Estimation of Time Series Models via Robust Wavelet Variance

Guerrier, Stéphane; Molinari, Roberto; Victoria‐Feser, Maria‐Pia

doi:10.17713/ajs.v43i4.45

Cited by 5 publications

(4 citation statements)

References 28 publications

(37 reference statements)

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“…Having stated this, the results of the simulation studies using the RMSE* are shown in Figure 1 where the MAR and INDI estimators are denoted as KUN-SCH since they are used in complementary settings. The first aspect to underline is that the RGMWM generally performs better than the MPWM in all the different settings and can therefore be considered as an improvement over the robust estimator investigated in Guerrier et al (2014). Having stated this, when considering the AR(1), AR(2) models, the RGMWM does not lose much in uncontaminated settings while it performs generally as well or better than the MAR estimator in contaminated ones.…”

Section: (Mpwm)mentioning

confidence: 91%

“…Aside from the above advantages, the reason for considering the GMWM for the robust parametric estimation of time series and spatial models resides in the fact that it can easily be made robust by using a robust estimator of the WV. In fact, Ronchetti and Trojani (2001) and Genton and Ronchetti (2003) highlight that a bounded auxiliary parameter or moment condition can guarantee the robustness of the resulting parametric estimator and this property was already investigated in the time series setting in Guerrier et al (2014) where simulation studies hinted that this approach constituted a valid means to bound the influence of contaminated observations in a dependent data scenario. However, in the latter the authors used the robust M-estimator of WV proposed by Mondal and Percival (2012b) that, although bounding the influence of outliers, does not benefit from clear asymptotic properties which would allow for inference when estimating parameters of random fields.…”

Section: Introductionmentioning

confidence: 96%

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Fast and Robust Parametric Estimation for Time Series and Spatial Models

Guerrier,

Molinari

2016

Preprint

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We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve parameter estimation for complex models. Using an M-estimator of the wavelet variance, this method can be made robust therefore allowing to estimate the parameters of a wide range of time series and spatial models when the data suffers from outliers or different forms of contamination. The paper presents a series of simulation studies as well as a range of applications where this new approach can be considered as a computationally efficient, numerically stable and robust method which performs at least as well as existing methods in bounding the influence of outliers on the estimation procedure.

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Section: (Mpwm)mentioning

confidence: 91%

Section: Introductionmentioning

confidence: 96%

Fast and Robust Parametric Estimation for Time Series and Spatial Models

Guerrier,

Molinari

2016

Preprint

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“…distributed errors." A similar commentary was given very recently in Guerrier et al [66], in which the authors note that "the robust estimation of time series parameters is still a widely open topic in statistics for various reasons." Such calls for the development of new methodologies further serve to underscore the potential impact of combining ideas from robust optimization with time series analysis, e.g.…”

Section: Additional Literature Reviewmentioning

confidence: 57%

Distributionally robust inventory control when demand is a martingale

Xin

Goldberg

2015

Preprint

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https://people.orie.cornell.edu/dag369/ Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification in this context, various forms of distributionally robust optimization have been applied. Although many of these methodologies suffer from the problem of time-inconsistency, the work of Klabjan, Simchi-Levi and Song [85] established a general time-consistent framework for such problems by connecting to the literature on robust Markov decision processes.Motivated by the fact that many forecasting models exhibit very special structure, as well as a desire to understand the impact of positing different dependency structures, in this paper we formulate and solve a time-consistent distributionally robust multi-stage newsvendor model which naturally unifies and robustifies several inventory models with demand forecasting. In particular, many simple models of demand forecasting have the feature that demand evolves as a martingale (i.e. expected demand tomorrow equals realized demand today). We consider a robust variant of such models, in which the sequence of future demands may be any martingale with given mean and support. Under such a model, past realizations of demand are naturally incorporated into the structure of the uncertainty set going forwards.We explicitly compute the minimax optimal policy (and worst-case distribution) in closed form, by combining ideas from convex analysis, probability, and dynamic programming. We prove that at optimality the worst-case demand distribution corresponds to the setting in which inventory may become obsolete at a random time, a scenario of practical interest. To gain further insight, we prove weak convergence (as the time horizon grows large) to a simple and intuitive process. We also compare to the analogous setting in which demand is independent across periods (analyzed previously in Shapiro [119]), and identify interesting differences between these models, in the spirit of the price of correlations studied in Agrawal et al. [2]. Finally, we complement our theoretical results by providing a targeted and concise numerical experiment further demonstrating the benefits of our model.

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“…The properties of the proposed M-estimator of WV can be directly carried over to the GMWM framework (see Guerrier et al 2013). Indeed, as suggested in Guerrier, Molinari, and Victoria-Feser (2014), one can replace the standard estimator used in the GMWM with a robust estimator which, in this case, is the proposed M-estimator allowing us to deliver the RGMWM defined aŝ…”

Section: Robust Gmwmmentioning

confidence: 99%

Robust Two-Step Wavelet-Based Inference for Time Series Models

Guerrier

Molinari

Victoria‐Feser

et al. 2021

Journal of the American Statistical Association

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Latent time series models such as (the independent sum of ) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.

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Estimation of Time Series Models via Robust Wavelet Variance

Cited by 5 publications

References 28 publications

Fast and Robust Parametric Estimation for Time Series and Spatial Models

Fast and Robust Parametric Estimation for Time Series and Spatial Models

Distributionally robust inventory control when demand is a martingale

Robust Two-Step Wavelet-Based Inference for Time Series Models

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