摘要:

Abstract.The performance of the Geweke‐Porter‐Hudak (GPH) test, the modified rescaled range (MRR) test and two Lagrange multiplier (LM) type tests for fractional integration in small samples is examined using Monte Carlo methods. Both the GPH and MRR tests are found to be robust to moderate autoregressive moving‐average components, autoregressive conditional heteroskedasticity effects and shifts in the variance. However, these two tests are sensitive to large autoregressive moving‐average components and shifts in the mean. It is also found that the LM tests are sensitive to deviations from the null hypothesis. As an illustration, the GPH test is applied to two economic data

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00149.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.A general Akaike‐type procedure is studied where the additive penalty is proportional to the autoregression order but the constant of proportionality has a general valueγ. For the procedure to be weakly consistent it is necessary and sufficient thatγ→0 andnγ∝ asn∝, wherendenotes the sample size. Ifn1‐εγ∝ for some ε>0 then the probability of erring when estimating the autoregression order converges to zero at a raten‐c, for allc>0, asn→∝. However, several procedures suggested for practical use haven1‐εγ→0 for each ε>0; in particular, they haveγ=n‐1lognorγ=n‐1log logn. To elucidate the properties of error probabilities in these circumstances we study the case of an AR(1) process. It is shown that in this case the probability of underestimating order is usually substantially less then the chance of overestimation, unless the autoregressive constant is particu

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00150.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.Assuming a normal distribution we supplement the proof of periodogram regression suggested by Geweke and Porter‐Hudak (J. Time Ser. Anal.4 (1983) 221–38) in order to estimate and test the difference parameter of fractionally integrated autoregressive moving‐average models. The procedure proposed by Kashyap and Eom (J. Time Ser. Anal.9 (1988) 35–41) arises as a special case and is found to be correct if the true parameter value is negative. Regression of the smoothed periodogram yields estimators for the difference parameter with much faster vanishing variance; no asymptotic distribution can be derived, however. In computer experiments we find that the smoothed periodogram regression may be superior to pure periodogram regression when we have to discriminate between autoregression and fractional int

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00151.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.A frequency domain smoothing procedure is presented which provides variance estimates for linear functions of the periodogram. The method provides consistent estimates of the true asymptotic variance, has good small‐sample efficiency properties in the Gaussian case and reflects non‐Gaussian structure. The relationship of the estimates to frequency domain bootstrap algorithms is discus

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00152.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.Suppose that {Xt} is a Gaussian stationary process with spectral densityf(Λ). In this paper we consider the testing problem, whereK(Λ) is an appropriate function andcis a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based onK{fn(Λ)}dΛwherefn(Λ) is a non‐parametric spectral estimator off(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00153.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.Let {X(n)} be a non‐observed strictly stationary process, {a(n)} a sequence independent of {X(n)} andY(n) =a(n)X(n) the observed process. This work deals with the estimation of the spectral density functionfx(Λ) of the process of interest, {X(n)}, using observations of the modulated process {Y(n)}. We obtain estimators offx(Λ) for three types of modulating functions:deterministic, random independent and random correla

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00154.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.An AIC type estimator for the number of cosinusoids is studied. The estimator is proved to be strongly consistent in the presence of colored noise.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00155.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY