Parametric inference of autoregressive heteroscedastic models with errors in variables

When a continuous-time diffusion is observed only at discrete times with measurement noise, in most cases the transition density is not known and the likelihood is in the form of a high-dimensional integral that does not have a closed-form solution and is difficult to compute accurately. Using Hermite expansions and deconvolution strategy, we provide a general explicit sequence of closed-form contrast for noisy and discretely observed diffusion processes. This work allows the estimation of many diffusion processes. We show that the approximation is very accurate and prove that minimizing the sequence results in a consistent and asymptotically normal estimator. Monte Carlo evidence for the Ornstein-Uhlenbeck process reveals that this method works well and outperforms the Euler expansion of the transition density in situations relevant for financial models.

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“…The proof of Corollary 3.1 stems mainly from Lemma 3.1 and assumptions A 2-A 4. For a complete detail see [17].…”

Section: Asymptotic Properties Of the Minimum Contrast Estimatormentioning

confidence: 99%

Contrast estimation for noisy observations of diffusion processes via closed-form density expansions

Kolei

Navarro

2021

Stat Inference Stoch Process

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“…Recently, in [13], the authors generalize this approach to models defined as X i = b θ 0 (X i−1 )+η i , where b θ 0 is the regression function assumed to be known up to θ 0 and for homoscedastic innovations η i . Also, in [21] and [23], the authors propose a consistent estimator for parametric models assuming knowledge of the stationary density f θ 0 up to the unknown parameters θ 0 for the construction of the estimator. For many processes, this density has no analytic expression, and even in some cases where it is known, it may be more complex to apply deconvolution techniques using this density rather than the transition density.…”

Section: Introductionmentioning

confidence: 99%

Parametric estimation of hidden Markov models by least squares type estimation and deconvolution

2022

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This paper develops a simple and computationally efficient parametric approach to the estimation of general hidden Markov models (HMMs). For non-Gaussian HMMs, the computation of the maximum likelihood estimator (MLE) involves a high-dimensional integral that has no analytical solution and can be difficult to approach accurately. We develop a new alternative method based on the theory of estimating functions and a deconvolution strategy. Our procedure requires the same assumptions as the MLE and deconvolution estimators. We provide theoretical guarantees about the performance of the resulting estimator; its consistency and asymptotic normality are established. This leads to the construction of confidence intervals. Monte Carlo experiments are investigated and compared with the MLE. Finally, we illustrate our approach using real data for ex-ante interest rate forecasts.MSC 2010 subject classifications: 62F12.

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Parametric inference of autoregressive heteroscedastic models with errors in variables

Cited by 2 publications

References 11 publications

Contrast estimation for noisy observations of diffusion processes via closed-form density expansions

Contrast estimation for noisy observations of diffusion processes via closed-form density expansions

Parametric estimation of hidden Markov models by least squares type estimation and deconvolution

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