Why Farima Models Are Brittle

Veitch, Darryl; Gorst‐Rasmussen, Anders; Gefferth, András

doi:10.1142/s0218348x13500126

Cited by 6 publications

(4 citation statements)

References 21 publications

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“…In this regard, the restriction on the sum of the coefficients in the moving average representation may be too strict for real data. It takes but a small deviation on any of the infinite coefficients to violate this restriction, providing further evidence of the brittleness of fractionally differenced processes; see Veitch et al (2013). We showed that CSA(a, b) processes do not share these restrictions and are thus less brittle.…”

Section: Nonfractional Long-range Dependence and The Antipersistent Propertysupporting

confidence: 52%

“…Granger argued that fractionally integrated processes fall into the "empty box" category of theoretical developments that do not arise in the real economy. Moreover, Veitch et al (2013) argued that "time series whose long-range dependence scaling derives directly from fractional differencing [...] are far from typical when it comes to their long-range dependence character". Thus, this paper developed a long-range dependence framework based on cross-sectional aggregation, the most predominant theoretical explanation for the presence of long-range dependence in data.…”

Section: Discussionmentioning

confidence: 99%

“…Notwithstanding its popularity, Granger argued that processes generated by the fractional difference operator fall into the area of "empty boxes", about theory-either economic or econometric-on topics that do not arise in the actual economy (Granger 1999). Moreover, Veitch et al (2013) showed that fractionally differenced processes are brittle in the sense that small deviations such as adding small independent noise change the asymptotic variance structure qualitatively.…”

Section: Introductionmentioning

confidence: 99%

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Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Vera-Valdés

2021

Econometrics

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This paper used cross-sectional aggregation as the inspiration for a model with long-range dependence that arises in actual data. One of the advantages of our model is that it is less brittle than fractionally integrated processes. In particular, we showed that the antipersistent phenomenon is not present for the cross-sectionally aggregated process. We proved that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for nonfractional long-range-dependent processes with negative degrees of persistence. As an application, we showed how we can approximate a fractionally differenced process using theoretically-motivated cross-sectional aggregated long-range-dependent processes. An example with temperature data showed that our framework provides a better fit to the data than the fractional difference operator.

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Section: Nonfractional Long-range Dependence and The Antipersistent Propertysupporting

confidence: 52%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Vera-Valdés

2021

Econometrics

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“…From this perspective FGN and ARFIMA processes have the same fixed point as the limit of these operations tend to infinity. However, ARFIMA processes do differ from FGN in that you could change the fixed point, i.e., alter the eventual limit under aggregation and rescaling, with the addition of additive noise [35], i.e., this class was less robust to the addition of noise. Hence, there may be some differences in behaviour when looking through an entropic lens.…”

Section: Entropy Rate Function For Arfima(pdq)mentioning

confidence: 99%

Differential Entropy Rate Characterisations of Long Range Dependent Processes

Feutrill¹,

Roughan²

2021

Preprint

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A quantity of interest to characterise continuousvalued stochastic processes is the differential entropy rate. The rate of convergence of many properties of LRD processes is slower than might be expected, based on the intuition for conventional processes, e.g. Markov processes. Is this also true of the entropy rate?In this paper we consider the properties of the differential entropy rate of stochastic processes that have an autocorrelation function that decays as a power law. We show that power law decaying processes with similar autocorrelation and spectral density functions, Fractional Gaussian Noise and ARFIMA(0,d,0), have different entropic properties, particularly for negatively correlated parameterisations. Then we provide an equivalence between the mutual information between past and future and the differential excess entropy for stationary Gaussian processes, showing the finiteness of this quantity is the boundary between long and short range dependence. Finally, we analyse the convergence of the conditional entropy to the differential entropy rate and show that for short range dependence that the rate of convergence is of the order O(n −1 ), but it is slower for long range dependent processes and depends on the Hurst parameter.

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An approximate fractional Gaussian noise model with $$\mathcal {O}(n)$$ O ( n ) computational cost

2018

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Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length n using a likelihood-based approach is O(n 2), exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to O(n 3). This paper presents an approximate fGn model of O(n) computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved Sigrunn H. Sørbye

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Why Farima Models Are Brittle

Cited by 6 publications

References 21 publications

Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Differential Entropy Rate Characterisations of Long Range Dependent Processes

An approximate fractional Gaussian noise model with $$\mathcal {O}(n)$$ O ( n ) computational cost

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