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Checking Second-Order Stationarity Of ARFIMA Models-Double-Order Selection Test

Posted on:2018-08-07Degree:MasterType:Thesis
Country:ChinaCandidate:L Y ZhouFull Text:PDF
GTID:2359330515984228Subject:Mathematical probability theory and mathematical statistics
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In this thesis,we work on theoretical foundations and simulations of using the double-order selection test to check the second-order stationarity of ARFIMA mod-els.First,we define long-memory time series and focus on ARFIMA models.We review the double-order selection test for short-memory time series,including defini-tions of systematic samples and the statistics.Under certain assumptions,we obtain the asymptotic distribution of the statistics.We then verify qualities of coefficients in stationary ARFIMA models,based on which we prove the feasibility of using the statistics to check stationarity of ARFIMA(p,d,q)models.We explain theorems under the situations-1<d<0 and 0<d<0.5 separately.The difference derives from convergence rates of autocovariances and reflects on the index of T(length of time se-ries)in the statistics.For-1<d<0,we give the specific statistics and its asymptotic distribution while for 0<d<0.5,we prove some convergence theorems.For certain T,we generate critical values under different significant levels by Monte-Carlo simulations.To calculate empirical type I error rates,we consider s-tationary ARFIMA series,including thin-tailed ones driven by Gaussian innovations and heavy-tailed ones driven by t innovations.Meanwhile,we get empirical powers by testing non-stationary(piecewise stationary)ARFIMA series.We adjust R(maximal order of autocovariances)and M(maximal number of systematic samples)to observe their effects on empirical powers.The empirical type I error rates are close to relevant significant levels and empirical powers are close to 1 when T is reasonably large.So we can apply the double-order selection test to check stationarity of ARFIMA models.
Keywords/Search Tags:Stationarity test, long-memory, ARFIMA models, double-order selection test, systematic samples, autocovariance
PDF Full Text Request
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