Fractional cointegration analysis of nonlinear time series with long memory.

da Silva, Afonso Goncalves (2008) Fractional cointegration analysis of nonlinear time series with long memory. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis develops theoretical tools for fractional cointegration analysis of nonlinear time series. These tools are employed to establish consistency of narrow band versions of Least Squares and Principal Components, in situations when the observables do not follow traditional linear process assumptions. Chapter 1 introduces the problem, and Chapter 2 reviews the tools and techniques used in the literature for analysing stationary fractional cointegration, emphasizing methods that will be the focus of subsequent chapters. Chapter 3 considers a bivariate factor model, where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated, but have strong dependence in higher moments. Assuming the latent variables are driven by long memory stochastic volatility models, and that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We consider a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence. Chapter 4 contains two Monte Carlo experiments: the first illustrates the performance of the Narrow Band Least Squares estimate in the setting of the previous chapter, while the second attempts to fill the gap in theoretical distributional results for nonlinear processes, by analysing distributional properties of the more general Weighted Narrow Band Least Squares estimate, under linear and nonlinear settings. Chapter 5 extends the techniques of Chapter 3 to a general multivariate setting, with more than two observables and multiple common factors. A narrow band version of the Principal Components estimate is introduced and shown to converge to the space spanned by the factor loadings, allowing their consistent estimation under suitable linear restrictions. A Monte Carlo study of finite sample performance and an empirical application to European equity indices are also presented.

Item Type:	Thesis (PhD)
Uncontrolled Keywords:	Economics, General
Sets:	Collections > ProQuest Etheses Departments > Economics
URI:	http://etheses.lse.ac.uk/id/eprint/2166

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