What is Fractional Integration?

Parke, William R.

doi:10.1162/003465399558490

Cited by 192 publications

(125 citation statements)

References 16 publications

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“…On the other hand, the limit process in (51) has independent increments while the summands have (covarance) long memory, meaning that this long memory does not persist in the distributional limit. A similar lack of persistence of long memory seems characteristic to some other econometric models, in particular to Parke's (1999) model (see Davidson and Sibbertsen, 2002). Similar properties were proved in for some models arising in telecommunications.…”

Section: Regime Switching Sv and Related Modelssupporting

confidence: 74%

Recent Advances in ARCH Modelling

Giraitis

Leipus

Сургайлис

Long Memory in Economics

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Section: Regime Switching Sv and Related Modelssupporting

confidence: 74%

Recent Advances in ARCH Modelling

Giraitis

Leipus

Сургайлис

Long Memory in Economics

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“…Various regime switching models leading to the long-memory property and related econometrical issues were discussed in Parke (1999), Liu (2000), Jensen and Liu (2006), Gourieroux and Jasiak (2001), Diebold and Inoue (2001), Leipus and Viano (2003), Davidson and Sibbertsen (2005), Granger and Hyung (2004), and Mikosch and Stȃricȃ (2004). Recently, Leipus and Surgailis (2003) and Leipus et al (2005) discussed the random-coefficient (autoregressive) AR(1) equation X t = a t X t−1 + ε t , t ∈ Z, (1.1)…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On a random-coefficient AR(1) process with heavy-tailed renewal switching coefficient and heavy-tailed noise

2006

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We discuss the limit behavior of the partial sums process of stationary solutions to the (autoregressive) AR(1) equation X t = a t X t−1 + ε t with random (renewalreward) coefficient, a t , taking independent, identically distributed values A j ∈ [0, 1] on consecutive intervals of a stationary renewal process with heavy-tailed interrenewal distribution, and independent, identically distributed innovations, ε t , belonging to the domain of attraction of an α-stable law (0 < α ≤ 2, α = 1). Under suitable conditions on the tail parameter of the interrenewal distribution and the singularity parameter of the distribution of A j near the unit root a = 1, we show that the partial sums process of X t converges to a λ-stable Lévy process with index λ < α. The paper extends the result of Leipus and Surgailis (2003) from the case of finite-variance X t to that of infinitevariance X t .

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“…Interested readers should consult some recent surveys which include Baillie (1996), Robinson (2003), and Doukhan, Oppenheim & M. S. Taqqu (2003). See also Parke (1999) for examples, intuition and discussion. Recent work in finance shows that volatility is a likely candidate for long memory even at Recently, high frequency financial data have revealed evidence for long memory in several series.…”

Section: Model Experimentsmentioning

confidence: 99%

The Impact of Imitation on Long Memory in an Order-Driven Market

LeBaron

Yamamoto

2008

Eastern Econ J

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Recent research has documented that learning and evolution are capable of generating many well known features in financial times series. We extend the results of LeBaron & Yamamoto (2007) to explore the impact of varying amounts of imitation and agent learning in a simple order driven market.We show that in our framework, imitation is critical to the generation of long memory persistence in many financial time series. This shows that imitation across trader behavior is probably crucial for understanding the dynamics of prices and trading volume.JEL Classification: G12, G14, D83

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What is Fractional Integration?

Cited by 192 publications

References 16 publications

Recent Advances in ARCH Modelling

Recent Advances in ARCH Modelling

On a random-coefficient AR(1) process with heavy-tailed renewal switching coefficient and heavy-tailed noise

The Impact of Imitation on Long Memory in an Order-Driven Market

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