Limits of VAR Models for Daily Financial Returns

Summary

The document raises the question of whether vector autoregression and related autoregressive models are useful for daily log returns in liquid financial markets. It contrasts the common use of these models in financial time-series analysis with practitioner skepticism about whether they capture meaningful return dynamics. No particular VAR specification, trading rule, dataset, or empirical result is presented.

The central concern is that arbitrage may make linear, second-order dependence in price changes difficult to distinguish from white noise. The quoted discussion points to autocovariance, ARMA, and spectral methods as potentially limited for describing asset-return dependence, and suggests nonlinear dependence measures as a possible alternative. The document is a request for practitioner experience and authoritative empirical research, rather than a review that answers that request. Its claims should therefore be treated as motivation for investigation, not as evidence that VAR models are universally ineffective or that nonlinear methods will necessarily perform better.

Key ideas

• The document questions whether autoregressive models capture useful structure in daily returns of liquid markets.
• It cites the view that arbitrage can weaken linear dependence in price changes.
• Second-order tools such as autocovariance analysis may fail to distinguish returns from white noise.
• Nonlinear dependence measures are proposed as a direction for further study.
• The document provides no empirical comparison or conclusion about model performance.

Tags

# VAR models for log-returns?


# VAR models for log-returns?












I am wondering if Vector Autoregression (and other autoregressive models) is a sound modelling for the daily (not high-frequency!) log-returns of time series from liquid financial markets.

One can find through google scholar or in many books on financial time series analysis this kind of approach.

However, partly from my practitioner experience, I am dubious about the relevance of such modelling. One can also read in Empirical properties of asset returns: stylized facts and statistical issues:

> Mandelbrot [85] expressed this property by stating that ‘arbitrage tends to whiten the spectrum of price changes’. This property implies that traditional tools of signal processing which are based on second-order properties, in the time domain—autocovariance analysis, ARMA modelling—or in the spectral domain— Fourier analysis, linear filtering—cannot distinguish between asset returns and white noise. This points out the need for nonlinear measures of dependence in order to characterize the dependence properties of asset returns.

I am thus looking for personal experience of (un)success with such autoregressive modelling, and authoritative paper with in-depth experimental analysis on real market data.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.