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Asymptotic properties of weighted least squares estimation in weak parma models

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Table 1.Empirical and asymptotic standard errors of the OLS estimators of φ1 and φ2 in the PAR2(1)model (4.2) and the rejection frequencies at the nominal level 0.05 of the standard Wald test computed underindependent errors for three types of white noises
Table 2.Bias, Empirical Standard Error (ESE), Mean Asymptotic Standard Error under the assumption of astrong noise (MASEwith(s)) and a weak noise (MASE(w)) of the QLS estimators of the PARMA2(1, 1) model (5.1) ⃗α = (0.05, −0.05, 0.8, 0.75, −0.5, −0.45)′, based on 1000 independent realisations for each series length NT .
Table 3. Rejection frquencies (%) at the nominal levels 1, 5 and 10% of the Wald test for the null hypothesisof non periodicity (H0) and for a fixed alternative (H1) under the assumption of a strong (WS) or a weak noise(WW) based on 1000 independent realisa
Table 5. QLS estimates and their estimated standard errors under the assumption of a weak white noise (inparentheses) of Model (6.1) fitted to the daily returns of the four European stock market indices

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