Jens-Peter Kreiss

Handbook of financial time series

Recent Developments in GARCH Modeling.- An Introduction to Univariate GARCH Models.- Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)#x2013 Processes.- ARCH(#x221E ) Models and Long Memory Properties.- A Tour in the Asymptotic Theory of GARCH Estimation.- Practical Issues in the Analysis of Univariate GARCH Models.- Semiparametric and Nonparametric ARCH Modeling.- Varying Coefficient GARCH Models.- Extreme Value Theory for GARCH Processes.- Multivariate GARCH Models.- Recent Developments in Stochastic Volatility Modeling.- Stochastic Volatility: Origins and Overview.- Probabilistic Properties of Stochastic Volatility Models.- Moment#x2013 Based Estimation of Stochastic Volatility Models.- Parameter Estimation and Practical Aspects of Modeling Stochastic Volatility.- Stochastic Volatility Models with Long Memory.- Extremes of Stochastic Volatility Models.- Multivariate Stochastic Volatility.- Topics in Continuous Time Processes.- An Overview of Asset-Price Models.- Ornstein-Uhlenbeck Processes and Extensions.- Jump-Type Levy Processes.- Levy-Driven Continuous-Time ARMA Processes.- Continuous Time Approximations to GARCH and Stochastic Volatility Models.- Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance.- Parametric Inference for Discretely Sampled Stochastic Differential Equations.- Realized Volatility.- Estimating Volatility in the Presence of Market Microstructure Noise: A Review of the Theory and Practical Considerations.- Option Pricing.- An Overview of Interest Rate Theory.- Extremes of Continuous-Time Processes..- Topics in Cointegration and Unit Roots.- Cointegration: Overview and Development.- Time Series with Roots on or Near the Unit Circle.- Fractional Cointegration.- Special Topics - Risk.- Different Kinds of Risk.- Value-at-Risk Models.- Copula-Based Models for Financial Time Series.- Credit Risk Modeling.- Special Topics - Time Series Methods.- Evaluating Volatility and Correlation Forecasts.- Structural Breaks in Financial Time Series.- An Introduction to Regime Switching Time Series Models.- Model Selection.- Nonparametric Modeling in Financial Time Series.- Modelling Financial High Frequency Data Using Point Processes.- Special Topics - Simulation Based Methods.- Resampling and Subsampling for Financial Time Series.- Markov Chain Monte Carlo.- Particle Filtering.

On the range of validity of the autoregressive sieve bootstrap

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear.

Bootstrap procedures for AR (∞) — processes

In this paper we will deal with an application of Efron’s 1979 bootstrap to stationary stochastic processes in discrete time. In many applications it is assumed that these processes are of autoregressive or more generally of autoregressive moving average type, i.e. the underlying stationary process X = (X t: t ∈ Z = {0, ±1, ±2,…}) is assumed to satisfy the following stochastic difference equation

The multiple hybrid bootstrap - Resampling multivariate linear processes

{X_t} = \sum\limits_{{v = 1}}^p {{a_v}{X_{{t - v}}} + {\varepsilon_t} + \sum\limits_{{\mu = 1}}^q {{b_{\mu }}{\varepsilon_{{t - \mu }}},\;t \in Z} }

Local asymptotic normality for autoregression with infinite order

Here e = (e t: t ∈ Z) denotes a white noise, that is a sequence of uncorrelated, zero mean random variables with finite variance σ 2 .

The Hybrid Wild Bootstrap for Time Series

In this paper we consider general first order autoregression, including the stationary, the explosive and the unstable cases. It is well-known in the literature that the usual bootstrap method for the least squares parameter estimator is asymptotically consistent for the stationary and the explosive cases, but does not work in the unstable case, where the parameter value is equal to +1 and or -1. We propose a modified bootstrap method, which turns out to be asymptotically consistent in all possible situations. Furthermore, we derive tests for stationarity and nonstationarity for first order autoregressions. The bootstrap method is used to obtain critical values. Some simulation results are also enclosed.

On the Vector Autoregressive Sieve Bootstrap

The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) [18]. Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the complete covariance structure of the underlying time series. We extend the AAPB in two directions. Our procedure explicitly leads to bootstrap observations in the time domain and it is applicable to multivariate linear processes, but agrees exactly with the AAPB in the univariate case, when applied to functionals of the periodogram. The asymptotic theory developed shows validity of the multiple hybrid bootstrap procedure for the sample mean, kernel spectral density estimates and, with less generality, for autocovariances.

Nonparametric Modeling in Financial Time Series

AbstractWe consider the empirical distribution functionFn of the innovations of a linear and stationary stochastic process, which are assumed to be independent and identically distributed random variables. If we denote by