Limit theorems for functionals of moving averages

Ho, Hwai Chung; Hsing, Tailen

doi:10.1214/aop/1023481106

Cited by 133 publications

(130 citation statements)

References 36 publications

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“…The proofs of the present paper (with the exception of Lem. 2.8) are also much simpler than those of Ho and Hsing [18].…”

Section: Remark 24mentioning

confidence: 94%

“…, n; however, its proof is rather involved. The convergences (17,18) easily follow from Lemma 2 whose proof is more simpler. Let us prove (17) (the proof of (18) is analogous).…”

Section: Proof Of Theorem 22mentioning

confidence: 95%

“…Some of the results of Theorems 2.2 and 2.6 referring to the volatility process V t follow from Ho and Hsing [18], who studied limit theorems for sums of general instantenous functionals of moving averages. However, their paper does not discuss functional convergence nor the asymptotics of covariance functions as in Theorem 2.1.…”

Section: Remark 24mentioning

confidence: 99%

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Long memory properties and covariance structure of the EGARCH model

Сургайлис¹,

Viano

2002

ESAIM: PS

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Abstract. The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a hyperbolic decay of the later covariance implies a similar hyperbolic decay of the former covariances. We show, in this case, that normalized partial sums of powers of the observed process tend to fractional Brownian motion. The paper also obtains a (functional) CLT for the corresponding partial sums' processes of the EGARCH model with short and moderate memory. These results are applied to study asymptotic behavior of tests for long memory using the R/S statistic.Mathematics Subject Classification. 60F17, 62M10, 91B70, 91B84.

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“…The proofs of the present paper (with the exception of Lem. 2.8) are also much simpler than those of Ho and Hsing [18].…”

Section: Remark 24mentioning

confidence: 94%

“…, n; however, its proof is rather involved. The convergences (17,18) easily follow from Lemma 2 whose proof is more simpler. Let us prove (17) (the proof of (18) is analogous).…”

Section: Proof Of Theorem 22mentioning

confidence: 95%

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Long memory properties and covariance structure of the EGARCH model

Сургайлис¹,

Viano

2002

ESAIM: PS

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“…The asymptotic behavior of S ψ for fractionally integrated processes depends on the value of d and on the properties of ψ and Y, and may be determined on a case-by-case basis, under additional assumptions about ψ and Y, by relying on the results in Ho and Hsing (1997), Koul andSurgailis (1997), andHo (2002), inter alia.…”

Section: Problem Assumptions and Test Statisticsmentioning

confidence: 99%

“…W being a real-valued Gaussian random measure on R with Lebesgue control measure (Ho and Hsing (1997); Koul and Surgailis (1997)). Similarly, for any r ∈ N such that |ξ 0 | 2r is integrable, n −1/2 U r is asymptotically normal, as n → ∞, when…”

Section: Problem Assumptions and Test Statisticsmentioning

confidence: 99%

Using the Bootstrap to Test for Symmetry Under Unknown Dependence

Psaradakis

2016

Journal of Business & Economic Statistics

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This paper considers tests for symmetry of the one-dimensional marginal distribution of fractionally integrated processes. The tests are implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the relevant test statistics. The sieve bootstrap allows inference on symmetry to be carried out without knowledge of either the memory parameter of the data or of the appropriate norming factor for the test statistic and its asymptotic distribution. The small-sample properties of the proposed method are examined by means of Monte Carlo experiments, and applications to real-world data are also presented.

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Estimation of Short- and Long-Term VaR for Long-Memory Stochastic Volatility Models

Ho¹,

Liu²

2010

Handbook of Quantitative Finance and Risk Management

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Limit theorems for functionals of moving averages

Cited by 133 publications

References 36 publications

Long memory properties and covariance structure of the EGARCH model

Long memory properties and covariance structure of the EGARCH model

Using the Bootstrap to Test for Symmetry Under Unknown Dependence

Estimation of Short- and Long-Term VaR for Long-Memory Stochastic Volatility Models

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