Specification Tests for Nonlinear Dynamic Models

Kheifets, Igor

doi:10.2139/ssrn.2404003

Cited by 5 publications

(21 citation statements)

References 43 publications

(64 reference statements)

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“…Specifically, under the null for r = (r 1 , r 2 ) ∈ [0, 1] 2 and for the lth lag (l = 1, 2, … ), we test for pairwise independence, that is, P(ũ t ⩽ r 1 ,ũ t−l ⩽ r 2 ) = r 1 r 2 . Following Kheifets (2015), we define the process…”

Section: Estimation Model Selection and Specification Testsmentioning

confidence: 99%

“…Critical values for Equation 7 can be obtained by i.i.d. bootstrap approximation as in Kheifets (2015).…”

Section: Estimation Model Selection and Specification Testsmentioning

confidence: 99%

“…For more details on these methods, seeDavis, Dunsmuir, and Streett (2003),Jung and Tremayne (2011), andDavis and Liu (2016).3 Note that the asymptotic distribution of the Kolmogorov-Smirnov tests is invalid due to the estimation of the model parameters(Kheifets, 2015). Therefore, we also consider an i.i.d.…”

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confidence: 99%

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PARX model for football match predictions

Angelini

Angelis

2017

Journal of Forecasting

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We propose an innovative approach to model and predict the outcome of football matches based on the Poisson autoregression with exogenous covariates (PARX) model recently proposed by Agosto, Cavaliere, Kristensen, and Rahbek (Journal of Empirical Finance, 2016, 38(B), 640–663). We show that this methodology is particularly suited to model the goal distribution of a football team and provides a good forecast performance that can be exploited to develop a profitable betting strategy. This paper improves the strand of literature on Poisson‐based models, by proposing a specification able to capture the main characteristics of goal distribution. The betting strategy is based on the idea that the odds proposed by the market do not reflect the true probability of the match because they may also incorporate the betting volumes or strategic price settings in order to exploit betters' biases. The out‐of‐sample performance of the PARX model is better than the reference approach by Dixon and Coles (Applied Statistics, 1997, 46(2), 265–280). We also evaluate our approach in a simple betting strategy, which is applied to English football Premier League data for the 2013–2014, 2014–2015, and 2015–2016 seasons. The results show that the return from the betting strategy is larger than 30% in most of the cases considered and may even exceed 100% if we consider an alternative strategy based on a predetermined threshold, which makes it possible to exploit the inefficiency of the betting market.

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Section: Estimation Model Selection and Specification Testsmentioning

confidence: 99%

“…Critical values for Equation 7 can be obtained by i.i.d. bootstrap approximation as in Kheifets (2015).…”

Section: Estimation Model Selection and Specification Testsmentioning

confidence: 99%

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PARX model for football match predictions

Angelini

Angelis

2017

Journal of Forecasting

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“…One approach uses martingale transformations (due to Khmaladze, 1981) to obtain asymptotically distribution-free tests (see, e.g., Bai, 2003). Another approach uses bootstrap approximations to overcome the problem of the data-dependent asymptotic distributions; see, e.g., Corradi and Swanson (2006), Hidalgo and Zaffaroni (2007) and Kheifets (2015). The third approach comprises nonparametric smoothing methods, which involve bandwidth selection; see, e.g., Lee (2003, 2005).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric bootstrap tests for independence of generalized errors

2016

The Econometrics Journal

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In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding-Blum-Kiefer-Rosenblatttype empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance-parameter-free. To circumvent this problem, we propose a multiplier-type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a re-estimation of the parameters in each bootstrap replication. Simulations and empirical applications to daily exchange rate data highlight the merits of our approach.

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“…setup with conditioning on covariates, Delgado and Stute (2008) proposed a consistent test using a two-parameter empirical process coupled with a Khmaladze martingale transformation. In a time series setup, where a Kolmogorov-type test does not capture misspecification in the dynamics, Kheifets (2015) proposed a test based on a multi-parameter empirical process and used a bootstrap to obtain critical values.…”

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confidence: 99%

Multivariate specification tests based on a dynamic Rosenblatt transform

Kheifets

2018

Computational Statistics & Data Analysis

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This paper considers parametric model adequacy tests for nonlinear multivariate dynamic models. It is shown that commonly used Kolmogorov-type tests do not take into account cross-sectional nor time-dependence structure, and a test, based on multi-parameter empirical processes, is proposed that overcomes these problems. The tests are applied to a nonlinear LSTAR-type model of joint movements of UK output growth and interest rate spreads. A simulation experiment illustrates the properties of the tests in finite samples. Asymptotic properties of the test statistics under the null of correct specification and under the local alternative, and justification of a parametric bootstrap to obtain critical values, are provided.

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Specification Tests for Nonlinear Dynamic Models

Cited by 5 publications

References 43 publications

PARX model for football match predictions

PARX model for football match predictions

Nonparametric bootstrap tests for independence of generalized errors

Multivariate specification tests based on a dynamic Rosenblatt transform

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