Journal Article10.1111/J.1467-9892.1980.TB00297.X
An introduction to long‐memory time series models and fractional differencing
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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.
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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.
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Citations
Impulse responses of fractionally integrated processes with long memory
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TL;DR: In this article, it was shown that this conjecture does not hold in such generality, and established a simple necessary and sufficient condition for the rate nd−1 to be inherited by fractionally integrated processes.
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A note on chambers's “long memory and aggregation in macroeconomic time series”*
TL;DR: This note reviews some results on aggregating discrete-time long memory processes, providing a formula for the spectrum of the aggregates that considers the aliasing effect.
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Foreign exchange, fractional cointegration and the implied-realized volatility relation
TL;DR: In this article, a new test for fractional cointegration is developed and shown to be robust to the relevant orders of integration, and the nonstandard asymptotic distribution of estimators when using fractionally integrated data is overcome by employing a bootstrap procedure in the frequency domain.
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A Note on Calculating Autocovariances of Long-memory Processes
TL;DR: In this paper, a splitting method for calculating the autocovariances of fractional integrated processes (ARFIMA) and generalized integrated process (GARMA) was proposed.
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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.
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