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Long-range Dependence (long-range + dependence)

Distribution by Scientific Domains

Mathematics and Statistics	55%
Earth and Environmental Science	16%
Business, Economics, Finance and Accounting	16%

Selected Abstracts

Long-Range Dependence of Markov Renewal Processes

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2004
R.A. Vesilo
Summary This paper examines long-range dependence (LRD) and asymptotic properties of Markov renewal processes generalizing results of Daley for renewal processes. The Hurst index and discrepancy function, which is the difference between the expected number of arrivals in (0, t] given a point at 0 and the number of arrivals in (0, t] in the time stationary version, are examined in terms of the moment index. The moment index is the supremum of the set of r > 0 such that the rth moment of the first return time to a state is finite, employing the solidarity results of Sgibnev. The results are derived for irreducible, regular Markov renewal processes on countable state spaces. The paper also derives conditions to determine the moment index of the first return times in terms of the Markov renewal kernel distribution functions of the process. [source]

Parameter Estimation of Stochastic Processes with Long-range Dependence and Intermittency

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2001
Jiti Gao
This paper considers the case where a stochastic process may display both long-range dependence and second-order intermittency. The existence of such a process is established in Anh, Angulo and Ruiz-Medina (1999). We systematically study the estimation of parameters involved in the spectral density function of a process with long-range dependence and second-order intermittency. An estimation procedure for the parameters is given. Numerical results are presented to support the estimation procedure proposed in this paper. [source]

Long-range dependence in Spanish political opinion poll series

JOURNAL OF APPLIED ECONOMETRICS, Issue 2 2003
Juan J. Dolado
This paper investigates the time series properties of partisanship for five political parties in Spain. It is found that pure fractional processes with a degree of integration, d, between 0.6 and 0.8 fit the time-series behaviour of aggregate opinion polls for mainstream parties quite well, whereas values of d in the range of 0.3 to 0.6 are obtained for opinion polls related to smaller regional parties. Those results are in agreement with theories of political allegiance based on aggregation of heterogeneous voters with different degrees of commitment and pragmatism. Further, those models are found to be useful in forecasting the results of the last general elections in Spain. As a further contribution, new econometric techniques for estimation and testing of ARFIMA model are used to provide the previous evidence. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Spatiotemporal generation of long-range dependence models and estimation

ENVIRONMETRICS, Issue 2 2006
M. P. Frías
Abstract A parametric family of spatiotemporal models displaying separable isotropic long-range dependence, in space and time, is introduced in a fractional generalized framework. The weak-sense implementation of estimation methods based on the integrated periodogram, the variogram and the wavelet transform, to estimate the long-memory parameter vector is discussed. The construction of separable and non-separable anisotropic long-range dependence spatiotemporal processes is also described considering fractional integration filters. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Cyclical long-range dependence and the warming effect in a long temperature time series

INTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 11 2008
L. A. Gil-Alana
Abstract In this paper, we propose a new approach for modelling a long temperature time series, using fractional cyclical integration. This model is based on the observation that the estimated spectrum of the series (the average annual temperature in Central England, 1659,2001) has its highest value at a frequency which is not zero, thus suggesting the existence of cycles at other frequencies. The results based on a fractional cyclical model show that there is a significant warming effect throughout the sample of about 0.22 °C/century. However, if we concentrate exclusively on the data corresponding to the 20th century that value increases to 0.64%. Moreover, the results in the paper show that a fractionally cyclically integrated model can be a competing alternative to other approaches based on fractional integration at the zero frequency. Copyright © 2007 Royal Meteorological Society [source]

Wavelet analysis of the Lisbon and Gibraltar North Atlantic Oscillation winter indices

INTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 5 2006
S. Barbosa
Abstract The North Atlantic Oscillation (NAO) is one of the most important climatic patterns in the Northern Hemisphere. Indices based on the normalised pressure difference between Iceland and a southern station, such as Lisbon or Gibraltar, have been defined in order to describe NAO temporal evolution. Although exhibiting interannual and decadal variability, the signals are statistically rather featureless and therefore it is difficult to discriminate between different types of stochastic models. In this study, Lisbon and Gibraltar NAO winter indices are analysed using the discrete wavelet transform discrete wavelet transform(DWT). A multi-resolution analysis (MRA) is carried out for a scale-based description of the indices and the wavelet spectrum is used to identify and estimate long-range dependence. The degree of association of the two NAO indices is assessed by estimating the wavelet covariance for the two signals. The scale-based approach inherent to the discrete wavelet methodology allows a scale-by-scale comparison of the signals and shows that although the short-term temporal pattern is very similar for both indices, the long-term temporal structure is distinct. Furthermore, the degree of persistence or ,memory' is also distinct: the Lisbon index is best described by a long-range dependent (LRD) process, while the Gibraltar index is adequately described by a short-range process. Therefore, while trend features in the Lisbon NAO index may be explainable by long-range dependence alone, with no need to invoke external factors, for the Gibraltar index such features cannot be interpreted as resulting only from internal variability through long-range dependence. Copyright © 2006 Royal Meteorological Society. [source]

Multiplicative multifractal modelling of long-range-dependent network traffic

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 8 2001
Jianbo Gao
Abstract We present a multiplicative multifractal process to model traffic which exhibits long-range dependence. Using traffic trace data captured by Bellcore from operations across local and wide area networks, we examine the interarrival time series and the packet length sequences. We also model the frame size sequences of VBR video traffic process. We prove a number of properties of multiplicative multifractal processes that are most relevant to their use as traffic models. In particular, we show these processes to characterize effectively the long-range dependence properties of the measured processes. Furthermore, we consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by our multifractal processes (the latter forming a MFe/MFg/1 queueing system model). In comparing the performance of both systems, we demonstrate our models to effectively track the behaviour exhibited by the system driven by the actual traffic processes. We show the multiplicative multifractal process to be easy to construct. Through parametric dependence on one or two parameters, this model can be calibrated to fit the measured data. We also show that in simulating the packet loss probability, our multifractal traffic model provides a better fit than that obtained by using a fractional Brownian motion model. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Long-memory forecasting of US monetary indices

JOURNAL OF FORECASTING, Issue 4 2006
John Barkoulas
Abstract Several studies have tested for long-range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long-memory models as forecast-generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out-of-sample fractional forecasts to benchmark forecasts. The long-memory parameter is estimated using Robinson's Gaussian semi-parametric and multivariate log-periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out-of-sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series.,,Copyright © 2006 John Wiley & Sons, Ltd. [source]

Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2005
Stilian Stoev
Primary 60G18; 60E07; Secondary 62M10; 63G20 Abstract., Methods for parameter estimation in the presence of long-range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long-range dependence in the case of heavy-tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/, for long-range dependent FARIMA time series with symmetric , -stable (1 < , < 2) innovations. We establish the consistency and the asymptotic normality of two types of wavelet estimators of the parameter H. We do so by exploiting the fact that the integrated series is asymptotically self-similar with parameter H. When the parameter , is known, we also obtain consistent and asymptotically normal estimators for the fractional differencing exponent d = H , 1/,. Our results hold for a larger class of causal linear processes with stable symmetric innovations. As the wavelet-based estimation method used here is semi-parametric, it allows for a more robust treatment of long-range dependent data than parametric methods. [source]

Parameter Estimation of Stochastic Processes with Long-range Dependence and Intermittency

Estimation of the Dominating Frequency for Stationary and Nonstationary Fractional Autoregressive Models

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2000
Jan Beran
This paper was motivated by the investigation of certain physiological series for premature infants. The question was whether the series exhibit periodic fluctuations with a certain dominating period. The observed series are nonstationary and/or have long-range dependence. The assumed model is a Gaussian process Xt whose mth difference Yt = (1 ,B)mXt is stationary with a spectral density f that may have a pole (or a zero) at the origin. the problem addressed in this paper is the estimation of the frequency ,max where f achieves the largest local maximum in the open interval (0, ,). The process Xt is assumed to belong to a class of parametric models, characterized by a parameter vector ,, defined in Beran (1995). An estimator of ,max is proposed and its asymptotic distribution is derived, with , being estimated by maximum likelihood. In particular, m and a fractional differencing parameter that models long memory are estimated from the data. Model choice is also incorporated. Thus, within the proposed framework, a data driven procedure is obtained that can be applied in situations where the primary interest is in estimating a dominating frequency. A simulation study illustrates the finite sample properties of the method. In particular, for short series, estimation of ,max is difficult, if the local maximum occurs close to the origin. The results are illustrated by two of the data examples that motivated this research. [source]

