Journal Article10.1111/J.1467-9892.1980.TB00297.X
An introduction to long‐memory time series models and fractional differencing
3.7K
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
read more
Abstract: . The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1-B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long-memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Reduced false positives in autism screening via digital biomarkers inferred from deep comorbidity patterns
Dmytro Onishchenko,Yi Huang,James van Horne,Peter K. Smith,Peter K. Smith,Michael E. Msall,Ishanu Chattopadhyay +6 more
TL;DR: The Autism Co-morbid Risk Score (ACoR), which predicts elevated risk during the earliest childhood years, when interventions are the most effective, is adopted in practice and could significantly reduce the median diagnostic age for ASD, and reduce long post-screen wait-times experienced by families for confirmatory diagnoses and access to evidence based interventions.
Statistical Analysis of Autoregressive Fractionally Integrated Moving Average Models
TL;DR: In this paper, the authors have implemented some of these statistical tools for analyzing ARFIMA models, including parameter estimation, exact autocovariance calculation, predictive ability testing, and impulse response function.
19
Stochastic orders of magnitude associated with two‐stage estimators of fractional arima systems
TL;DR: In this article, the authors provide a stochastic order of magnitude associated with an estimator in this class, and discuss this result with respect to the performance of the estimators in the second stage.
19
A closed formula for the durbin-levinson's algorithm in seasonal fractionally integrated processes
TL;DR: The Durbin-Levinson's algorithm is fully calculated for the SARFIMA (0, D, 0)"s processes and shows a hypergeometric identity, namely (l-D)@?j=0l-1, which will have smaller error under the use of the right-hand side formula.
19
On deterministic chaos in software reliability growth models
Omolbanin Yazdanbakhsh,Scott Dick,I. Reay,E. Mace +3 more
- 01 Dec 2016
TL;DR: An analysis of four software reliability growth datasets, including ones drawn from the Android and Mozilla open-source software communities, finds fractal state-space attractors in 3 of the 4 datasets, and compares a deterministic time series forecasting algorithm against a statistical one on both datasets to evaluate whether exploiting the apparent chaotic behavior might lead to more accurate reliability forecasts.
19
References
Spurious regressions in econometrics
Clive W. J. Granger,P. Newbold +1 more
TL;DR: In this paper, it is pointed out that it is very common to see reported in applied econometric literature time series regression equations with an apparently high degree of fit, as measured by the coefficient of multiple correlation R2 or the corrected coefficient R2, but with an extremely low value for the Durbin-Watson statistic.
6.8K
Long memory relationships and the aggregation of dynamic models
TL;DR: In this paper, it was shown that the aggregate series may have univariate long-memory models and obey integrated, or infinite length transfer function relationships, and that if series obeying such models occur in practice, from aggregation, then present techniques being used for analysis are not appropriate.
1.7K
Fractional integrals of stationary processes and the central limit theorem
Abstract: A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.
17