Regression with Nonstationary Volatility

Bruce E. Hansen

90 citations0/0 files storedEconometrica

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Financial Risk and Volatility Modeling Advanced Statistical Methods and Models Statistical and numerical algorithms

Abstract

A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic volatility processes with autoregressive roots that are local to unity. The author finds conditions under which the least squares estimates are consistent and asymptotically normal. A simple adaptive estimator is proposed which achieves the same asymptotic distribution as the generalized least squares estimator without requiring parameter assumptions for the stochastic volatility process. Copyright 1995 by The Econometric Society.

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References

1987The Pricing of Options on Assets with Stochastic Volatilities 1990Alternative models for conditional stock volatility 1991Optimal Inference in Cointegrated Systems 1990ARCH models as diffusion approximations 1987Option values under stochastic volatility: Theory and empirical estimates 1988Statistical Inference in Regressions with Integrated Processes: Part 1 1990Pricing foreign currency options with stochastic volatility 1991Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations

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