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Asymptotics for the Conditional‐Sum‐of‐Squares Estimator in Multivariate Fractional Time‐Series Models
Author(s) -
Nielsen Morten Ørregaard
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12100
Subject(s) - mathematics , estimator , multivariate statistics , strong consistency , conditional variance , asymptotic distribution , statistics , series (stratigraphy) , truncation (statistics) , conditional expectation , autoregressive integrated moving average , econometrics , time series , autoregressive conditional heteroskedasticity , volatility (finance) , paleontology , biology
This article proves consistency and asymptotic normality for the conditional‐sum‐of‐squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time‐series models. The model is parametric and quite general and, in particular, encompasses the multivariate non‐cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where uniform convergence fails is handled using a truncation argument.