TY - JOUR
T1 - Higher-order kernel semiparametric M-estimation of long memory
AU - Robinson, Peter M.
AU - Henry, Marc
N1 - Funding Information:
We thank two referees for helpful comments which have led to improvements in presentation. We also thank Fabrizio Iacone for help in computing the theoretical bandwidths and theoretical mean-squared errors in Tables 4–6 . The first author's research was supported by a Leverhulme Trust Personal Research Professorship and ESRC Grant R000238212. The second author's research was supported by an FRS Grant from IRES.
PY - 2003/5
Y1 - 2003/5
N2 - Econometric interest in the possibility of long memory has developed, as a flexible alternative to or compromise between the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We introduce a broad class of such semiparametric estimates that also covers pooling across frequencies. A leading "Box-Cox" sub-class, indexed by a single tuning parameter, interpolates between the popular local log-periodogram and local Whittle estimates, leading to a smooth interpolation of asymptotic variances. The bias of these two estimates also differs to higher order, and we also show how bias, and asymptotic mean-squared error, can be reduced, across the class of estimates studied, by means of a suitable version of higher-order kernels. We thence calculate an optimal bandwidth (the number of low-frequency periodogram ordinates employed) which minimizes this mean-squared error. Finite sample performance is studied in a small Monte Carlo experiment, and an empirical application to intra-day foreign exchange returns is included.
AB - Econometric interest in the possibility of long memory has developed, as a flexible alternative to or compromise between the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We introduce a broad class of such semiparametric estimates that also covers pooling across frequencies. A leading "Box-Cox" sub-class, indexed by a single tuning parameter, interpolates between the popular local log-periodogram and local Whittle estimates, leading to a smooth interpolation of asymptotic variances. The bias of these two estimates also differs to higher order, and we also show how bias, and asymptotic mean-squared error, can be reduced, across the class of estimates studied, by means of a suitable version of higher-order kernels. We thence calculate an optimal bandwidth (the number of low-frequency periodogram ordinates employed) which minimizes this mean-squared error. Finite sample performance is studied in a small Monte Carlo experiment, and an empirical application to intra-day foreign exchange returns is included.
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U2 - 10.1016/S0304-4076(02)00208-7
DO - 10.1016/S0304-4076(02)00208-7
M3 - Article
AN - SCOPUS:0012653345
SN - 0304-4076
VL - 114
SP - 1
EP - 27
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -