• Corpus ID: 10508

NONLINEARITY OF ARCH AND STOCHASTIC VOLATILITY MODELS AND BARTLETT'S FORMULA

@inproceedings{Kokoszka2011NONLINEARITYOA,
  title={NONLINEARITY OF ARCH AND STOCHASTIC VOLATILITY MODELS AND BARTLETT'S FORMULA},
  author={Piotr Kokoszka and Dimitris Nicolas Politis},
  year={2011}
}
We review some notions of linearity of time series and show that ARCH or stochastic volatility (SV) processes are not only non-linear: they are not even weakly linear, i.e., they do not even have a martingale representation. Consequently, the use of Bartlett's formula is unwarranted in the context of data typically modeled as ARCH or SV processes such as financial returns. More surprisingly, we show that even the squares of an ARCH or SV process are not weakly linear. Finally, we discuss an… 

Tables from this paper

Local Mispricing and Microstructural Noise: A Parametric Perspective
We extend the classic ''martingale-plus-noise'' model for high-frequency returns to accommodate an error correction mechanism and endogenous pricing errors. It is motivated by (i) novel empirical
Model-Based Prediction in Autoregression
TLDR
This work develops a coherent methodology for the construction of bootstrap prediction intervals for time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and presents detailed algorithms for these different models.
Asymptotics for Autocovariances and Integrated Periodograms for Linear Processes Observed at Lower Frequencies
One of the most frequently used class of processes in time series analysis is the one of linear processes. For many statistical quantities, among them sample autocovariances and sample
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,
Predictive Inference for Locally Stationary Time Series
TLDR
It is shown how Model-free Prediction can be applied to handle time series that are only locally stationary, i.e., they can be modeled as stationary only over short time-windows.
Model-Free Inference for Markov Processes
TLDR
The scope of the paper is expanded by assuming only that {Y t } is a Markov process of order p ≥ 1 without insisting that any specific autoregressive equation is satisfied.
Robust Tests for White Noise and Cross-Correlation
Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for
Robust Tests for White Noise and Cross-Correlation
Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for
...
1
2
3
...

References

SHOWING 1-10 OF 45 REFERENCES
Point process convergence of stochastic volatility processes with application to sample autocorrelation
TLDR
The aim of the paper is to show how point process techniques can be used to derive the asymptotic behavior of the sample autocorrelation function of this process with heavy-tailed marginal distributions.
Bartlett's formula for a general class of nonlinear processes
Abstract.  A Bartlett‐type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are
On Bartlett’s Formula for Non‐linear Processes
Bartlett’s formula is widely used in time series analysis to provide estimates of the asymptotic covariance between sample autocovariances. However, it is derived under precise assumptions (namely
MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS
This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity,
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional
Inference for Autocorrelations under Weak Assumptions
Abstract In this article we consider the large-sample behavior of estimates of autocorrelations and autoregressive moving average (ARMA) coefficients, as well as their distributions, under weak
The sample autocorrelations of heavy-tailed processes with applications to ARCH
We study the sample ACVF and ACF of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying. This includes linear and
STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a
Generalized Autoregressive Conditional Heteroskedasticity in Credit Risk Measurement
This paper presents a modified model for Chinese credit risk management. The model is based on KMV model with consideration of Generalized Autoregressive Conditional Heteroskedasticit (GARCH). Data
Estimating the Variances of Autocorrelations Calculated from Financial Time Series
SUMMARY Autocorrelation coefficients calculated from n observations are known to have variances approxi- mately equal to 1/n, for a series of independent and identically distributed variables. The
...
1
2
3
4
5
...