Likelihood Inference for a Nonstationary Fractional Autoregressive Model

2017

SSRN Journal

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We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and show that the test statistic for the ususal CVAR model is asymptotically chi-squared distributed. Because the usual CVAR model lies on the boundary of the parameter space for the fractional CVAR in Johansen and Nielsen (2012a), the analysis requires the study of the fractional CVAR model on a slightly larger parameter space so that the CVAR model lies in the interior. This in turn implies some further analysis of the asymptotic properties of the fractional CVAR model.

“…which proves (11). Proof of (10) for the terms involving 0t : These terms are only present if d 0 1=2, which we therefore assume in the remainder of the proof.…”

Section: Assumption 4 the True Parameter Valuementioning

confidence: 75%

Testing the CVAR in the Fractional CVAR Model

Johansen

2017

SSRN Journal

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“…For the proof of Lemma A.3, see Lemma A.1 of Nielsen (2015) and Lemma B.3 of Johansen and Nielsen (2010), and for the proof of Lemma A.4, see Lemma B.4 of Johansen and Nielsen (2010).…”

Section: S33 Proofs Of Lemmas A3 and A4mentioning

confidence: 99%

“…The proof is given in Lemma C.3 in Johansen and Nielsen (2010), which also applies under Assumption 1 on ε t in place of their i.i.d. assumption.…”

Section: S42 Proof Of Lemma B1mentioning

confidence: 99%

Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form

Cavaliere

Journal of Econometrics

Taylor

2017

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We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-ofsquares estimators in the context of parametric fractional time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short memory parameters of the model. The limiting null distributions of these test statistics are shown to be non-pivotal under heteroskedasticity, while that of a robust Wald statistic (based around a sandwich estimator of the variance) is pivotal. We show that wild bootstrap implementations of the tests deliver asymptotically pivotal inference under the null. We demonstrate the consistency and asymptotic normality of the bootstrap estimators, and further establish the global consistency of the asymptotic and bootstrap tests under fixed alternatives. Monte Carlo simulations highlight significant improvements in finite sample behaviour using the bootstrap in both heteroskedastic and homoskedastic environments. Our theoretical developments and Monte Carlo simulations include two bootstrap algorithms which are based on model estimates obtained either under the null hypothesis or unrestrictedly. Our simulation results suggest that the former is preferable to the latter, displaying superior size control yet largely comparable power.

“…In our empirical analysis we use the FCVAR model of Johansen (2008) and Johansen and Nielsen (2010, 2012. This model is a generalization of Johansen's (1995) CVAR model to allow for fractional processes of order d that cointegrate to order d − b.…”

Section: The Fcvar Model With a Deterministic Linear Trendmentioning

confidence: 99%

“…This model is a generalization of Johansen's (1995) CVAR model to allow for fractional processes of order d that cointegrate to order d − b. However, the development of the model in Johansen (2008) and Johansen and Nielsen (2010, 2012 does not accommodate drift in prices, i.e. deterministic linear trends in the observed variables.…”

Section: The Fcvar Model With a Deterministic Linear Trendmentioning

confidence: 99%

A fractionally cointegrated VAR model with deterministic trends and application to commodity futures markets

Dolatabadi

Journal of Empirical Finance

2016

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. (aluminium, copper, lead, nickel, and zinc). To this end, we first extend the FCVAR model to accommodate deterministic trends in the levels of the processes. The methodological contribution is to provide representation theory for the FCVAR model with deterministic trends, where we show that the presence of the deterministic trend in the process induces both restricted and unrestricted constant terms in the vector error correction model. The consequences for the cointegration rank test are also briefly discussed. In our empirical application we use the data from FiguerolaFerretti and Gonzalo (2010), who conduct a similar analysis using the usual (non-fractional) cointegrated VAR model. The main conclusion from the empirical analysis is that, when using the FCVAR model, there is more support for the cointegration vector (1, −1) in the long-run equilibrium relationship between spot and futures prices, and hence less evidence of long-run backwardation, compared to the results from the non-fractional model. Specifically, we reject the hypothesis that the cointegration vector is (1, −1) using standard likelihood ratio tests only for the lead and nickel markets. Terms of use: Documents inJEL codes: C32, G14.