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The application of the Kalman filter...

Wang, Zhu.

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The application of the Kalman filter to nonstationary time series through time deformation.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The application of the Kalman filter to nonstationary time series through time deformation./
作者:	Wang, Zhu.
面頁冊數:	124 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-06, Section: B, page: 2992.
Contained By:	Dissertation Abstracts International65-06B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3137868
ISBN:	0496850385

The application of the Kalman filter to nonstationary time series through time deformation.
Wang, Zhu.

The application of the Kalman filter to nonstationary time series through time deformation. - 124 p.

Source: Dissertation Abstracts International, Volume: 65-06, Section: B, page: 2992.

Thesis (Ph.D.)--Southern Methodist University, 2004.

Nonstationary time series process with time-varying frequencies are common in speech, biological and geophysical data. Classical Fourier methods and ARMA models under the assumption of stationarity are not appropriate tools for this type of data. Time deformation provides a solution, which transforms the time axis to obtain a stationary process. Stock (1988) made time deformation popular in economic applications where the time series is regarded as evolving in operational time rather than calendar time. Gray and Zhang (1988) developed a class of continuous multiplicative-stationary (M-stationary) processes. A continuous M-stationary process can be transformed to a continuous stationary process, which is referred to as the dual process, through a logarithmic time transformation. A special class of M-stationary process are the Euler processes where the corresponding dual process is the AR process. Here we show that an evenly spaced sample from a first order continuous Euler process is equivalent to a time-varying discrete AR process. To analyze the unevenly spaced dual using the conventional discrete AR model, Gray et al. (2004) considered using interpolation to obtain evenly spaced data, and they then re-interpolated on the original time scale for forecasting. Although these interpolation procedures may suffice for many purposes, they may introduce noise and distortion.

ISBN: 0496850385Subjects--Topical Terms:

517247
Statistics.

The application of the Kalman filter to nonstationary time series through time deformation.
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520 $a Nonstationary time series process with time-varying frequencies are common in speech, biological and geophysical data. Classical Fourier methods and ARMA models under the assumption of stationarity are not appropriate tools for this type of data. Time deformation provides a solution, which transforms the time axis to obtain a stationary process. Stock (1988) made time deformation popular in economic applications where the time series is regarded as evolving in operational time rather than calendar time. Gray and Zhang (1988) developed a class of continuous multiplicative-stationary (M-stationary) processes. A continuous M-stationary process can be transformed to a continuous stationary process, which is referred to as the dual process, through a logarithmic time transformation. A special class of M-stationary process are the Euler processes where the corresponding dual process is the AR process. Here we show that an evenly spaced sample from a first order continuous Euler process is equivalent to a time-varying discrete AR process. To analyze the unevenly spaced dual using the conventional discrete AR model, Gray et al. (2004) considered using interpolation to obtain evenly spaced data, and they then re-interpolated on the original time scale for forecasting. Although these interpolation procedures may suffice for many purposes, they may introduce noise and distortion.
520 $a To avoid any interpolation, continuous AR models (CAR) are fit to the unequally spaced dual process. To estimate the parameters of this model using the maximum likelihood criteria, the efficient Kalman filter is applied to decompose the prediction error based on Belcher et al. (1994). Relative to the interpolation approach, this method not only provides more accurate estimation of the spectrum and forecasts, but it also can help to confirm results acquired from the interpolation approach. In addition, the state model formulation has the physical interpretation that the model integrates the combined effect of several distinct sources of variation, each of which is illustrated by a low order process which might have a meaningful interpretation itself. These estimated components may be used further to filter out desired frequencies. Here, these techniques are also applied to G(lambda)-stationary processes, which are generalizations of M-stationary processes.
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