Noncausal vector AR processes with application to economic time series

Davis, Richard A.; Song, Li

doi:10.1016/j.jeconom.2020.01.017

Cited by 18 publications

(20 citation statements)

References 16 publications

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“…Using obvious notations, we then have:Ṽ t = (I −ΘL)ε t . Note that the eigenvalues ofΘ are the roots of det Θ(L) [see Davis and Song (2012) and Gouriéroux and Jasiak (2017) where the problem is completely treated in the dual case, where the roots of det Φ(L) can be inside or outside the unit circle].…”

Section: Recovering Structural Shocksmentioning

confidence: 99%

Identification and Estimation in Non-Fundamental Structural VARMA Models

Gouriéroux

Monfort

Renne

2019

The Review of Economic Studies

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Abstract The basic assumption of a structural vector autoregressive moving average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is “static” and is due to the fact that there is an infinite number of linear transformations of a given random vector making its components uncorrelated. The second identification problem is “dynamic” and is a consequence of the fact that, even if a SVARMA admits a non-invertible moving average (MA) matrix polynomial, it may feature the same second-order dynamic properties as a VARMA process in which the MA matrix polynomials are invertible (the fundamental representation). The aim of this article is to explain that these difficulties are mainly due to the Gaussian assumption, and that both identification challenges are solved in a non-Gaussian framework if the structural shocks are assumed to be instantaneously and serially independent. We develop new parametric and semi-parametric estimation methods that accommodate non-fundamentalness in the MA dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.

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Section: Recovering Structural Shocksmentioning

confidence: 99%

Identification and Estimation in Non-Fundamental Structural VARMA Models

Gouriéroux

Monfort

Renne

2019

The Review of Economic Studies

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“…So far results for the (vector) AR models have been derived under the assumption that the innovations " t have mean zero, and a …nite variance 2 , or some time-varying, possibly conditional, variance 2 t when discussing heteroskedasticity. To allow for more extreme events, and phenomena such as "bubble" periods with local explosive behavior, this assumption was relaxed in Davis and Resnick (1985a, 1985b, 1986 and Davis and Song (2020) where the i.i.d. innovations " t are allowed to have in…nite variance.…”

Section: Heavy-tailed Autoregressive Modelsmentioning

confidence: 99%

An Introduction to Bootstrap Theory in Time Series Econometrics

2020

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This article provides an introduction to methods and challenges underlying application of the bootstrap in econometric modelling of economic and …nancial time series. Validity, or asymptotic validity, of the bootstrap is discussed as this is a key element in deciding whether the bootstrap is applicable in empirical contexts. That is, as detailed here, bootstrap validity relies on regularity conditions, which need to be veri…ed on a case-by-case basis. To …x ideas, asymptotic validity is discussed in terms of the leading example of bootstrap-based hypothesis testing in the well-known …rst order autoregressive model. In particular, bootstrap versions of classic convergence in probability and distribution, and hence of laws of large numbers and central limit theorems, are discussed as crucial ingredients to establish bootstrap validity. Regularity conditions and their implications for possible improvements in terms of (empirical) size and power for bootstrap-based testing, when compared to asymptotic testing, are illustrated by simulations. Following this, an overview of selected recent advances in the application of bootstrap methods in econometrics is also given.

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“…However, for the sake of completeness, we do not rule out the alternative representation (3). Note that Davis and Song () propose a different way to characterize the MVAR, which does not involve the multiplicative structure of lag and lead polynomial coefficient matrices from the outset. Even though Gouriéroux and Jasiak () prove that this alternative representation is more general than the multiplicative one, we adhere to the representations in (1) and (3) as they offer a more explicit and natural way to disentangle the ‘causal’ and ‘non‐causal’ parts of the process.…”

Section: Causal and Non‐causal Modelsmentioning

confidence: 99%

“…The non‐causal VAR has been investigated in the literature to a much lesser extent and is defined as the analogue model in reverse time (see e.g. Davis and Song, ; Lanne and Saikkonen, ; Gouriéroux and Jasiak, ). In this framework, variables are modelled to depend on their future values.…”

Section: Introductionmentioning

confidence: 99%

Detecting Co‐Movements in Non‐Causal Time Series

2018

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This paper introduces the notion of common non-causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non-causal (i.e. forward-looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non-causal VAR processes of order P > 1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward-or forward-looking dynamics of the series. The proposed definitions of co-movements are also valid for the mixed causal-non-causal VAR, with the exception that a non-Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co-movements are found in a conventional causal VAR, but they are detected when considering a purely non-causal VAR. ). We thank the participants for helpful comments and suggestions. Additionally, we are greatly in debt to Lenard Lieb for fruitful discussions and two anonymous referees for valuable comments and suggestions.

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Noncausal vector AR processes with application to economic time series

Cited by 18 publications

References 16 publications

Identification and Estimation in Non-Fundamental Structural VARMA Models

Identification and Estimation in Non-Fundamental Structural VARMA Models

An Introduction to Bootstrap Theory in Time Series Econometrics

Detecting Co‐Movements in Non‐Causal Time Series

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