Maximum Entropy Spectral Analysis to Time Series with Missing Value

• Activity Number: 523
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Aladdin Shamilov and Cigdem Giriftinoglu*+
• Companies: Anadolu University and Anadolu University
• Keywords: Maximum entropy spectral analysis ; MinMaxEnt distribution ; Time series ; Missing value ; Power spectrum ; MinMaxEnt Spectral Analysis

Abstract

Maximum entropy formalism enables us to obtain a distribution for a time series when the knowledge is given as the expected values of the autocovariance up to a lag m. Although the autocovariance functions and spectral density function form a Fourier transform pair, Power Spectrum cannot be exactly obtained since only a limited number of autocovariances are available. Therefore, the principle of maximum entropy can be used to extract the best estimate of power spectrum. In this study, in order to obtain Maximum Entropy distribution and spectral density function, a process determined by values of Lagrange multipliers is presented for a stationary time series. Moreover, when the missing value is appeared in time series, power spectrum is calculated by means of a new estimation method based on MinMaxEnt Distribution.