Robust spectral estimator from M-estimation point of view: application to the Korean housing price index Pak, Ro Jin;
In analysing a time series on the frequency domain, the spectral estimator (or periodogram) is a very useful statistic to identify the periods of a time series. However, the spectral estimator is very sensitive in nature to outliers, so that the spectral estimator in terms of M-estimation has been studied by some researchers. Pak (2001) proposed an empirical method to choose a tuning parameter for the Huber`s M-estimating function. In this article, we try to implement Pak`s estimation proposal in the spectral estimator. We use the Korean housing price index as an example data set for comparing various M-estimating results.
Bartlett, M. S. (1948). Smoothing periodograms from time-series with continuous spectra, Nature, 161, 686-687.
Bartlett, M. S. (1950). Periodogram analysis and continuous spectra, Biometrika, 37, 1-16.
Huber, P. J. (1964). Robust estimation of location parameters, Annals of Mathematical Statistics, 35, 73-101.
Pak, R. J. (2001). The bending constant in Huber's function in terms of a bandwidth in density estimator, The Korean Journal of Applied Statistics, 14, 357-367.
Proakis, J. G. and Manolakis, D. K. (2006). Digital Signal Processing: Principles, Algorithms, and Applications, Prentice Hall, New York.
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall, London.
Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society: Series B, 53, 683-690.
Spangl, B. and Dutter, R. (2005). On robust estimation of power spectra, Austrian Journal of Statistics, 34, 199-210.
Welch, P. D. (1967). The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodogram, IEEE Transactions on Audio Electroacoustics, AU-15, 70-73.