ARFIMA Process Research Articles

The weak form efficiency of the stock market : The Case of moroccan market

This research work aims at studying the weak form of informational efficiency of the Moroccan stock market developed by Fama. We apply classical econometric tests to this end. Many studies have focused on the presence of non-linearity or long memory in the return series. In this paper, we propose to study these phenomena through the development of an ARFIMA process as suggested by Granger and Joyeux (1980) and Hosking (1981). We used the MASI composite index and our results provide solid proof that does not support the efficiency hypothesis of the Moroccan stock market and the ARFIMA process shows that the MASI series is characterized by a long memory structure.

Statistical inference of one-dimensional persistent nonlinear time series and application to predictions

We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonlinear auto-regressive toy model with multiplicative noise. We reconstruct a model for daily mean temperature data recorded at Potsdam (Germany) and use it to predict the first frost date by computing the mean first passage time of the reconstructed process and the zero degree Celsius temperature line, illustrating the potential of long-memory models for predictions in the subseasonal-to-seasonal range.

The Optimal Bandwidth Parameter Selection in GPH Estimation

In this paper, the optimal bandwidth parameter is investigated in the GPH algorithm. Firstly, combining with the stylized facts of financial time series, we generate long memory sequences by using the ARFIMA (1, d, 1) process. Secondly, we use the Monte Carlo method to study the impact of the GPH algorithm on existence test, persistence or antipersistence judgment of long memory, and the estimation accuracy of the long memory parameter. The results show that the accuracy of above three factors in the long memory test reached a relatively high level within the bandwidth parameter interval of 0.5 < a < 0.7. For different lengths of time series, bandwidth parameter a = 0.6 can be used as the optimal choice of the GPH estimation. Furthermore, we give the calculation accuracy of the GPH algorithm on existence, persistence or antipersistence of long memory, and long memory parameter d when a = 0.6.

EFFECT OF FILTERS ON MULTIVARIATE MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS

We investigate how various linear and nonlinear filters affect the scaling properties of long-range power-law multivariate synthetic series quantified by multivariate multifractal detrended fluctuation analysis (MV-MFDFA). We consider four types of transforms which are often encountered in physical and physiological processes: linear, nonlinear polynomial, logarithmic and power-law filters. The effect of filters is analyzed by numerical simulation of synthetic series generated by ARFIMA process and binomial multifractal model. The representation of auto-correlation properties of synthetic series before and after the transforms is illustrated by 3D Hurst surface, and the difference of effect is quantified by the proposed generalized mean distance. We find that the linear filters do not change the scaling properties of both synthetic series, while the effect of nonlinear polynomial is correlated with the power of the polynomial filter. For logarithmic and exponential filter, the scaling behavior is not affected for some values of the parameters.

DCCA cross-correlation analysis in time-series with removed parts

In this paper we analyze the effect of removing pieces in time-series with long range-memory by DFA method and detrended cross-correlation coefficient. To achieve this purpose, initially simulated time-series are produced by ARFIMA process (long time dependence). From these simulated time-series cuts and removals are produced. The results show that for up to 50% of removed parts, compared to the original time-series, there is no change in the final results for detrended auto and cross-correlations. Therefore, with this paper we show that the DFA method and the detrended cross-correlation coefficient are robust for time-series analysis even for time-series with removed parts. This result ensures that these methods can be applied to real time-series, which in many cases lacks measurement for a variety of reasons and causes.

Testing weak form informational efficiency on the Tunisian stock market using long memory models

The purpose of this paper is to test the weak-form market efficiency of the Tunisian stock market using recent developments in time series econometrics. The efficiency hypothesis was tested by using the class of long memory models namely ARFIMA-FIGARCH. For this, we will attempt to examine the long memory behavior in the returns and the volatility series of the Tunisian stock market index namely Tunindex. Our empirical study covers a sample covering the Tunindex during the period: 02/01/1998 to 16/03/2018. Our results show the presence of the long memory property in the return and volatility specified respectively by an ARFIMA and FIGARCH process. This result implies that it is possible to predict future stock prices and an extraordinary gain could be obtained when trading in this market, which displays that the Tunisian stock market is not efficient in its weak-form.

