Asymptotics for general nonstationary fractionally integrated
processes without prehistoric influence

Wang, Qiying; Lin, Yang; Gulati, Chandra

doi:10.1155/s1173912602000184

Cited by 6 publications

(11 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In principle, this work meshes the idea behind the latter article with the results on the asymptotics for fractionally integrated processes presented in Wang et al . (). The results from the latter article were chosen particularly for their weak assumptions.…”

Section: Resultsmentioning

confidence: 97%

“…However, as discussed in Wang et al . (), for the purpose set out here, this assumption can be significantly weakened to the one stated earlier. Assumption (c) is the same as assumption

A_{2}

in Cavaliere and Xu () and is also required by Wang et al .…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 93%

“…Assumption (c) is the same as assumption

A_{2}

in Cavaliere and Xu () and is also required by Wang et al . (). Assumptions (d) and (e) are similar but different from assumptions

B_{1}

and

B_{2}

in Cavaliere and Xu ().…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 97%

“…Then, for d > − 1/2,

{true (κ^{2} (d) T^{2 (d + 1 / 2)})}^{- 1 / 2} \sum_{j = 1}^{[T_{t}]} w_{t} \Rightarrow \int_{0}^{italict} {(t - s)}^{d} normald W ((), s), 0 \leq t \leq 1.

Proof Lemma is Corollary 2 in Wang et al . ().□…”

Section: Asymptotic Analysis Of the Rfi(d) Processmentioning

confidence: 97%

“…If we now assume that only terms with a positive time index are of interest, as is the case in practice, then it can be shown (see Appendix 2 of Wang et al . ()) that z t reduces to

z_{t} = {((), 1 - B)}_{+}^{- d} u_{t} \equiv Δ_{+}^{- d} u_{t} = \sum_{k = 0}^{t - 1} c_{k}^{((), d)} u_{t - k},

where

c_{k}^{((), d)} = \frac{Γ (d + k)}{Γ (d) Γ (k + 1)}, k \geq 0, c_{0}^{((), 0)} = 1, c_{k}^{((), 0)} = 0, k \geq 1 .

…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 99%

See 4 more Smart Citations

Regulated fractionally integrated processes

Trokić

2013

Journal Time Series Analysis

View full text Add to dashboard Cite

Regulated (bounded) integrated time series are of significant practical importance and a recent development in the time series literature. Although regulated integrated series are characterized by asymptotic distributions that differ substantially from their unregulated counterparts, most inferential exercises continue to be performed with complete disregard for this potential feature of time series data. To date, only Cavaliere (2005) and Cavaliere and Xu (2011) have attempted to develop a theory for regulated integrated time series, particularly in the context of unit root testing. Unfortunately, no such theory has been developed for regulated fractionally integrated series, which are particularly important in financial time series and also in some unit root testing literature. This article achieves just this: it establishes a framework for regulated fractionally integrated processes and develops their functional central limit distributions. In addition, this article presents some simulation evidence and discusses several algorithms for obtaining the limiting distributions for these processes.

show abstract

Section: Resultsmentioning

confidence: 97%

“…However, as discussed in Wang et al . (), for the purpose set out here, this assumption can be significantly weakened to the one stated earlier. Assumption (c) is the same as assumption

A_{2}

in Cavaliere and Xu () and is also required by Wang et al .…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 93%

“…Assumption (c) is the same as assumption

A_{2}

in Cavaliere and Xu () and is also required by Wang et al . (). Assumptions (d) and (e) are similar but different from assumptions

B_{1}

and

B_{2}

in Cavaliere and Xu ().…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 97%

“…Then, for d > − 1/2,

{true (κ^{2} (d) T^{2 (d + 1 / 2)})}^{- 1 / 2} \sum_{j = 1}^{[T_{t}]} w_{t} \Rightarrow \int_{0}^{italict} {(t - s)}^{d} normald W ((), s), 0 \leq t \leq 1.

Proof Lemma is Corollary 2 in Wang et al . ().□…”

Section: Asymptotic Analysis Of the Rfi(d) Processmentioning

confidence: 97%

“…If we now assume that only terms with a positive time index are of interest, as is the case in practice, then it can be shown (see Appendix 2 of Wang et al . ()) that z t reduces to

z_{t} = {((), 1 - B)}_{+}^{- d} u_{t} \equiv Δ_{+}^{- d} u_{t} = \sum_{k = 0}^{t - 1} c_{k}^{((), d)} u_{t - k},

where

c_{k}^{((), d)} = \frac{Γ (d + k)}{Γ (d) Γ (k + 1)}, k \geq 0, c_{0}^{((), 0)} = 1, c_{k}^{((), 0)} = 0, k \geq 1 .

…”

Section: Regulated Fractionally Integrated Processesmentioning

confidence: 99%

See 3 more Smart Citations

Regulated fractionally integrated processes

Trokić

2013

Journal Time Series Analysis

View full text Add to dashboard Cite

show abstract

A nonparametric unit root test under nonstationary volatility

Eroğlu

Yigit

2016

Economics Letters

View full text Add to dashboard Cite

Invariance principles for fractionally integrated nonlinear processes

Wu¹,

Shao²

2006

Institute of Mathematical Statistics Lecture Notes - Monograph Series

View full text Add to dashboard Cite

We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory linear processes to a more general setting. The invariance principles are applied to the popular R/S and KPSS tests.Comment: Published at http://dx.doi.org/10.1214/074921706000000572 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

show abstract

Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence

Cited by 6 publications

References 17 publications

Regulated fractionally integrated processes

Regulated fractionally integrated processes

A nonparametric unit root test under nonstationary volatility

Invariance principles for fractionally integrated nonlinear processes

Contact Info

Product

Resources

About