Fractional Integration and Cointegration: An Overview and an Empirical Application

Gil-Alana, Luís A.; Hualde, Javier

doi:10.1057/9780230244405_10

Cited by 100 publications

(66 citation statements)

References 205 publications

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“…Therefore, shocks to pulp for paper production are more likely to be persistent. It can be noted that additional tests, like fractional integration, e.g., [37], could have been used to test for shocks.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of Wood Pulp Production: Evidence from OECD Countries

Jaunky

Lundmark

2017

Forests

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This paper investigates whether shocks to pulp for paper production for 17 Organisation for Economic Co-Operation and Development (OECD) members over the period 1980-2012 are transitory or permanent. A variety of univariate and panel data unit root tests are employed. The presence of structural breaks is taken into account when performing those tests. Based on the Narayan-Popp univariate unit root test, wood production series for approximately 64.71% of countries is found to follow a non-stationary process. However, univariate unit root tests tend to have low power when the time span is relatively short. Consequently, three generations of panel unit root tests are considered. Cross-sectional dependence is detected. The first generation of unit roots do not effectively control for cross-sectional dependence, while the second and third generations do. The third generation accounts mainly for cross-sectional co-integration. As a confirmatory analysis, both unit root tests that tests for the null of non-stationarity and stationarity are considered. Most of the panel unit root tests point towards a non-stationary process. Hence, while these shocks can be transmitted to other economic sectors, past behaviours of wood production cannot be used for forecasting purposes. Forest conservation policies can have a permanent impact on pulp for paper production.

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Section: Discussionmentioning

confidence: 99%

Dynamics of Wood Pulp Production: Evidence from OECD Countries

Jaunky

Lundmark

2017

Forests

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“…In Assumption 4 about the true values, we include the condition that 0 ≤ d 0 − b 0 < 1/2 which appears to be perhaps the most empirically relevant range of values for d 0 − b 0 (see, e.g., Henry and Zaffaroni (2003), Gil-Alana and Hualde (2009), and the references in the Introduction), because in this case, β 0 X t is (asymptotically) stationary with mean zero. with eight moments; we later specify the existence of further moments needed for the asymptotic properties of the maximum likelihood estimator.…”

Section: Assumptionmentioning

confidence: 99%

“…1 We are very grateful to Jim Stock and five referees for many useful and constructive comments that were above and beyond the call of duty and led to significant improvements to the paper. Fractional processes are a useful tool for describing time series with slowly decaying autocorrelation functions and have played a prominent role in econometrics (see, e.g., Henry and Zaffaroni (2003) and Gil-Alana and Hualde (2009) for reviews and examples). A previous version of this paper was circulated under the title "Likelihood Inference for a Vector Autoregressive Model Which Allows for Fractional and Cofractional Processes."…”

Section: Introductionmentioning

confidence: 99%

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

2012

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We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X t to be fractional of order d and cofractional of order d b; that is, there exist vectors for which 0 X t is fractional of order d b:Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1=2 b d d 1 for any d 1 d 0 . To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also …nd the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

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“…In the standard I(1)/I(0) framework this includes Corbae and Ouliaris (1988) and Kim (1990), whereas in the fractional setting Cheung and Lai (1993) analysed a fractional version of the PPP model, which has recently been revisited by Gil-Alana and Hualde (2009), who employed the parametric techniques proposed by RH to discuss the plausibility of the absolute or homogeneous version of the PPP. Basically, these authors justified the fractionally cointegrated bivariate model…”

Section: Empirical Examplementioning

confidence: 99%

Semiparametric inference in multivariate fractionally cointegrated systems

Hualde

Robinson

2010

Journal of Econometrics

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a b s t r a c tA semiparametric multivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I(0) unobservable inputs having nonparametric spectral density. Two estimates of the vector of cointegrating parameters ν are considered. One involves inverse spectral weighting and the other is unweighted but uses a spectral estimate at frequency zero. Both corresponding Wald statistics for testing linear restrictions on ν are shown to have a standard null χ 2 limit distribution under quite general conditions. Notably, this outcome is irrespective of whether cointegrating relations are ''strong'' (when the difference between integration orders of observables and cointegrating errors exceeds 1/2), or ''weak'' (when that difference is less than 1/2), or when both cases are involved. Finite-sample properties are examined in a Monte Carlo study and an empirical example is presented.

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Fractional Integration and Cointegration: An Overview and an Empirical Application

Cited by 100 publications

References 205 publications

Dynamics of Wood Pulp Production: Evidence from OECD Countries

Dynamics of Wood Pulp Production: Evidence from OECD Countries

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

Semiparametric inference in multivariate fractionally cointegrated systems

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