Wavelet Variance--Based Estimation for Composite Stochastic Processes

• Activity Number: 400
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Stephane Guerrier*+
• Keywords: State space models ; generalized method of moments ; time series ; indirect inference

Abstract

This paper presents a new estimation method for the parameters of a times series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which in turn explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood that is rather straightforward to implement and often the only feasible estimation method with more complex models. The estimator results as the optimization of a 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 (GMM). It is very straightforward to implement in practice with complex models, and can also be computed using simulations. We derive its asymptotic properties for inference and perform a simulation study to compare our estimator to the MLE with different models. We also use it to estimate the stochastic error's parameters of gyroscope composing inertial navigation systems by means of a sample of over 800, 000 measurements, for which no other estimation method can be used.