Bootstrap and Asymptotic Tests of Long‐run Relationships in Cointegrated Systems

Fachin, Stefano

doi:10.1111/1468-0084.00187

Cited by 20 publications

(14 citation statements)

References 20 publications

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“…Previous simulation studies of bootstrap tests on co-integrating relations in VAR models include Fachin (2000), Gredenhoff and Jacobson (2001), and Omtzigt and Fachin (2006). Compared to these, the Monte Carlo simulation study reported here differs substantially.…”

Section: B4 Summary Of Results and Relation To Existing Literaturementioning

confidence: 89%

“…More specifically, Fachin (2000) considers empirical size and power of a bootstrap version of the Wald test, using a bootstrap generating process (BGP) based on restricted estimates and i.i.d. resampling of unrestricted residuals.…”

Section: B4 Summary Of Results and Relation To Existing Literaturementioning

confidence: 99%

“…Bootstrap schemes based on restricted parameter estimates were originally proposed without theory in Fachin (2000) and Gredenhoff and Jacobson (2001); see also Li andMaddala (1996, 1997) for the case of co-integrating regressions. Based on simulations, they suggest to estimate (1) under H 0 and then use the corresponding (restricted) estimatesα, τ, andΓ i , i = 1 k − 1, in the bootstrap generating process (BGP).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

Cavaliere¹,

Nielsen²,

Rahbek³

2015

Econometrica

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It is well known that the finite‐sample properties of tests of hypotheses on the co‐integrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett‐type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic χ2 tests fail most severely. In this paper, we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co‐integration rank (Cavaliere, Rahbek, and Taylor, 2012), establishing the validity of the bootstrap in the framework of hypotheses on the co‐integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein–Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.

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Section: B4 Summary Of Results and Relation To Existing Literaturementioning

confidence: 89%

Section: B4 Summary Of Results and Relation To Existing Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

Cavaliere¹,

Nielsen²,

Rahbek³

2015

Econometrica

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“…The relatively small sample size of available data is the main constraint that delimits the available techniques to be used to only a couple of them that can potentially provide more valuable results: the ARDL model (see for example, Caporale and Chui 1999;Boyd et al 2001) and the bootstraps technique (a combination of bootstraps on cointegration is provided by Fachin 2000). In this paper, the latter will not be included due to space limitations.…”

Section: Econometric Backgroundmentioning

confidence: 99%

Trade liberalization and lagged reactions of trade flows, productivity and internal demand: an application to the Australian PMV industry

Sanidas

Jayanthakumaran

2007

Journal of the Asia Pacific Economy

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A literature review regarding the consequences of trade liberalization on trade flows, productivity and internal demand has led us to consider a simple operational model of how to measure these consequences. This model is applied to the passenger motor vehicle (PMV) industry in Australia. There is clear evidence that this liberalization has increased the volume of trade and productivity, but reduced the locally produced cars for internal consumption. In addition, there are significant estimated lags concerning the reaction of these variables as a consequence of trade liberalization. Econometrically, this paper is an application of the bounds-testing procedure based on the Autoregressive Distributed Lag (ARDL) approach to cointegration.

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“…Hence, the asymptotic LR test is consistent. Now, consider a restricted bootstrap for H 0 , as initially proposed in Fachin (2000), Gredenho¤ and Jacobson (2001) and later discussed in Fachin and Omzigt (2006). This bootstrap requires estimation of (14) under H 0 and then use the corresponding (restricted) estimates~ n and to generate the bootstrap sample as…”

Section: Preliminaries and Bootstrap Consistencymentioning

confidence: 99%

A Primer on Bootstrap Testing of Hypotheses in Time Series Models: With an Application to Double Autoregressive Models

Cavaliere

Rahbek

2019

SSRN Journal

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In this paper we discuss the general application of the bootstrap as a tool for statistical inference in econometric time series models. We do this by considering the implementation of bootstrap inference in the class of double-autoregressive [DAR] models discussed in Ling (2004). DAR models are particularly interesting to illustrate implementation of the bootstrap to time series: …rst, standard asymptotic inference is usually di¢ cult to implement due to the presence of nuisance parameters under the null hypothesis; second, inference involves testing whether one or more parameters are on the boundary of the parameter space; third, under the alternative hypothesis, fourth or even second order moments may not exist. In most of these cases, the bootstrap is not considered an appropriate tool for inference. Conversely, and taking testing (non-) stationarity to illustrate, we show that although a standard bootstrap based on unrestricted parameter estimation is invalid, a correct implementation of a bootstrap based on restricted parameter estimation (restricted bootstrap) is …rst-order valid; that is, it is able to replicate, under the null hypothesis, the correct limiting null distribution. Importantly, we also show that the behaviour of this bootstrap under the alternative hypothesis may be di¤erent because of possible lack of …nite second-order moments of the bootstrap innovations. This features makes -for some parameter con…gurationsthe restricted bootstrap unable to replicate the null asymptotic distribution when the null is false. We show that this drawback can be …xed by using a new 'hybrid' bootstrap, where the parameter estimates used to construct the bootstrap data are obtained with the null imposed, while the bootstrap innovations are sampled with replacement from the unrestricted residuals. We show that this bootstrap, novel in this framework, mimics the correct asymptotic null distribution, irrespetively of the null to be true or false. Throughout the paper, we use a number of examples from the bootstrap time series literature to illustrate the importance of properly de…ning and analyzing the bootstrap generating process and associated bootstrap statistics.

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Bootstrap and Asymptotic Tests of Long‐run Relationships in Cointegrated Systems

Cited by 20 publications

References 20 publications

Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

Trade liberalization and lagged reactions of trade flows, productivity and internal demand: an application to the Australian PMV industry

A Primer on Bootstrap Testing of Hypotheses in Time Series Models: With an Application to Double Autoregressive Models

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