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Author: Herman Peter Boswijk Publisher: ISBN: Category : Languages : en Pages :
Book Description
To what extent can the bootstrap be applied to conditional mean models | such as regression or time series models | when the volatility of the innovations is random and possibly non-stationary? In fact, the volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated exogenous volatility processes as well as near-integrated GARCH processes, where the conditional variance has a diffusion limit; a further important example is the case where volatility exhibits infrequent jumps. This paper fills this gap in the literature by developing conditions for bootstrap validity in time series and regression models with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proofs of bootstrap consistency, based on the notion of weak convergence in probability of the bootstrap statistic, fail to deliver the required validity results. Instead, we use the concept of 'weak convergence in distribution' to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change using CUSUM-type functionals, and testing for a unit root in autoregressive models. Importantly, we show that sufficient conditions for conditional wild bootstrap validity include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results of the paper are illustrated using Monte Carlo simulations, which indicate that a wild bootstrap approach leads to size control even in small samples.
Author: Herman Peter Boswijk Publisher: ISBN: Category : Languages : en Pages :
Book Description
To what extent can the bootstrap be applied to conditional mean models | such as regression or time series models | when the volatility of the innovations is random and possibly non-stationary? In fact, the volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated exogenous volatility processes as well as near-integrated GARCH processes, where the conditional variance has a diffusion limit; a further important example is the case where volatility exhibits infrequent jumps. This paper fills this gap in the literature by developing conditions for bootstrap validity in time series and regression models with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proofs of bootstrap consistency, based on the notion of weak convergence in probability of the bootstrap statistic, fail to deliver the required validity results. Instead, we use the concept of 'weak convergence in distribution' to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change using CUSUM-type functionals, and testing for a unit root in autoregressive models. Importantly, we show that sufficient conditions for conditional wild bootstrap validity include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results of the paper are illustrated using Monte Carlo simulations, which indicate that a wild bootstrap approach leads to size control even in small samples.
Author: Giuseppe Cavaliere Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The 'fixed regressor' - or 'fixed design' - bootstrap is usually considered in the context of classic regression, or conditional mean (autoregressive) models, see for example, Gonçalves and Kilian, 2004). We consider here inference for a general class of (non)linear ARCH models of order , based on a 'Fixed Volatility' bootstrap. In the Fixed Volatility bootstrap, the lagged variables in the conditional variance equation are kept fixed at their values in the original series, while the bootstrap innovations are, as is standard, resampled with replacement from the estimated residuals based on quasi maximum likelihood estimation. We derive a full asymptotic theory to establish validity for the Fixed Volatility bootstrap applied to Wald statistics for general restrictions on the parameters. A key feature of the Fixed Volatility bootstrap is that the bootstrap sample, conditional on the original data, is an independent sequence. Inspection of the proof of bootstrap validity reveals that such conditional independence simplifies the asymptotic analysis considerably. In contrast to other bootstrap methods, one does not have to take into account the conditional dependence structure of the bootstrap process itself. We also investigate the finite sample performance of the Fixed Volatility bootstrap by means of a small scale Monte Carlo experiment. We find evidence that for small sample sizes, the Fixed Volatility bootstrap test is superior to the asymptotic test, and to the recursive bootstrap-based test. For large samples, both bootstrap schemes and the asymptotic test share properties, as expected from the asymptotic theory. Its appealing theoretical properties, together with its good finite sample performance, suggest that the proposed Fixed Volatility bootstrap may be an important tool for the analysis of the bootstrap in more general volatility models.
Author: John Hunter Publisher: Springer ISBN: 113731303X Category : Business & Economics Languages : en Pages : 508
Book Description
This book examines conventional time series in the context of stationary data prior to a discussion of cointegration, with a focus on multivariate models. The authors provide a detailed and extensive study of impulse responses and forecasting in the stationary and non-stationary context, considering small sample correction, volatility and the impact of different orders of integration. Models with expectations are considered along with alternate methods such as Singular Spectrum Analysis (SSA), the Kalman Filter and Structural Time Series, all in relation to cointegration. Using single equations methods to develop topics, and as examples of the notion of cointegration, Burke, Hunter, and Canepa provide direction and guidance to the now vast literature facing students and graduate economists.
Author: Jaya P. N. Bishwal Publisher: Springer Nature ISBN: 3031038614 Category : Mathematics Languages : en Pages : 634
Book Description
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Author: Kenichi Shimizu Publisher: Vieweg+Teubner Verlag ISBN: 9783834809926 Category : Mathematics Languages : en Pages : 148
Book Description
Im Jahre 1979 hat Bradley Efron mit seiner Arbeit Bootstrap Methods: Another Look at the Jackknife das Tor zu einem in den vergangenen 30 Jahren intensiv bearbeiteten Forschungsgebiet aufgestoßen. Die simulationsbasierte Methode des Bootstraps hat sich in den verschiedensten Bereichen als ein außerordentlich - ?zientes Werkzeug zur Approximation der stochastischen Fluktuation eines Sch- zers um die zu schätzende Größe erwiesen. Präzise Kenntnis dieser stochastischen Fluktuation ist zum Beispiel notwendig, um Kon'denzbereiche für Schätzer an- geben, die die unbekannte interessierende Größe mit einer vorgegebenen Wa- scheinlichkeit von, sagen wir, 95 oder 99% enthalten. In vielen Fällen und bei korrekter Anwendung ist das Bootstrapverfahren dabei der konkurrierenden und auf der Approximation durch eine Normalverteilung basierenden Methode üb- legen. Die Anzahl der Publikationen im Bereich des Bootstraps ist seit 1979 in einem atemberaubenden Tempo angestiegen. Die wesentliche und im Grunde e- fache Idee des Bootstraps ist die Erzeugung vieler (Pseudo-) Datensätze, die von ihrer wesentlichen stochastischen Struktur dem Ausgangsdatensatz möglichst ä- lich sind. Die aktuellen Forschungsinteressen im Umfeld des Bootstraps bewegen sich zu einem großen Teil im Bereich der stochastischen Prozesse. Hier stellt sich die zusätzliche Herausforderung, bei der Erzeugung die Abhängigkeitsstruktur der Ausgangsdaten adäquat zu imitieren. Dabei ist eine präzise Analyse der zugrunde liegenden Situation notwendig, um beurteilen zu können, welche Abhängigkei- aspekte für das Verhalten der Schätzer wesentlich sind und welche nicht, um a- reichend komplexe, aber eben auch möglichst einfache Resamplingvorschläge für die Erzeugung der Bootstrapdaten entwickeln zu können.
Author: Philippe Barbe Publisher: Springer Science & Business Media ISBN: 1461225329 Category : Mathematics Languages : en Pages : 236
Book Description
INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.
Author: Peter Reinhard Hansen Publisher: Oxford University Press, USA ISBN: 9780198776086 Category : Business & Economics Languages : en Pages : 178
Book Description
Aimed at graduates and researchers in economics and econometrics, this is a comprehesive exposition of Soren Johansen's remarkable contribution to the theory of cointegration analysis.
Author: Rob J Hyndman Publisher: OTexts ISBN: 0987507117 Category : Business & Economics Languages : en Pages : 380
Book Description
Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.
Author: Herman Peter Boswijk
Author: Herman Peter Boswijk
Author: Giuseppe Cavaliere
Author: John Hunter
Author: Jaya P. N. Bishwal
Author: Kenichi Shimizu
Author: Philippe Barbe
Author: W. J. Fitzgerald
Author: Peter Reinhard Hansen
Author: Rob J Hyndman
Author: