High-dimensional volatility matrix estimation via wavelets and thresholding

@article{Fryzlewicz2013HighdimensionalVM,
  title={High-dimensional volatility matrix estimation via wavelets and thresholding},
  author={Piotr Fryzlewicz},
  journal={Biometrika},
  year={2013},
  volume={100},
  pages={921-938}
}
We propose a locally stationary linear model for the evolution of high-dimensional financial returns, where the time-varying volatility matrix is modelled as a piecewise constant function of time. We introduce a new wavelet-based technique for estimating the volatility matrix, which 10 combines four ingredients: a Haar wavelet decomposition, variance stabilization of the Haar coefficients via the Fisz transform prior to thresholding, a bias correction, and extra time-domain thresholding, soft… 

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References

SHOWING 1-10 OF 38 REFERENCES

A Haar-Fisz technique for locally stationary volatility estimation

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations,

VAST VOLATILITY MATRIX ESTIMATION FOR HIGH-FREQUENCY FINANCIAL DATA

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate

Data-driven wavelet-Fisz methodology for nonparametric function estimation

TLDR
This work proposes a wavelet-based technique for the nonparametric estimation of functions contaminated with noise whose mean and variance are linked via a possibly unknown variance function, and establishes an exponential inequality for the Nadaraya-Watson variance function estimator.

Time Inhomogeneous Multiple Volatility Modeling

Price variations observed at speculative markets exhibit positive autocorrelation and cross correlation among a set of assets, stock market indices, exchange rates etc. A particular problem in

NORMALISED LEAST-SQUARES ESTIMATION IN TIME-VARYING ARCH MODELS: TECHNICAL REPORT

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial

Modelling and forecasting financial log-returns as locally stationary wavelet processes

In this article, we model financial log-return series in the Locally Stationary Wavelet (LSW) framework proposed by Nason et al. (2000). We slightly alter the LSW set-up to include time- modulated

LOCALLY STATIONARY FACTOR MODELS: IDENTIFICATION AND NONPARAMETRIC ESTIMATION

In this paper we propose a new approximate factor model for large cross-section and time dimensions. Factor loadings are assumed to be smooth functions of time, which allows considering the model as

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

Generalized Thresholding of Large Covariance Matrices

TLDR
It is shown that generalized thresholding has the “sparsistency” property, meaning it estimates true zeros as zeros with probability tending to 1, and, under an additional mild condition, is sign consistent for nonzero elements.

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