An Introduction to Long‐memory Time Series Models and Fractional Differencing

Granger, Clive W. J.; Joyeux, Roselyne

doi:10.1111/j.1467-9892.1980.tb00297.x

Cited by 2,870 publications

(1,234 citation statements)

References 8 publications

Supporting

Mentioning

1,194

Contrasting

Unclassified

Order By: Relevance

“…The ARFIMA model (see Granger and Joyeux 1980), which is a generalization of the ARIMA model, can capture long-term dependencies between observations of series. The ARFIMA ( p, d, q) model can be written as:…”

Section: Econometric Methodsmentioning

confidence: 99%

Monetary policy in steering the EONIA and POLONIA rates in the Eurosystem and Poland: a comparative analysis

Fiszeder

Pietryka

2017

Empir Econ

View full text Add to dashboard Cite

The effectiveness of the monetary policies of the European Central Bank (ECB) and the Narodowy Bank Polski (NBP) is compared directly in terms of influencing the spread between the interbank overnight rate and the main rates of the central banks during periods of different economic conditions, i.e. the global financial crisis of 2008, the European sovereign debt crisis and the period of relative stability. Three categories of determinants of the Euro Overnight Index Average/Polish Overnight Index Average (EONIA/POLONIA) spreads are considered: (1) monetary policy instruments such as open market operations, standing facilities and minimum reserve requirements; (2) measures of liquidity conditions; and (3) market expectations and risk measures. Applying the ARFIMA-GARCH models, we show that the statistical and economic properties of the EONIA and POLONIA spreads are quite different. The EONIA spread has a long memory while the POLONIA spread is characterized by a short memory. This difference is important from the viewpoint of a stabilizing monetary policy. The impact of shocks on the future levels of the spread was stronger for the POLONIA spread, but it was short-lived in comparison with the EONIA spread. Most of the analysed variables significantly influenced the spreads during the financial crisis, while the biggest differences in the impact of determinants between the EONIA and POLONIA spreads occurred during the period of relative stability. Substantial differences also exist between the volatilities of both spreads.

show abstract

Section: Econometric Methodsmentioning

confidence: 99%

Monetary policy in steering the EONIA and POLONIA rates in the Eurosystem and Poland: a comparative analysis

Fiszeder

Pietryka

2017

Empir Econ

View full text Add to dashboard Cite

show abstract

“…Une extension importante, quoique en apparence évidente, que l'on peut apporter à la définition originale des processus FARMA fournie par HOSKING (1981) et GRANGER et JOYEUX (1980), consiste à ne pas tenir compte de l'hypo-thèse que la moyenne de la série soit nulle. L'extension du modèle présenté précédemment qui correspond au cas où la moyenne est non-nulle, est obtenue directement.…”

Section: Modélisation Des Séries Chronologiques Par Le Modèle Farma (unclassified

“…En plus de son utilisation pour des séries géophysiques, la classification « mémoire à long terme » et « mémoire à court terme » est aussi utile dans plusieurs autres domaines (cox, 1984 ;PARZEN, 1982) et particulièrement en économie (GRANGER, 1988 ;GRANGER et JOYEUX, 1980). Cette classification a aussi été utilisée pour d'autres types de processus stochastiques (COX, 1984) avec des définitions différentes pour la mémoire.…”

Section: Introductionunclassified

“…Ces modèles à mémoire longue incluent les modèles « bruit Gaussien » (MANOELBROT et WALLIS, 1969a , b, c), de « ligne brisée»» (MEJIA et al, 1972), «niveau variable» (BOES et SALAS, 1978;BALLERINI et BOES, 1985), et « autorégressif et moyennes mobiles sur différen-ces fractionnaires »» (GRANGER, 1980 ;GRANGER et JOYEUX, 1980 ;HOSKING, 1981HOSKING, , 1984HOSKING, , 1985Ll et McLEOD, 1986). Plusieurs de ces modèles à mémoire longue sont aussi présentés dans des ouvrages d'hydrologie stochastique (KOTTEGODA, 1980 ;SALAS et al, 1980 ;BRASS et RODRIGUEZ-ITURBE, 1984 ; HIPEL et MCLEOD, 1990).…”