Econometric Analysis of Fisher's Equation

AMERICAN JOURNAL OF ECONOMICS AND SOCIOLOGY, Issue 1 2005
Peter C. B. Phillips
Fisher's equation for the determination of the real rate of interest is studied from a fresh econometric perspective. Some new methods of data description for nonstationary time series are introduced. The methods provide a nonparametric mechanism for modelling the spatial densities of a time series that displays random wandering characteristics, like interest rates and inflation. Hazard rate functionals are also constructed, an asymptotic theory is given, and the techniques are illustrated in some empirical applications to real interest rates for the United States. The paper ends by calculating semiparametric estimates of long-range dependence in U.S. real interest rates, using a new estimation procedure called modified log periodogram regression and new asymptotics that covers the nonstationary case. The empirical results indicate that the real rate of interest in the United States is (fractionally) nonstationary over 1934,1997 and over the more recent subperiods 1961,1985 and 1961,1997. Unit root nonstationarity and short memory stationarity are both strongly rejected for all these periods. [source]

Persistence in some energy futures markets

THE JOURNAL OF FUTURES MARKETS, Issue 5 2010
Juncal Cunado
In this study, we examine the possibility of long-range dependence in some energy futures markets for different maturities. In order to test for persistence, we use a variety of techniques based on non-parametric, semi-parametric and parametric methods. The results indicate that there is little or no evidence of long memory in gasoline, propane, oil and heating oil at different maturities. However, when we focus on the volatility process, proxied by the absolute returns, we find strong evidence of long memory in all the variables at different contracts. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:490,507, 2010 [source]

One-way analysis of variance with long memory errors and its application to stock return data

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 6 2007
Jaechoul Lee
Abstract Recent empirical results indicate that many financial time series, including stock volatilities, often have long-range dependencies. Comparing volatilities in stock returns is a crucial part of the risk management of stock investing. This paper proposes two test statistics for testing the equality of mean volatilities of stock returns using the analysis of variance (ANOVA) model with long memory errors. They are modified versions of the ordinary F statistic used in the ANOVA models with independently and identically distributed errors. One has a form of the ordinary F statistic multiplied by a correction factor, which reflects slowly decaying autocorrelations, that is, long-range dependence. The other is a test statistic such that the degrees of freedom of the denominator in the ordinary F test statistic is calibrated by the so-called effective sample size. Empirical sizes and powers of the proposed test statistics are examined via Monte Carlo simulation. An application to German stock returns is presented. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Reinsurance control in a model with liabilities of the fractional Brownian motion type

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2007
N. E. Frangos
Abstract We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Scaling of Central England temperature fluctuations?

ATMOSPHERIC SCIENCE LETTERS, Issue 1-4 2001
Joanna Syroka
Abstract Central England temperature fluctuations are found to be monoscaling with long-range dependence. Monoscaling can be explained in terms of the dominance of Gaussian temperature advection. Simulations of the UK Meteorological Office Hadley Centre general circulation model do not capture many of these features. Copyright © 2002 Royal Meteorological Society. [source]

Long-Range Dependence of Markov Renewal Processes

Marginalized Models for Moderate to Long Series of Longitudinal Binary Response Data

BIOMETRICS, Issue 2 2007
Jonathan S. Schildcrout
Summary Marginalized models (Heagerty, 1999, Biometrics55, 688,698) permit likelihood-based inference when interest lies in marginal regression models for longitudinal binary response data. Two such models are the marginalized transition and marginalized latent variable models. The former captures within-subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing response dependence using random intercepts. In this article, we extend the class of marginalized models by proposing a single unifying model that describes both serial and long-range dependence. This model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject, where both serial and exchangeable forms of response correlation can be identified. We describe maximum likelihood and Bayesian approaches toward parameter estimation and inference, and we study the large sample operating characteristics under two types of dependence model misspecification. Data from the Madras Longitudinal Schizophrenia Study (Thara et al., 1994, Acta Psychiatrica Scandinavica90, 329,336) are analyzed. [source]