Feasible invertibility conditions and maximum likelihood estimation for observation-driven models

Blasques, Francisco; Gorgi, Paolo; Koopman, Siem Jan; Wintenberger, Olivier

doi:10.1214/18-ejs1416

Cited by 45 publications

(20 citation statements)

References 44 publications

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“…Following the discussion in Blasques et al (), a sufficient condition for invertibility can be found by generalizing the result in Harvey and Lange (, p. 182). The proposition below is for the Beta‐t‐EGARCH‐M model, to , but with the ARCH‐M score term dropped from .…”

Section: Model Formulationmentioning

confidence: 86%

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Harvey

Lange

2018

Journal Time Series Analysis

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An EGARCH-M model, in which the logarithm of scale is driven by the score of the conditional distribution, is shown to be theoretically tractable as well as practically useful. A two-component extension makes it possible to distinguish between the short-and long-run effects of returns on volatility, and the resulting short-and long-run volatility components are then allowed to have different effects on returns, with the long-run component yielding the equity risk premium. The EGARCH formulation allows for more flexibility in the asymmetry of the volatility response (leverage) than standard GARCH models and suggests that, for weekly observations on two major stock market indices, the short-term response is close to being anti-symmetric. component, as found by Engle and Lee (1999) and others. Indeed, short-run volatility may even decrease after a good day, because it calms the market. Standard GARCH models are unable to identify this effect.Adrian and Rosenberg (2008) proposed a two-component exponential GARCH-M (EGARCH-M) model. They showed that it captures the asymmetric response of short-and long-term volatility to returns, and that the long-run component is positively correlated with the equity risk premium. Here we demonstrate that letting the dynamics be driven by the score of the conditional distribution yields a model that is theoretically tractable as well as practically useful. Models constructed using the conditional score were introduced into the literature by Creal et al. (2011Creal et al. ( , 2013, where they are called Generalized Autoregressive Score (GAS) models, and Harvey (2013), where they are called Dynamic Conditional Score (DCS) models. The classic EGARCH specification in Nelson (1991), which is the one used by Adrian and Rosenberg, is sensitive to outliers and it has the unfortunate theoretical property that unconditional moments do not exist when the conditional distribution is Student's t. The DCS model resolves these problems and, in doing so, yields a specification which is open to the development of a full asymptotic theory for the distribution of the maximum likelihood estimator. This contrasts with standard formulations of ARCH-M models, where the asymptotic theory appears to be intractable.Section 2 sets out the DCS formulation of the basic EGARCH-M model with a conditional Student's t-distribution and outlines the associated statistical theory, including an easily implemented condition for invertibility. This is followed by subsections on the asymmetric response of volatility to returns (leverage), two components, skewness and splines. In Section 3 various models are fitted to weekly data on NASDAQ and NIKKEI returns. The risk-free rate of return is then introduced as an explanatory variable, as in Scruggs (1998), and the model is fitted to weekly excess returns on S&P500 over a 60-year period. Section 4 reports the results of a small forecasting study to provide reassurance on the predictive performance of DCS models. Section 5 concludes. Appendices A to C are provided online as Ap...

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Section: Model Formulationmentioning

confidence: 86%

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Harvey

Lange

2018

Journal Time Series Analysis

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“…Condition A3 ensures thatμ t (•) converges to a stationary and ergodic F t−1 -measurable functionμ t (•) as t → ∞. This is typically referred in the literature as invertibility (Straumann and Mikosch, 2006;Blasques et al, 2018). Condition A4 sets bounds on the updating function.…”

Section: A7mentioning

confidence: 99%

Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects

Gorgi

Koopman

2020

SSRN Journal

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We consider a general class of observation-driven models with exogenous regressors for double bounded data that are based on the beta distribution. We obtain a stationary and ergodic beta observation-driven process subject to a contraction condition on the stochastic dynamic model equation. We derive conditions for strong consistency and asymptotic normality of the maximum likelihood estimator. The general results are used to study the properties of a beta autoregressive process with threshold effects and to establish the asymptotic properties of the maximum likelihood estimator. We employ the threshold autoregressive model with leverage effects to analyze realized correlations for several sets of stock returns. We find that the impact of past values of realized correlation on future values is at least 10% higher when stock returns are negative rather than positive. This finding supports the conjecture that correlation between stock returns tends to be higher when stock prices are falling, and lower when there is a surge in stock prices. Finally, we conduct an out-of-sample study that shows that our model with leverage effects can enhance the accuracy of point and density forecasts of realized correlations.

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“…Due to the dependence on moving averages that are not available as difference combinations for the first q periods are unavailable, the algorithm requires an initialization ofε t for t ≤ q. As T → ∞, the impact of the initialization on the filter fades exponentially fast almost surely for a stationary process, see for example Blasques et al (2018). For small T however, the impact remains.…”

Section: Penalized Estimationmentioning

confidence: 99%

“…See for exampleBlasques et al (2018) for results on the relation between filters and DGP s. 7 Proofs for Stationarity and Ergodicity of data generated by VARMA models are widespread and can be found for example in(Nsiri and Roy, 1993) Stelzer (2008). treat multivariate Generalized ARMA models including nonidentity links,(Zheng et al, 2015) treat nonlinear theory for Multivariate Markov-switching ARMA processes, finallyAndree et al (2017) show that multivariate ARMA structures can generate geometrically Ergodic data even when a nonlinear observation-driven spatial dependence process is considered.…”

mentioning

confidence: 99%

Pollution and Expenditures in a Penalized Vector Spatial Autoregressive Time Series Model with Data-Driven Networks

Andrée

Spencer

Chamorro

et al. 2019

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The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

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Feasible invertibility conditions and maximum likelihood estimation for observation-driven models

Cited by 45 publications

References 44 publications

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Modeling the Interactions between Volatility and Returns using EGARCH‐M

Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects

Pollution and Expenditures in a Penalized Vector Spatial Autoregressive Time Series Model with Data-Driven Networks

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