# 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…

## Figures from this paper

## 13 Citations

### Large covariance estimation by thresholding principal orthogonal complements

- Computer ScienceJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2013

It is shown that the effect of estimating the unknown factors vanishes as the dimensionality increases, and the principal orthogonal complement thresholding method ‘POET’ is introduced to explore such an approximate factor structure with sparsity.

### Risks of Large Portfolios

- Economics
- 2013

Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the…

### A Multiple Testing Approach to the Regularisation of Large Sample Correlation Matrices

- MathematicsJournal of Econometrics
- 2019

### Approaches to High-Dimensional Covariance and Precision Matrix Estimations

- Economics, Computer Science
- 2016

The factor pricing model is explained, which is one of the most fundamental results in finance and elucidates estimating risks of large portfolios and large panel test of factor pricing models, and the recent developments of efficient estimations in panel data models.

### Estimation of covariance, correlation and precision matrices for high-dimensional data

- Mathematics
- 2016

The thesis concerns estimating large correlation and covariance matrices and their inverses. Two new methods are proposed. First, tilting-based methods are proposed to estimate the precision matrix…

### NOVELIST estimator of large correlation and covariance matrices and their inverses

- MathematicsTEST
- 2018

We propose a “NOVEL Integration of the Sample and Thresholded covariance” (NOVELIST) estimator to estimate the large covariance (correlation) and precision matrix. NOVELIST estimator performs…

### Robust Inference of Risks of Large Portfolios.

- Economics, Computer ScienceJournal of econometrics
- 2016

### Consistent estimation of breakpoints in time series, with application to wavelet analysis of Citigroup returns

- Computer Science
- 2014

A novel feature of this paper is that it is able to identify common breakpoints for multiple time series, even when they collect data at different frequencies, and facilitates the reconciliation of breakpoint outputs from the two standard wavelet filters.

### Robust Inference of Risks of Large Portfolios

- Economics, Computer Science
- 2015

A bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios that exploits rank-based and quantile-based estimators and can be viewed as a robust extension of the H- CLUB method.

## References

SHOWING 1-10 OF 38 REFERENCES

### A Haar-Fisz technique for locally stationary volatility estimation

- Economics, Computer Science
- 2006

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

- Economics, Mathematics
- 2010

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

- Mathematics
- 2007

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

- Economics
- 2000

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

- Mathematics
- 2007

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

- Mathematics
- 2005

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

- Mathematics, EconomicsEconometric Theory
- 2011

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

- Mathematics
- 1982

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

- Computer Science
- 2009

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

- Economics, Mathematics
- 2009

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…