Section: Introductionunclassified

See 1 more Smart Citation

Développements récents dans la modélisation de la persistance à long terme

Jimenez¹,

Hipel²,

McLeod³

2005

rseau

View full text Add to dashboard Cite

Afin de modéliser efficacement la persistance dans les séries chronologiques rencontrées en hydrologie, des développements récents autour du modèle fractionnaire auto-régressif à moyenne mobile (FARMA) (fractional autoregressive-moving average model) sont présentés. On s'intéresse particulièrement ici à de nouvelles procédures permettant d'estimer les paramètres du modèle FARMA d'une manière efficace au point de vue calcul. Pour obtenir les distributions d'échantillons des estimateurs des paramètres à partir de petits échantillons, une technique faisant appel au bootstrap peut être utilisée. Des applications pratiques à des séries de débits en rivière, de précipitations et de températures, montrent l'utilité des modèles FARMA.In order to model effectively persistence in hydrologic tune series, recent developments in fractional autoregressive-moving average (FARMA) models are presented. A time series possesses persistence or long memory if it has an autocorrelation structure that attenuates slowly to zero with increasing lags. Based on the controversy surrounding the Hurst phenomenon, some hydrologists claim that it is important to employ stochastic models which have the ability to model long memory when it is present in a given time series. Fractional Gaussian noise models and approximations thereof were developed within the field of hydrology in order to be able to model long memory. However, a particularly flexible set of models having the capability to describe long memory is the FARMA family of models, which constitutes a direct generalization of autoregressive integrated moving average (ARIMA) models.In particular, like an ARIMA model, a FARMA model contains autoregressive and moving average parameters. Whereas the differencing operator d is restricted to be zero or take on positive integer values in an ARIMA model, the parameter d in a FARMA model can have real values and is estimated along with the other model parameters. For a specified range of values for the d parameter, a FARMA model has long memory. Besides reviewing the background and main theoretical properties of FARMA models, simulation and forecasting techniques are presented. Additionally, procedures for estimating the parameters of a FARMA model are given and a bootstrapping technique is described to obtain the small sample distributions of the estimated parameters.To explain how to apply FARMA models in practice and demonstrate their usefulness, they are fitted to riverflow, precipitation and temperature time series

show abstract

“…Many mathematical and statistical models [11][12][13][14][15][16] are available nowadays for a phenomenological description of financial data, while rigorous theoretical frameworks have shown to be able to encapsulate some conjectures like the Elliot waves [17].…”

Section: Introductionmentioning

confidence: 99%

Microeconomic co-evolution model for financial technical analysis signals

Rotundo

Ausloos²

2007

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

Technical analysis (TA) has been used for a long time before the availability of more sophisticated instruments for financial forecasting in order to suggest decisions on the basis of the occurrence of data patterns. Many mathematical and statistical tools for quantitative analysis of financial markets have experienced a fast and wide growth and have the power for overcoming classical TA methods. This paper aims to give a measure of the reliability of some information used in TA by exploring the probability of their occurrence within a particular microeconomic agent-based model of markets, i.e., the co-evolution Bak-Sneppen model originally invented for describing species population evolutions. After having proved the practical interest of such a model in describing financial index so-called avalanches, in the prebursting bubble time rise, the attention focuses on the occurrence of trend line detection crossing of meaningful barriers, those that give rise to some usual TA strategies. The case of the NASDAQ crash of April 2000 serves as an illustration. r

show abstract

An Introduction to Long‐memory Time Series Models and Fractional Differencing

Cited by 2,870 publications

References 8 publications

Monetary policy in steering the EONIA and POLONIA rates in the Eurosystem and Poland: a comparative analysis

Monetary policy in steering the EONIA and POLONIA rates in the Eurosystem and Poland: a comparative analysis

Développements récents dans la modélisation de la persistance à long terme

Microeconomic co-evolution model for financial technical analysis signals

Contact Info

Product

Resources

About