Wavelets and estimation of long memory in nonstationary models: Does anything beat the exact local whittle estimator?

ABSTRACT

In this article, we analyze the performance of five estimation methods for the long memory parameter d. The goal of our article is to construct a wavelet estimate for the fractional differencing parameter in nonstationary long memory processes that dominate the well-known estimate of Shimotsu and Phillips (2005). The simulation results show that the wavelet estimation method of Lee (2005) with several tapering techniques performs better under most cases in nonstationary long memory. The comparison is based on the empirical root mean squared error of each estimate.

Keywords:

• Long memory
• Nonstationary models
• Wavelets

Mathematics Subject Classification:

• 91B84
• 91B82
• 91B84

Notes

1 See Beran (1994) for more details on long memory processes.

2 See Jensen (1999) for more details about the estimation method.

3 See Shimotsu and Phillips (2005) for more details about the consistency of the estimate.

4 See Geweke and Porter-Hudak (1983) for more details.

5 In this study we are not interested in the estimation of the short memory parameters p and q in the ARFIMA(p,d,q); for some discussion and results, see Boutahar and Khalfaoui (2011).

6 We have also tried other wavelet filters, but have never observed any effect in the robustness of estimates (they are available upon request). For some examples, see also Boubaker and Boutahar (2011).

7 http://tonto.eia.doe.gov/dnav/pet/pet_pri_spt_s1_w.htm