Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)

Agosto, Arianna; Cavaliere, Giuseppe; Kristensen, Dennis; Rahbek, Anders

doi:10.1016/j.jempfin.2016.02.007

Cited by 94 publications

(151 citation statements)

References 32 publications

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“…Fuller (1996, Theorem 9.1.1) shows asymptotic normality of the least squares estimator for a regression model with time series errors under even more general conditions which allow the presence of certain types of trends in the covariates. For the special case of a Poisson model with the identity link, Agosto, Cavaliere, Kristensen, and Rahbek (2015) show asymptotic normality of the MLE for a model with covariates that are functions of Markov processes with finite second moments and that are not collinearly related to the response. The asymptotic normality of the QMLE in our context is supported by the simulations presented in Appendix B.1.…”

Section: Estimation and Inferencementioning

confidence: 99%

tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models

Liboschik¹,

Fokianos²,

Fried³

2017

J. Stat. Soft.

174

163

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The R package tscount provides likelihood-based estimation methods for analysis and modeling of count time series following generalized linear models. This is a flexible class of models which can describe serial correlation in a parsimonious way. The conditional mean of the process is linked to its past values, to past observations and to potential covariate effects. The package allows for models with the identity and with the logarithmic link function. The conditional distribution can be Poisson or negative binomial. An important special case of this class is the so-called INGARCH model and its log-linear extension. The package includes methods for model fitting and assessment, prediction and intervention analysis. This paper summarizes the theoretical background of these methods. It gives details on the implementation of the package and provides simulation results for models which have not been studied theoretically before. The usage of the package is illustrated by two data examples. Additionally, we provide a review of R packages which can be used for count time series analysis. This includes a detailed comparison of tscount to those packages.

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Section: Estimation and Inferencementioning

confidence: 99%

tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models

Liboschik¹,

Fokianos²,

Fried³

2017

J. Stat. Soft.

174

163

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show abstract

“…One particular feature of the model in Equations is that, in the case of a single covariate, x t −1 = x t −1 , the expected value of the number of goals is given by

E ([], y_{t}) = E ([], λ_{t}) = \frac{ω + E ([], x_{t - 1})}{1 - \sum_{j = 1}^{\max false(p, q false)} ((), α_{j} + β_{j})}

and

var ([], y_{t}) ⩾ E ([], y_{t})

; that is, the model is able to capture overdispersion in the marginal distribution. The reader is referred to Agosto, Cavaliere, Cavaliere, and Rahbek, () for more details and properties of the PARX model.…”

Section: Modeling Football Goals With Parxmentioning

confidence: 99%

“…Following the formalization in Agosto et al (), the conditional log‐likelihood of the model in Equations for the parameter vector

θ = {((), ω, α_{1}, ⋯, α_{p}, β_{1}, ⋯, β_{q}, italicγ)}^{'}

is given by

ℓ_{T} (θ) = \sum_{t = 1}^{T} l_{t} (θ), l_{t} (θ) = y_{t} normall normalo normalg λ_{t} (θ) - λ_{t} (θ) .

The maximum likelihood estimator of θ is given by

\hat{θ} = \underset{θ}{arg max} ℓ_{T} (θ) .

The maximization problem in Equation is subject to the restrictions ω >0,

α_{1}, ⋯, α_{p}, β_{1}, ⋯, β_{q}, italicγ ⩾ 0

, and

\sum_{j = 1}^{\max false(p, q false)} ((), α_{j} + β_{j}) < 1

. The first set of conditions is required to ensure that λ t >0, while the latter is used to ensure the stability of the process.…”

Section: Modeling Football Goals With Parxmentioning

confidence: 99%

“…The second tool is the (randomized) probability integral transform (PIT) introduced by Brockwell () and generally adopted to evaluate the misspecification of Poisson autoregressive models as in Davis and Liu (), Agosto et al (), and Liboschik, Fokianos, and Fried (). For any t , the PIT is defined as

ũ_{t} = F_{t} false(y_{t} - 1 false) + υ_{t} false[F_{t} false(y_{t} false) - F_{t} false(y_{t} - 1 false) false],

where υ t is a sequence of i.i.d.…”

Section: Modeling Football Goals With Parxmentioning

confidence: 99%

“…All these results underscore the fact that the (marginal) empirical goals distribution is not a Poisson, and this is mainly due to overdispersion. As discussed in Agosto et al (, section 3), PARX models are able to capture overdispersion in marginal distributions and therefore are potentially suitable for analyzing and forecasting the dynamics of the goals distribution.…”

Section: Forecasting Football Matches With Parxmentioning

confidence: 99%

See 2 more Smart Citations

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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References

2018

An Introduction to Discrete‐Valued Time Series

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Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)

Cited by 94 publications

References 32 publications

tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models

tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models

PARX model for football match predictions

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