Persistence in Nonlinear Time Series: A Nonparametric Approach

Abstract

The purpose of the present paper is to relate two important concepts of time series analysis, namely, nonlinearity and persistence. Traditional measures of persistence are based on correlations or periodograms, which may be inappropriate under nonlinearity and/or non-Gaussianity. This article proves that nonlinear persistence can be characterized by cumulative measures of dependence. The new cumulative measures are nonparametric, simple to estimate and do not require the use of any smoothing user-chosen parameters. In addition, we propose nonparametric estimates of our measures and establish their limiting properties. Finally, we employ our measures to analyze the nonlinear persistence properties of some international stock market indices, where we …nd an ubiquitous nonlinear persistence in conditional variance that is not accounted for by popular parametric models or by classical linear measures of persistence. This …nding has important economic implications in, e.g., asset pricing and hedging. Conditional variance persistence in bull and bear markets is also analyzed and compared.

The lower regression function and testing expectation dependence dominance hypotheses

“…Likewise, we can write for all x; m < (x) = R x 1 m(x 0 )f (x 0 )dx 0 R x 1 f (x 0 )dx 0 : The lower regression function fm < (x); x 2 R d g contains essentially the same information as the regression function fm(x); x 2 R d g. Escanciano and Hualde (2009) consider the integrated regression function (assume for simplicity that y is centered)…”