Indirect inference in spatial autoregression

Kyriacou, Maria; Phillips, Peter C.B.; Rossi, Francesca

doi:10.1111/ectj.12084

Cited by 21 publications

(19 citation statements)

References 28 publications

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“…The jackknife uses analytical (rather than simulation-based) results to achieve bias reduction at minimal computational cost along the same lines as indirect inference methods based on analytical approximations in Phillips (2012) and Kyriacou et al (2017). Apart from computational simplicity, an evident advantage of analytical-based methods over simulation-based alternatives such as bootstrap or (traditional, simulation-based) indirect inference methods is that they require no distributional assumptions on the error term.…”

Section: Discussionmentioning

confidence: 99%

Jackknife Bias Reduction in the Presence of a Near-Unit Root

Chambers

Kyriacou

2018

Econometrics

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This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error, as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter and a quantity that is related to the long-run variance of the disturbance process, which are typically unknown in practice, and so, this dependence is characterised fully and a discussion provided of the issues that arise in practice in the most general settings.

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Section: Discussionmentioning

confidence: 99%

Jackknife Bias Reduction in the Presence of a Near-Unit Root

Chambers

Kyriacou

2018

Econometrics

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“…as the Group Interaction model (see, e.g., Case, 1992, Kelejian et al, 2006, Lee, 2007, Davezies et al, 2009, Carrell et al, 2013, and Boucher et al, 2014. It is sometimes also known as the districts model (Kyriakou et al, 2017). For this model Λ = (−(m 1 − 1), 1).…”

Section: Examplesmentioning

confidence: 99%

Exact and higher-order properties of the MLE in spatial autoregressive models, with applications to inference

Hillier

Martellosio

2018

Journal of Econometrics

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The quasi-maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data. A rigorous analysis of the first-order asymptotic properties of the estimator, under some assumptions on the evolution of the spatial design matrix, is available in Lee (2004), but very little is known about its exact or higher-order properties. In this paper we first show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written in terms of that of a particular quadratic form. Simple examples are used to illustrate important exact properties of the estimator that follow from this representation. In general models a complete exact analysis is not possible, but a higher-order (saddlepoint) approximation is made available by the main result. We use this approximation to construct confidence intervals for the autoregressive parameter. Coverage properties of the proposed confidence intervals are studied by Monte Carlo simulation, and are found to be excellent in a variety of circumstances.

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“…The authors applied the indirect inference method to macroeconomics, microeconomics, finance, and auction models; see as well Monfort (1996) and Phillips and Yu (2009) for applications to continuous-time models, Gouriéroux et al (2000) and Kyriacou et al (2017) for applications to time series models, and Monfardini (1998) for applications to stochastic volatility models. In addition indirect inference is used for bias reduction in finite samples as, for example, in Gouriéroux et al (2000), Gouriéroux et al (2010), Yu (2011), Kyriacou et al (2017), and do Rêgo Sousa et al (2019). An alternative approach for bias correction is given in Wang et al (2011) for univariate and multivariate diffusion models.…”

Section: Introductionmentioning

confidence: 99%

Robust estimation of stationary continuous‐time arma models via indirect inference

Fasen‐Hartmann¹,

Kimmig²

2020

Journal Time Series Analysis

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In this article, we present a robust estimator for the parameters of a stationary, but not necessarily Gaussian, continuous-time ARMA(p, q) (CARMA(p, q)) process that is sampled equidistantly. Therefore, we propose an indirect estimation procedure that first estimates the parameters of the auxiliary AR(r) representation (r ≥ 2p − 1) of the sampled CARMA process using a generalized M-(GM-)estimator. Since the map which maps the parameters of the auxiliary AR(r) representation to the parameters of the CARMA process is not given explicitly, a separate simulation part is necessary where the parameters of the AR(r) representation are estimated from simulated CARMA processes. Then, the parameters which take the minimum distance between the estimated AR parameters and the simulated AR parameters give an estimator for the CARMA parameters. First, we show that under some standard assumptions the GM-estimator for the AR(r) parameters is consistent and asymptotically normally distributed. Then, we prove that the indirect estimator is also consistent and asymptotically normally distributed when the asymptotically normally distributed LS-estimator is used in the simulation part. The indirect estimator satisfies several important robustness properties such as weak resistance, d n -robustness and it has a bounded influence functional. The practical applicability of our method is illustrated in a small simulation study with replacement outliers.

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Indirect inference in spatial autoregression

Cited by 21 publications

References 28 publications

Jackknife Bias Reduction in the Presence of a Near-Unit Root

Jackknife Bias Reduction in the Presence of a Near-Unit Root

Exact and higher-order properties of the MLE in spatial autoregressive models, with applications to inference

Robust estimation of stationary continuous‐time arma models via indirect inference

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