Regime switching with structural breaks in output convergence

Abstract In this paper, we examine empirically GDP per capita convergence using an approach that explicitly allows for regime switching in the long memory parameter d within the context of a Markov Switching (MS)–ARFIMA framework. As existing methods used in the estimation of standard MS models, such as the EM algorithm are no longer appropriate, we will make use of the Viterbi algorithm to estimate the long memory MS model used by Tsay and Härdle (Tsay, W.-J., and W. K. Härdle. 2009. “A Generalized Arfima Process with Markov-Switching Fractional Differencing Parameter.” Journal of Statistical Computation and Simulation 79: 731–745.). We will classify the output gap series into two regimes, a high d and a low d regime, where a high d close to unity would imply persistence and lack of convergence. By examining the path of d parameter over time which enables us to observe non-convergent behavior in more detail, we find that converging behavior is diminishing over time and divergence is the dominant force.

Effect of Outliers and Non-consecutive Data Points on the Detrended Cross-Correlation Analysis

In this paper, we investigate the robustness of the well-known DCCA (detrended cross-correlation analysis) methodology and give a qualitative analysis result. Due to the non-stationarity inherent in most observational data sets, the results of DCCA and its variants may be spurious. In particular, oceanographic data sets contaminated with measurement errors are subject to unusual records, making it difficult to trust DCCA results. To ensure the validity of the DCCA methodology for the oceanographic time series, we conduct simulation studies based on the ARFIMA process and perform statistical tests using surrogate methods. First, so-called outliers due to measurement error lead to the spurious results of DCCA methods while discontinuities in the time series have been found to have little effect on the results. This means that the cross-correlation structure is robust to the discontinuity of time series. Second, statistical significance of cross-correlation was obtained through a surrogate statistical test for the oceanographic time series.

The detection of local irreversibility in time series based on segmentation

We propose a strategy for the detection of local irreversibility in stationary time series based on multiple scale. The detection is beneficial to evaluate the displacement of irreversibility toward local skewness. By means of this method, we can availably discuss the local irreversible fluctuations of time series as the scale changes. The method was applied to simulated nonlinear signals generated by the ARFIMA process and logistic map to show how the irreversibility functions react to the increasing of the multiple scale. The method was applied also to series of financial markets i.e., American, Chinese and European markets. The local irreversibility for different markets demonstrate distinct characteristics. Simulations and real data support the need of exploring local irreversibility.

Quantifying two-dimensional nonstationary signal with power-law correlations by detrended fluctuation analysis

In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.

EWMA control charts for detecting changes in the mean of a long-memory process

In this paper EWMA control charts are introduced for detecting changes in the mean of a long-memory process. Besides the modified EWMA scheme the EWMA residual chart is also considered. The control design of the charts is calculated for an ARFIMA(p,d,q) process. In order to assess the introduced charts, the average run length is used as a performance criterion. Using an extensive simulation study, the control charts are compared with each other. The target process is assumed to be an ARFIMA(1,d,1) process.

Fractional Integration of the Price-Dividend Ratio in a Present-Value Model of Stock Prices

We re-examine the dynamics of returns and dividend growth within the present-value framework of stock prices. We find that the finite sample order of integration of returns is approximately equal to the order of integration of the first-differenced price-dividend ratio. As such, the traditional return forecasting regressions based on the price-dividend ratio are invalid. Moreover, the nonstationary long memory behaviour of the price-dividend ratio induces antipersistence in returns. This suggests that expected returns should be modelled as an ARFIMA process and we show this improves the forecast ability of the present-value model in-sample and out-of-sample.

Can we distinguish regime switching from long memory? A simulation evidence

It is well known that long memory can be caused by regime switching and is easily confused with it. However, recent study suggests that if the cause of confusion was properly controlled for, long memory and regime switching could be distinguished. Motivated by this idea, our study aims to distinguish regime switching from long memory for the financial time series. In this article, we model long memory and regime switching via the ARFIMA and Markov regime-switching (MRS) frameworks, respectively. A theoretical proof is provided to show that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. We then propose a two-stage two-state-ARFIMA (2S-ARFIMA) model to control for the effect of the smoothing probability and use a simulation study to demonstrate that it can effectively distinguish the pure MRS process from the pure ARFIMA process.

