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Recent advances in ARCH modelling
 In: Teyssière G. and Kriman A. (eds): Long Memory in Economics
, 2006
"... Econometric modelling of financial data received a broad interest in the last 20 years and the literature on ARCH and related models is vast. Starting with the path breaking works by Engle (1982) and Bollerslev (1986), one of the most popular models became the Generalized AutoRegressive Conditionall ..."
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Econometric modelling of financial data received a broad interest in the last 20 years and the literature on ARCH and related models is vast. Starting with the path breaking works by Engle (1982) and Bollerslev (1986), one of the most popular models became the Generalized AutoRegressive Conditionally
Detection of multiple change–points in multivariate time series
, 2005
"... We consider the multiple change–point problem for multivariate time series, including strongly dependent processes, with an unknown number of change–points. We assume that the covariance structure of the series changes abruptly at some unknown common change–point times. The proposed adaptive method ..."
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We consider the multiple change–point problem for multivariate time series, including strongly dependent processes, with an unknown number of change–points. We assume that the covariance structure of the series changes abruptly at some unknown common change–point times. The proposed adaptive method is able to detect changes in multivariate i.i.d., weakly and strongly dependent series. This adaptive method outperforms the Schwarz criteria, mainly for the case of weakly dependent data. We consider applications to multivariate series of daily stock indices returns and series generated by an artificial financial market. 1
The increment ratio statistic
 Journal of Multivariate Analysis
, 2008
"... We introduce a new statistic written as a sum of certain ratios of second order increments of partial sums process Sn = Pn t=1Xt of observations, which we call the Increment Ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d−integrated (−1/2 < d < 3/2 ..."
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We introduce a new statistic written as a sum of certain ratios of second order increments of partial sums process Sn = Pn t=1Xt of observations, which we call the Increment Ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d−integrated (−1/2 < d < 3/2) behavior of time series Xt, including short memory (d = 0), (stationary) long–memory (0 < d < 1/2) and unit roots (d = 1). If Sn behaves asymptotically as an (integrated) fractional Brownian motion with parameter H = d+1/2, the IR statistic converges to a monotone function Λ(d) of d ∈ (−1/2, 3/2) as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations Xt, we obtain a rate of decay of the bias EIR−Λ(d) and a central limit theorem (N/m)1/2(IR−EIR) → N (0, σ2(d)), in the region −1/2 < d < 5/4. Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d = 0) against stationary long–memory alternatives (0 < d < 1/2) has good size and power properties and is robust against changes in mean, slowly
Adaptive detection of multiple change–points in asset price volatility, dans
 G. Teyssière et A. Kirman (Éditeurs.), Long–Memory in Economics
, 2005
"... Summary. This chapter considers the multiple change–point problem for time series, including strongly dependent processes, with an unknown number of change– points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change–points τ with the optimal level of resolution. ..."
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Summary. This chapter considers the multiple change–point problem for time series, including strongly dependent processes, with an unknown number of change– points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change–points τ with the optimal level of resolution. This optimal segmentation ˆτ is obtained by minimizing a penalized contrast function J(τ, y)+βpen(τ). For a given contrast function J(τ, y) and a given penalty function pen(τ), the adaptive procedure for automatically choosing the penalization parameter β is such that the segmentation ˆτ does not strongly depend on β. This algorithm is applied to the problem of detection of change–points in the volatility of financial time series, and compared with Vostrikova’s (1981) binary segmentation procedure. 1
Wavelet analysis of nonlinear long range dependent processes. Applications to financial time series
 In Long Memory in Econometrics, G. Teyssière and
, 2007
"... Summary. We present and study the performance of the semiparametric wavelet estimator for the long–memory parameter devised by Veitch and Abry (1999). We compare this estimator with two semiparametric estimators in the spectral domain, the local Whittle (LW) estimator developed by Robinson (1995a) a ..."
