Asymptotics for the conditional-sum-of-squares estimator in fractional time series models
AbstractThis paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in fractional time series models. The model is parametric and quite general, and, in particular, encompasses the fractional ARIMA model. The novelty of the consistency result is that it applies to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity thus making the proof much more challenging than usual. The neighborhood around the critical point where uniform convergence fails is handled using a truncation argument. Finally, all arguments, assumptions, and proofs are stated entirely in the time domain, which is somewhat remarkable for this literature.
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Bibliographic InfoPaper provided by Queen's University, Department of Economics in its series Working Papers with number 1259.
Length: 26 pages
Date of creation: Jan 2011
Date of revision:
Asymptotic normality; conditional-sum-of-squares estimator; consistency; fractional integration; fractional time series; likelihood inference; long memory; nonstationary; uniform convergence; uniform convergence;
Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-30 (All new papers)
- NEP-ECM-2011-01-30 (Econometrics)
- NEP-ETS-2011-01-30 (Econometric Time Series)
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- Søren Johansen & Morten Ørregaard Nielsen, 2012.
"The role of initial values in nonstationary fractional time series models,"
1300, Queen's University, Department of Economics.
- Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," CREATES Research Papers 2012-47, School of Economics and Management, University of Aarhus.
- Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," Discussion Papers 12-18, University of Copenhagen. Department of Economics.
- Giuseppe Cavaliere & Morten Ã˜rregaard Nielsen & A.M. Robert Taylor, 2013. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," Working Papers 1309, Queen's University, Department of Economics.
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