Local polynomial Whittle estimation of perturbed fractional processes

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in ‡ate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal for d 2 (0; 3=4), and if the spectral density is su¢ ciently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, p n. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator. Terms of use: Documents inJEL Classi…cations: C22.

On the risk comovements between the crude oil market and U.S. dollar exchange rates

“…3 Hence, we report the results (see Table 1) for several bandwidths running from m = n 0.4 to m = n 0.5 and thereby taking into account an appropriate bandwidth requirement (see e.g. Frederiksen et al , 2012). Interestingly, the results reveal that the volatility of the raw series have long memory, confirming the findings of many studies (see e.g.…”

On Estimation of Hurst Parameter Under Noisy Observations

“…Abry et al (1995) discuss the relationship between wavelet method and spectrum analysis in the situation of estimating the Hurst parameter. In the context of a long memory time series with additional noise, there exist many estimating methods to estimate the long memory parameter, see, e.g., Deo and Hurvich (2001), Arteche (2004Arteche ( , 2006Arteche ( , 2012, Hurvich et al (2005), Frederiksen et al (2012), Hou and Perron (2014), Dattatreya (2005) and their references.…”

Comparing Predictive Accuracy under Long Memory, With an Application to Volatility Forecasting*

“…Furthermore, it is well known that local Whittle estimates can be biased in presence of short run dynamics. We therefore also report results of the local polynomial Whittle plus noise (LPWN) estimator of Frederiksen et al (2012). Similar to the ALPW estimator of Andrews and Sun (2004), the LPWN estimator reduces the bias due to short memory dynamics by approximating the log-spectral density of the short memory 7 For a better comparison, all variables in this section are scaled towards a monthly basis.…”

“…We test that a more complex model outperforms its parsimonious version. For the sake of a better comparability, all kernel-8 We choose Ry = 1 and Rw = 0 concerning the polynomial degrees and a bandwidth m d = T 0.8 (see Frederiksen et al (2012) for details on the estimator). 9 As a robustness check, we repeat the analysis for a larger window of 2500 observations and obtain qualitatively similar results.…”