Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola, Alessandra; Francq, Christian

doi:10.1002/9780470748916.ch10

Cited by 13 publications

(13 citation statements)

References 150 publications

(190 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Considering mainly this approach, several authors have established constraints on the coefficients of different non-linear models under which a stationary solution is reached. In particular, results by Amendola and Francq (2009) for EXPAR(1) models, Pham and Tran (1981) for bilinear models, An and Huang (1996) for non-linear autoregressive models, Chen et al (2011) for GJR-GARCH models, and Fan and Yao ( 2005) for ARCH, GARCH and EGARCH models, ensure stationarity for the specific models forming our simulation scenarios.…”

Section: Clustering Of Conditional Heteroskedastic Modelsmentioning

confidence: 71%

Robust fuzzy clustering based on quantile autocovariances

2018

View full text Add to dashboard Cite

Robustness to the presence of outliers in time series clustering is addressed. Assuming that the clustering principle is to group realizations of series generated from similar dependence structures, three robust versions of a fuzzy C-medoids model based on comparing sample quantile autocovariances are proposed by considering, respectively, the so-called metric, noise, and trimmed approaches. Each method achieves its robustness against outliers in different manner. The metric approach considers a suitable transformation of the distance aimed at smoothing the effect of the outliers, the noise approach brings together the outliers into a separated artificial cluster, and the trimmed approach removes a fraction of the time series. All the proposed approaches take advantage of the high capability of the quantile autocovariances to discriminate between independent realizations from a broad range of stationary processes, including linear, non-linear and conditional heteroskedastic models. An extensive simulation study involving scenarios with different generating models and contaminated with outliers is performed. Robustness against (i) outliers generated from different generating patterns, and (ii) outliers characterized by isolated, temporary or persistent level changes is evaluated. The influence of the input parameters required by the different algorithms is analyzed. Regardless of the considered models, the results show that the proposed robust procedures are able to neutralize the effect of the anomalous series preserving the true clustering structure, and fairly outperform other robust algorithms based on alternative metrics. Two applications to financial data sets permit to illustrate the usefulness of the proposed models.

show abstract

Section: Clustering Of Conditional Heteroskedastic Modelsmentioning

confidence: 71%

Robust fuzzy clustering based on quantile autocovariances

2018

View full text Add to dashboard Cite

show abstract

“…However note that the assumed heteroscedasticity is only conditional while the unconditional variance is still constant in this case. This kind of situation can arise if we (spuriously) assume that the innovations process is driven by a GARCH model or any other model displaying nonlinearities such as models driven by hidden Markov chains or All-Pass models (see Amendola and Francq (2009) (1997)). Denote byÂ m,1 , .…”

Section: Tests Based On the Assumption Of Constant Error Variancementioning

confidence: 99%

Testing Instantaneous Causality in Presence of Nonconstant Unconditional Covariance

Gianetto

Raïssi

2015

Journal of Business & Economic Statistics

View full text Add to dashboard Cite

This article investigates the problem of testing instantaneous causality between vector autoregressive (VAR) variables with time-varying unconditional covariance. It is underlined that the standard test does not control the Type I errors, while the tests with White and heteroscedastic autocorrelation consistent (HAC) corrections can suffer from a severe loss of power when the covariance is not constant. Consequently, we propose a modified test based on a bootstrap procedure. We illustrate the relevance of the modified test through a simulation study. The tests considered in this article are also compared by investigating the instantaneous causality relations between U.S. macroeconomic variables.

show abstract

“…When the usual stationary assumption is met, it is well known that, in general, considering stochastic volatility for the error process entails second-order dynamics, see, for example, Amendola and Francq (2009). This explains why autocorrelations of the squared residuals are commonly used to detect nonlinear effects.…”

Section: Extending the Scopementioning

confidence: 99%

Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

Patilea¹,

Raïssi²

2014

Journal of the American Statistical Association

View full text Add to dashboard Cite

This article considers the volatility modeling for autoregressive univariate time series. A benchmark approach is the stationary autoregressive conditional heteroscedasticity (ARCH) model of Engle. Motivated by real data evidence, processes with nonconstant unconditional variance and ARCH effects have been recently introduced. We take into account this type of nonstationarity in variance and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking the presence of such second-order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. The failure of these standard tests with time-varying unconditional variance is highlighted. The theoretical results are illustrated by means of simulated and real data. Supplementary materials for this article are available online.

show abstract

Concepts of and tools for Nonlinear Time‐Series Modelling

Cited by 13 publications

References 150 publications

Robust fuzzy clustering based on quantile autocovariances

Robust fuzzy clustering based on quantile autocovariances

Testing Instantaneous Causality in Presence of Nonconstant Unconditional Covariance

Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

Contact Info

Product

Resources

About