear dynamics on labor markets is mixed. It is unclear whether nonlinear relationships are responsible for the dynamic patterns observed in Europe during the past decades. In this paper, we test German labor market data for the null hypothesis of an i.i.d. process with the BDS test. As several processes including chaotic, nonlinear deterministic, and stochastic linear and nonlinear systems are nested within the alternative hypothesis, time series are whitened with linear and nonlinear filters. Lyapunov exponents and correlation dimensions are applied to the residuals of the filtered time series to test for chaotic dynamics. There seems to be a nonlinear deterministic core to German labor market dynamics. Chaos does not occur.

Independence in time series: another look at the BDS test

1994 ◽  
Vol 348 (1688) ◽  
pp. 383-395 ◽  
Keyword(s):  
Time Series ◽  
Ad Hoc ◽  
Null Distribution ◽  
Spatial Arrangement ◽  
Testing Procedure ◽  
Correlation Integral ◽  
Geometrical Properties ◽  
The Central Limit Theorem ◽  
Original Time ◽  
Bds Test

This paper examines a statistical method derived from chaos theory. The correlation integral was proposed over a decade ago as a way of detecting chaos in a possibly partial realization of a dynamical system, because it depends on the spatial arrangement of the reconstructed attractor of the system. We exploit geometrical properties of an embedded time series to establish a test of independence in the original time series. Earlier efforts here have used the Central Limit Theorem to obtain normality as the null distribution; however, the testing procedure was, to an extent, ad hoc . By making moderately weak assumptions about the marginal distribution of the given series, we obtain a Poisson law for the correlation integral under the null hypothesis of independence, and use nonparametric methods to specify the test precisely. We compare the size and power of the present test with its predecessor and with other non-parametric tests for serial dependence.

Working paper test

2020 ◽  
Author(s):  
Doe Daisy
Keyword(s):  
Paper Test ◽  
Working Paper

Study on the nonlinear and chaotic behavior of exchange traded funds listed in Hong Kong Stock Exchanges

2020 ◽  
Author(s):  
Patrick Kuok Kun Chu
Keyword(s):  
Time Series ◽  
Hong Kong ◽  
Correlation Dimension ◽  
Model Building ◽  
Chaotic Behavior ◽  
Return Time ◽  
Stock Exchanges ◽  
Garch Models ◽  
Exchange Traded Funds ◽  
Bds Test

This study examines the nonlinearity and chaotic behavior of the time series of returns of two exchange traded funds (ETFs) listed in Hong Kong Stock Exchanges, namely Hong Kong Tracker Fund (HKTF) and iShares FTSE A50 (ISFT), and the adequacy of autoregressive-generalized autoregressive conditional heteroskedasticity (AR-GARCH) models to capture nonlinearity. A set of nonlinearity tests consistently indicates the presence of nonlinearity in both return time series and the Brock–Dechert–Scheinkman (BDS) test of nonlinearity on AR-GARCH residuals, and the inability of AR-GARCH models to capture the nonlinearity in the return series at different stages of the model-building process. Testing for chaos is a rather delicate part in this study and is done by estimating the correlation dimension for both ETFs’ return series. The correlation dimension saturates at a finite value, and the saturation indicates the presence of chaos in two ETFs considered for this study.

NONLINEAR TIME-SERIES ANALYSIS OF THE GREEK EXCHANGE-RATE MARKET

2000 ◽  
Vol 10 (07) ◽  
pp. 1729-1758 ◽  
Author(s):  
A. S. ANDREOU ◽  
G. PAVLIDES ◽  
A. KARYTINOS
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
Deterministic Chaos ◽  
Data Series ◽  
Nonlinear Dynamical ◽  
Series Analysis ◽  
Low Dimensional ◽  
Bds Test

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.

Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series

1997 ◽  
Vol 13 (6) ◽  
pp. 818-848 ◽  
Author(s):  
Timothy J. Vogelsang
Keyword(s):  
Time Series ◽  
Asymptotic Theory ◽  
Test Statistics ◽  
Asymptotic Results ◽  
Paper Test ◽  
Trend Function ◽  
Univariate Time Series ◽  
Macroeconomic Time Series ◽  
The Mean ◽  
Dynamic Time

In this paper, test statistics for detecting a break at an unknown date in the trend function of a dynamic univariate time series are proposed. The tests are based on the mean and exponential statistics of Andrews and Ploberger (1994, Econometrica 62, 1383–1414) and the supremum statistic of Andrews (1993, Econometrica 61, 821–856). Their results are extended to allow trending and unit root regressors. Asymptotic results are derived for both I(0) and I(1) errors. When the errors are highly persistent and it is not known which asymptotic theory (I(0) or I(1)) provides a better approximation, a conservative approach based on nearly integrated asymptotics is provided. Power of the mean statistic is shown to be nonmonotonic with respect to the break magnitude and is dominated by the exponential and supremum statistics. Versions of the tests applicable to first differences of the data are also proposed. The tests are applied to some macroeconomic time series, and the null hypothesis of a stable trend function is rejected in many cases.

scholarly journals Forecasting time series with multivariate copulas

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Clarence Simard ◽  
Bruno Rémillard
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Financial Data ◽  
Practical Implementation ◽  
Estimation Errors ◽  
Marginal Distributions ◽  
Test Of Independence ◽  
Multivariate Method ◽  
Forecasting Method ◽  
The Impact

AbstractIn this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.

scholarly journals Dinámica no lineal estocástica del mercado cambiario mexicano

2017 ◽  
Vol 8 (16) ◽  
Author(s):  
Klender Aimer Cortez Alejandro, ◽  
Martha del Pilar Rodríguez García ◽  
Adrián Wong Boren
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Exchange Rate Volatility ◽  
Linear Dynamic ◽  
Starting Point ◽  
Non Linear ◽  
Show Evidence ◽  
The Garch Model ◽  
Time Serie ◽  
Bds Test

Keywords: BDS test, bootstrapping, exchange rate, GARCH, time series, volatilityAbstract: This paper presents an analysis of the exchange rate volatility in the Mexican market during the flotation regime adopted since December 1994. The time series under study are the bid and ask interbank daily exchange rates from 1995 to 2010. As a starting point we begin analyzing the temporary structure of the variance, and later we look for a time serie model that best fits the data. In order to detect the non-linear dynamic of the time series, we use the BDS test. The results show evidence in favor of the caractertización of the exchange change pesos/dollar fluctuations with non-linear stochastic models, particularly the GARCH model. In order to validate the model we propose to use the bootstrapping technique together with the BDS test.Palabras clave: GARCH, muestreo autodocimante, prueba BDS, series temporales, tipo de cambio, volatilidadResumen: En este trabajo se presenta un análisis de la volatilidad del mercado cambiario en México durante el periodo de flotación adoptado a partir de diciembre de 1994. Las series temporales de estudio son el tipo de cambio interbancario de 1995 a 2010 en su cotización diaria a la compra y a la venta. Como punto de partida se analiza la estructura temporal de la varianza de los datos y posteriormente se busca un modelo de series temporales que se ajuste mejor a las observaciones. Para detectar el carácter no lineal de la serie se utiliza la metodología BDS. Los resultados muestran evidencia a favor de la caractertización de la variación del tipo de cambio pesos/dólar con la utilización de modelos estocásticos no lineales, en particular, el modelo GARCH. Para validar el modelo se propone utilizar la técnica de bootstrapping sobre los residuos en conjunto con la técnica BDS.

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