A simple microstructure return model explaining microstructure noise and Epps effects

We present a novel simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of both microstructure and macrostructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time-scale used to estimate it. The Epps effect states that cross correlations between asset returns are increasing functions of the time-scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time-scale in the presence of the long memory process (i).

Coupling between time series: A network view

Recently, the visibility graph has been introduced as a novel method for analyzing time series, which maps a time series to a complex network. In this paper we introduce a new algorithm of visibility, “cross-visibility”, which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, “the cross-visibility graph”, to demonstrate the correlation between them. We have applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process, in order to better understand the results of the cross-visibility of empirical series. The comparison between the degree distribution of coupled and uncoupled (shuffled) series' networks demonstrates the emergence of super nodes (extremely high-degree nodes) in the uncoupled ones. Furthermore, we have applied the algorithm to real-world data from the financial trades of two companies and oil, and observed significant small-scale coupling in their dynamics.

Long memory and regime switching properties of current account deficits in the US

Chen (2011) [Are current account deficits really sustainable in the G-7 countries? Japan and the World Economy, 23(3), 190–201.] examines whether or not the current account deficits of the US can be characterized by a unit root process with regime switching (MS-ADF). In this paper, we find that, if the empirical sample ends in 2008:Q4, the estimates obtained from the Markov switching unit root regression retain a reasonable two-state classification. If the sample is extended to 2009:Q1 or beyond, then the estimates of the Markov switching unit root regression become quite unreasonable and it is difficult to explain the results. We also find that this contradictory phenomenon can be resolved by estimating the Markov switching autoregressive fractionally integrated moving average model (MS-ARFIMA) proposed by Tsay and Härdle (2009) [A generalized ARFIMA process with Markov-switching fractional differencing parameter, Journal of Statistical Computation and Simulation, 79, 731–745.]. The estimates of the MS-ADF and MS-ARFIMA models show that there is a red signal that the current account deficits observed during the period were probably not on a sustainable path.

The Quasi Maximum Likelihood Approach to Statistical Inference on a Nonstationary Multivariate ARFIMA Process

The editorial board announced this article has been retracted on September 29, 2013. If you have any further question, please contact us at: ijsp@ccsenet.org

Financial Markets between Efficiency and Persistence: Empirical Evidence on Daily Data

Today, the assumption of efficient capital markets is very controversial, especially in these times of crisis, and is challenged by research showing that the pricing was distorted by detection of long memory. This study aims to test the existence of the persistence effect using statistical analysis such as R/S, its corollary named Hurst exponent and the ARFIMA process. In practical terms, our research was conducted on daily data on stock returns of 21 countries classified into three groups according to their levels of development over the period from January 2000 to December 2010. The results obtained allowed us to conclude that the property of of long rang dependence tend to be associated with relatively thin stocks

Recursive predictive tests for structural change of long-memory ARFIMA processes with unknown break points

This paper considers the theoretical justifications of Lütkpohl’s (1988) test statistics when the data-generating process is relaxed to be a stationary ARFIMA process. Under suitable regularity conditions, we prove the applicability of Lütkpohl’s (1988) method to the stationary ARFIMA (p, d, q) process with d∈ (−0.5, 0.5). The practical advantages of our results imply that the potential one or more change points of an ARFIMA process can be detected via recursive predictive tests based on AR regression, even though the exact order of the ARFIMA (p, d, q) is unknown. The spurious break considered in Kuan and Hsu (1998) can also be resolved by Lütkpohl’s (1988) predictive tests, and the simulations conducted in this paper confirm our theoretical results.

DISCRIMINATING SHORT AND LONG MEMORY IN FINITE SAMPLES USING SENSITIVITY ANALYSIS: AN APPLICATION TO GROWTH CONVERGENCE

ABSTRACTThe standard linear model where ut is generated from an ARFIMA process, is considered. The sensitivity of the predictor and sensitivity of variance estimates of the linear model to long memory are investigated by constructing the statistical measures BL/S and DL/S, respectively. BL/S and DL/S is interpreted as a sensitivity measure for the long‐memory process without the short‐memory effects. As an application, the memory characteristics of per capita GDP of 30 countries are investigated from the Maddison GDP dataset. It is found that per‐capita GDP exhibits long memory characteristics, and the long‐run growth estimates are sensitive to the long memory characteristics.