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Summary. We present and study the performance of the semiparametric wavelet estimator for the long–memory parameter devised by Veitch and Abry (1999). We compare this estimator with two semiparametric estimators in the spectral domain, the local Whittle (LW) estimator developed by Robinson (1995a) and the “log– periodogram ” (LP) estimator by Geweke and Porter–Hudak (1983). The wavelet estimator performs well for a wide range of nonlinear long–memory processes in the conditional mean and the conditional variance, and is reliable for discriminating between change–points and long–range dependence in volatility. We also address the issue of selection of the range of octaves used as regressors by the weighted least squares estimator. We will see that using the feasible optimal bandwidths for either the LW and LP estimators, respectively studied by Henry and Robinson (1996) and Henry (2001), is a useful rule of thumb for selecting the lowest octave. We apply the wavelet estimator to volatility series of high frequency (intra–day) Foreign Exchange (FX) rates, and to the volatility and volume of stocks of the Dow Jones Industrial Average Index. 1
Testing for bubbles and changepoints
, 2002
"... A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding “wrong ” beliefs and bubbl ..."
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A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding “wrong ” beliefs and bubble–like phenomena in the asset price occur. We consider tests for detecting bubbles in the conditional mean and multiple changes in the conditional variance of the process. A wavelet analysis of the series generated by our models shows that the strong persistence in the volatility is likely to be the outcome of a mix of changes in regimes and a moderate level of long–range dependence. These results are consistent with what has been observed by Kokoszka and Teyssière (2002) and Teyssière (2003).
Testing for structural breaks in variance with additive outliers and measurement errors. Working Paper, Universidad de Alicante
, 2006
"... participants at the Humboldt University of Berlin for comments and suggestions. Any remaining error is our own. Financial support from POCTI / FEDER (grant ref. POCTI/ECO/49266/2002) and the SEJ200509372/ECON project is gratefully acknowledged. ..."
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participants at the Humboldt University of Berlin for comments and suggestions. Any remaining error is our own. Financial support from POCTI / FEDER (grant ref. POCTI/ECO/49266/2002) and the SEJ200509372/ECON project is gratefully acknowledged.
Interaction Models for Common LongRange Dependence in Asset Prices Volatility
"... Abstract. We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: nonlinearities in levels and common degree of longmemory in the volatilities and covolatilities of multivariate time series. For these models, longrange ..."
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Abstract. We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: nonlinearities in levels and common degree of longmemory in the volatilities and covolatilities of multivariate time series. For these models, longrange dependence in asset price volatility is the consequence of swings in opinions and herding behavior of market participants, which generate switches in the heteroskedastic structure of asset prices. Thus, the observed longmemory in asset prices volatility might be the outcome of a changepoint in the conditional variance process, a conclusion supported by a wavelet anaysis of the volatility series. This explains why volatility processes share only the properties of the second moments of longmemory processes, but not the properties of the first moments. 1 LongRange Dependence in Finance Asset prices time series are characterized by several features: leptokurtic distribution, nonlinear variations, volatility clustering, unit roots in the conditional mean, and strong dependence in the volatility. These empirical features have been documented in [38,39], [48], [9], [22,23], [3] among others.
INTERACTION MODELS FOR COMMON LONG–RANGE DEPENDENCE IN ASSET PRICE VOLATILITIES
, 2003
"... We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: nonlinearities in levels and common degree of longmemory in the volatilities and covolatilities of multivariate time series. For these models, longrange dependenc ..."
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We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: nonlinearities in levels and common degree of longmemory in the volatilities and covolatilities of multivariate time series. For these models, longrange dependence in asset price volatility is the consequence of swings in opinions and herding behavior of market participants, which generate switches in the heteroskedastic structure of asset prices. Thus, the observed longmemory in asset prices volatility might be the outcome of a change–point in the conditional variance process, a conclusion supported by a wavelet analysis of the volatility series. This explains why volatility processes share only the properties of the second moments of longmemory processes, but not the properties of the first moments.