A comparison of techniques of estimation in long-memory processes

Bisaglia, Luisa; Guégan, Dominique

doi:10.1016/s0167-9473(97)00045-5

Cited by 37 publications

(15 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical approach using the best linear relationship between log[E(R/S(t))] and log(t) yields a biased estimate unless t is large [71][72][73][74]. Corresponding approaches to measure L, M , and H also suffer from analogous finite-time corrections.…”

Section: Results From Simulations a Finite-size Correctionsmentioning

confidence: 99%

Anomalous scaling of stochastic processes and the Moses effect

et al. 2017

View full text Add to dashboard Cite

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t 1 2 . However, processes where the probability distribution is not normal and the scaling exponent differs from 1 2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, auto-correlations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect the Noah effect, respectively. If the increments are non-stationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data is analyzed, revealing that its anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

show abstract

Section: Results From Simulations a Finite-size Correctionsmentioning

confidence: 99%

Anomalous scaling of stochastic processes and the Moses effect

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Other evidence of the data non-linearity can be found in Bisaglia and Guégan (1998) who studied the same time series with a long memory approach. They have shown that the transformed squared series and absolute value series have very strong long memory behavior which confirms our analysis here.…”

Section: Financial Intra-day Datamentioning

confidence: 88%

Prediction in chaotic time series: methods and comparisons with an application to financial intra-day data

Guégan

Mercier

2005

The European Journal of Finance

View full text Add to dashboard Cite

Different prediction methods for chaotic deterministic systems are compared. Two methods of reconstructing the dynamics of the systems are considered with a view to producing a profitable trading model. The methods developed are the 'nearest neighbours' method and the 'radial basis functions' method. The optimal prediction horizon according to the sampling time step, and a reliable method to measure the prediction error are discussed. These methods are applied to the intra-day series of exchange rates, namely DEM/FRF. Developments concerning the importance of noise when chaotic systems are studied are provided.Chaotic systems, nearest neighbors, prediction radial basis functions,

show abstract

“…A new class of Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic (FIGARCH) processes was introduced by Baillie et al (1996). Empirical evidence of long memory has also been found in monthly river flows (Ooms & Franses, 1998), stock market prices (Cheung & Lai, 1995), (Barkoulas & Baum, 1996), Willinger et al (1999) or exchange rates (Cheung, 1993), Bisaglia andGuégan (1998), Velasco (1999). Caporale and Gil-Alana (2011) modeled European inflation rates using Multi-Factor Gegenbauer Processes.…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling and Forecasting Gambia’s Inflation Rates

Manjang¹,

Diongue²,

Odongo³

2014

IJEF

View full text Add to dashboard Cite

In this paper, we examine the most appropriate method for modeling and forecasting Gambia's inflation rates. We investigate the statistical properties of the inflation data and specify two models namely seasonal autoregressive integrated moving average (SARIMA) and k-factor Gegenbauer Autoregressive Moving Average (k-factor GARMA). The first model seasonal ARIMA(1, 1, 1)(0, 0, 1) 12 was selected using the H-K Algorithm developed by Hyndman and Khandakar (2008) and 3-factor GARM A from both the spectral density graph and further analysis of the residuals from the 3-factor Gegenbauer model. The in-sample characteristics such as the Akaike Criterion and Schwarz Criterion following estimation using the first data set show that the ARIMA(1, 1, 1)(0, 0, 1) 12 outperforms the 3-factor GARM A model. However, the second data set that was preserved and used for out-of-sample forecasting suggest that the 3-factor GARM A model outperforms the seasonal ARIMA(1, 1, 1)(0, 0, 1) 12 model in out-of -sample forecasting. Our results indicated that inflation in Gambia is stationary with long-memory behavior at three distinct frequencies. We also found that the k-factor GARMA outperforms the seasonal ARIMA in out-sample forecasting which may be ascribed to the forecast horizon been large and series strongly long-range dependent.

show abstract

A comparison of techniques of estimation in long-memory processes

Cited by 37 publications

References 16 publications

Anomalous scaling of stochastic processes and the Moses effect

Anomalous scaling of stochastic processes and the Moses effect

Prediction in chaotic time series: methods and comparisons with an application to financial intra-day data

Modeling and Forecasting Gambia’s Inflation Rates

Contact Info

Product

Resources

About