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Generalized Method of Wavelet Moments

Stebler, Yannick
Skaloud, Jan
Publication University of Geneva, 2011
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Abstract This paper presents a new estimation method for the parameters of a model generating times series. Given some conditions on the form of the power spectral density associated to the process, it is possible to indirectly recover pa- rameter estimates from wavelet variances (WV) associated to the process. We propose an optimization criterion based on a standardized distance between the sample WV estimates and the model based WV, as is done e.g. with the generalized method of moments and therefore call the new estimator the generalized method of Wavelet Moments (GMWM) estimator. Moreover, it can be computed using simulations, so that it is very straightforward to implement in practice, since the only specification that is needed for a given model, is the data generating process. We derive its asymptotic properties for inference and perform a simulation study to compare the GMWM estimator to the MLE and another estimator with different models. We also use it to estimate the the stochastic error's parameters in accelerometer and gyroscopes composing inertial navigation systems by means of a sample of over 8000000 measurements, for which no other estimation method can be used.
Keywords State space modelsGeneralized method of momentsTime seriesWavelet varianceIndirect inference
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GUERRIER, Stéphane et al. Generalized Method of Wavelet Moments. 2011 https://archive-ouverte.unige.ch/unige:16813

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Deposited on : 2011-08-23

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