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36
Inference on the Cointegration Rank in Fractionally Integrated Processes
, 2000
"... For univariate time s eie we sugge t a n e variant ofe #cie t score te ts against fractional alte native s. This te t has thr e important me rits. First, by meK s of simulations we obs e ve that it is supe rior in te ms of size and powe r in some situations of practical intee st. Se cond, it ise asi ..."
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Cited by 26 (2 self)
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For univariate time s eie we sugge t a n e variant ofe #cie t score te ts against fractional alte native s. This te t has thr e important me rits. First, by meK s of simulations we obs e ve that it is supe rior in te ms of size and powe r in some situations of practical intee st. Se cond, it ise asilyunde rstood and imple me nte d as a slight modification of the DickeFulle te t, although our score te t has a limiting normal distribution. Third and most important, our te st ge ne ralize s to multivariate cointen ation teK just as the Dicke#4 ulle teN doe s. Thus it allows to de te mine the cointen ation rankof fractionally inte4 ate time se ri e . It doe s so by solving a ge ealize eize value prob le of the type propos e by Johans e (1988). Howe e , the limiting distribution of the corre sponding trace statistic is # 2 ,whe re the de gre e s offre e domde pe nd only on the cointe gration ranunde r the null hypothe sis.The use fulne ss of the asymptotic the ory for finite sample ise stablishe d in a Monte Carlo eke rime nt. #The first author grateENE4 acknowleK e s financial support from the Sonderforschungsbereich 373 of the DFG. We than Luis GilAlana, Eiji Kurozumi, thr e anonymous r eeNeN and the participants of the Cardi# Confe re ce on Long Me ory and NonlineN Time Se riek July 9th11th 2000, for he pful comme nts and sugge2 ions. 1 1 IntroductiW With his seminal paper introdu9z3 fractional integration and cointegration Granger (1981) opened a pro du tive research avenu . Since then cointegration techniquz have become standard in the econometrician's tool kit. Fractional cointegration techniqu es, however, are still to be developed, see Robinson (1994a) and Baillie (1996) for overviews on fractional integration in econometrics. A vector of time series variab...
Gaussian semiparametric estimation of fractional cointegration
 Journal of Time Series Analysis
, 2003
"... Abstract. We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multivariate Gaussian semiparametric estimate, b ..."
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Cited by 25 (2 self)
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Abstract. We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multivariate Gaussian semiparametric estimate, based on initial consistent estimates and possibly tapered observations, is asymptotically normal. The estimates of the memory parameters can rely either on original (for stationary errors) or on differenced residuals (for nonstationary errors) assuming only a convergence rate for a preliminary slope estimate. If this rate is fast enough, semiparametric memory estimates are not affected by the use of residuals and retain the same asymptotic distribution as if the true cointegrating relationship were known. Only local conditions on the spectral densities around zero frequency for linear processes are assumed. We concentrate on a bivariate system but discuss multivariate generalizations and show the performance of the estimates with simulated and real data.
A Model of Fractional Cointegration, and Tests Cointegration Using the Bootstrap
 Journal of Econometrics
, 2001
"... The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simu ..."
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Cited by 24 (7 self)
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The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of noncointegration in a vector autoregressive modelling framework. The simulations are used to estimate pvalues for alternative regressionbased test statistics, including the F goodnessoffit statistic, the DurbinWatson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residualbased tests, although the DurbinWatson in turn dominates the test based on the residual d.
Periodic heteroskedastic RegARFIMA models for daily electricity spot prices
 Tinbergen Institute Discussion Paper, TI
, 2003
"... for daily electricity spot prices ..."
Maximum likelihood estimation of stationary multivariate ARFIMA processes
, 2007
"... This paper considers the maximum likelihood estimation (MLE) of a class of stationary and invertible vector autoregressive fractionally integrated movingaverage (VARFIMA) processes considered in (26) of Luceño [1] or Model A of Lobato [2] where each component yi,t is a fractionally integrated pro ..."
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Cited by 6 (0 self)
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This paper considers the maximum likelihood estimation (MLE) of a class of stationary and invertible vector autoregressive fractionally integrated movingaverage (VARFIMA) processes considered in (26) of Luceño [1] or Model A of Lobato [2] where each component yi,t is a fractionally integrated process of order di, i = 1,..., r. Under the conditions outlined in Assumption 1 of this paper, the conditional likelihood function of this class of VARFIMA models can be efficiently and exactly calculated with a conditional likelihood DurbinLevinson (CLDL) algorithm proposed herein. This CLDL algorithm is based on the multivariate DurbinLevinson algorithm of Whittle [3] and the conditional likelihood principle of Box and Jenkins [4]. Furthermore, the conditions in the aforementioned Assumption 1 are general enough to include the model considered in Andersen et al. [5] for describing the behavior of realized volatility and the model studied in Haslett and Raftery [6] for spatial data as its special cases. As the computational cost of implementing the CLDL algorithm is much lower than that of using the algorithms proposed in Sowell [7], we are thus able to conduct a Monte Carlo experiment to investigate the finite sample performance of the CLDL algorithm for the 3dimensional VARFIMA processes with the sample size of 400. The simulation results are very satisfactory and reveal the great potentials of using the CLDL method for empirical applications.
ResidualBased Tests for Fractional Cointegration: A Monte Carlo Study
, 1998
"... This paper reports on an extensive Monte Carlo study of seven residualbased tests of the hypothesis of no cointegration. Critical values and the power of the tests under the alternative of fractional cointegration are simulated and compared. It turns out that the PhillipsPerron ttest when applied ..."
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Cited by 6 (1 self)
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This paper reports on an extensive Monte Carlo study of seven residualbased tests of the hypothesis of no cointegration. Critical values and the power of the tests under the alternative of fractional cointegration are simulated and compared. It turns out that the PhillipsPerron ttest when applied to regression residuals is more powerful than GewekePorterHudak tests and the Augmented DickeyFuller test. Only the Modified Rescaled Range test is more powerful than the PhillipsPerron test in a few situations. Moreover in large samples, the power of the PhillipsPerron test increases if a time trend is included in the cointegrating regression.
A PureJump TransactionLevel Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects. Working paper
, 2008
"... We propose a new transactionlevel bivariate logprice model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lowerfrequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting ti ..."
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Cited by 5 (2 self)
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We propose a new transactionlevel bivariate logprice model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lowerfrequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times {τk} between trades, and a pair of stationary noise processes ({ek} and {ηk}) which determine the jump sizes in the purejump logprice process. Our model includes feedback between the disturbances of the two logprice series at the transaction level, which induces standard or fractional cointegration for any fixed sampling interval ∆t. We prove that the cointegrating parameter can be consistently estimated by the ordinary leastsquares estimator, and obtain a lower bound on the rate of convergence. We propose transactionlevel methodofmoments estimators of the other parameters in our model and discuss the consistency of these estimators.
A ReEvaluation of Empirical Tests of the Fisher Hypothesis
 Boston College Department of Economics
, 2000
"... We acknowledge suggestions oered by participants at the Fifth International Conference of the Society for ..."
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Cited by 3 (0 self)
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We acknowledge suggestions oered by participants at the Fifth International Conference of the Society for
A representation theory for polynomial cofractionality in vector autoregressive models. Econometric Theory, forthcoming
, 2009
"... We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given and it is shown under which condition the solution of the ..."
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Cited by 3 (3 self)
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We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given and it is shown under which condition the solution of the model is fractional of order d and displays cofractional relations of order d − b and polynomial cofractional relations of order d−2b,..., d−cb ≥ 0 for integer c; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For c = 1 and c = 2 we find the results of Johansen (2008).