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.