This paper used ARMA-GARCH model for forecasting daily return series of stock index of NASDAQ stock exchange. Furthermore, we investigate the efficiency and fractal feature of NASDAQ stock exchange to study its effects on efficiency and fractal perspectives in NASDAQ stock exchange, which has theoretical and practical significance in the application of effective market hypothesis (EMH) in NASDAQ stock exchange.
In this study, in the literature review we have reviewed many studies about financial time series forecasting and modeling, and we have discussed about efficient market hypothesis (EMH) and fractal market hypothesis (FMH) and have showed that how the stock markets could be efficient. In recent years, researchers have found some empirical evidences about the importance of financial time series variables in explaining the abnormal returns on portfolios consisting of various diversified assets in it. Therefore, financial time series forecasting and modeling are an important category in empirical analysis of financial time series variables. Also, by comparison different studies about market efficiency and fractal feature of the stock markets, the results show that predominantly in developed stock markets, it is found that developed stock markets are efficient.
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P. M 2003r. Heavy tails in finance for independent or multifractal price increments. Handbook on Heavy Tailed Distributions in Finance. Edited by Svetlozar T. Rachev (Handbooks in Finance: 30, Senior Editor: William T. Ziemba): 1, 1-34. [ PDF (295.1 KB) ]
Mandelbrot and Ness has laid the foundations of multifractal analysis by introducing fractional Brownian motions, fractional noises and its applications (Mandelbrot & Van Ness, 1968). Later, multifractal de-trended fluctuation analysis (MF-DFA) has been proposed as an alternative method in analyzing financial time series by (Kantelhardt et al., 2002). Heretofore, there have been many researchers using this method in their analysis. Zhang et al. have investigated asymmetric multiscale multifractal analysis of wind speed signals (Zhang et al., 2017). Multifractal and wavelet analysis of epileptic seizures have been studied by (Dick & Mochovikova, 2011). An in-depth analysis of stocks of the company GE was performed by Thomson and Wilson by contrasting the results with those obtained using multifractal de-trended fluctuation analysis and using conventional time series models (Thompson & Wilson, 2014). Benbachir and Alaoui employed the MF-DFA method in order to explore the multifractal properties of the Moroccan Dirham compared with the US Dollars (Benbachir & Alaoui, 2011). Zhu and Zhang studies the multifractal property of Chinese stock market in the CSI 800 index based on MF-DFA approach (Zhu & Zhang, 2017) and concluded that the shape and width of multifractal spectrum are dependent on the weighing order and Hurst exponents can account for the market crash. (Sensoy, 2013) studies the time-varying efficiency of 15 Middle East and North African (MENA) stock markets by generalized Hurst exponent analysis of daily data with a rolling window technique and concludes that all MENA stock markets exhibits different long range dependence. In other study, Sensoy and Tabak proposes an alternative index to model time-varying inefficiency in stock markets using generalized Hurst exponents calculations (Sensoy & Tabak, 2015). (Tiwari et al., 2017) in 2016 challenges efficient hypothesis using the generalized Hurst exponent and MF-DFA methods. In our study, we will show that obtaining coherent time series lead to more accurate forecasting results because not only the long-run effects but also the short and long term dynamics can be taken into considerations simultaneously.
Gold is treated as hedging instrument against inflation and exchange rates (Hammoudeh et al., 2010) and, in many papers, reported as an indicator of inflation (Ranson & Wainright, 2005). Likewise, Mahdavi and Zhou points that commodity prices respond to new information faster than any consumer price (Mahdavi & Zhou, 1997). Therefore, results obtained from a successful forecasting of gold with smaller error bands may help and support both finance researchers as well as many different players in financial world such as monetary policymakers, hedge fund managers, portfolio managers, centrals banks and investors while making investment decisions. As far as we know there is no general method about forecasting of data possessing multifractal nature and we believe our paper will serve well during these type of decision-making processes.
In this paper, we will look deep into co-movement of metal prices in time and frequency space by using multiple wavelet coherence. Once highly correlated time interval and frequency is determined, the multifractal behavior of the real series will be validated. A new time series of fluctuation function at the specified scale will be obtained out of its local Hurst exponents calculations. Finally, we will compare and discuss the performance of modeling and forecasting using these series with the help of univariate and multivariate models.
It is expected in this paper that the better performance of forecasting will be obtained due to the long range dependence and the multifractal behavior of the time series obtained. In Table 3, it is shown that the real time series data of all metals have generalized Hurst exponent even greater than 1, indicating a strong long range dependence.
Additionally, the present results may assist members of the financial world at varying degrees in their field. Vast number of the research papers report that the price of gold is an indicator of inflation (Ranson & Wainright, 2005). This is because of commodity prices can respond to new information faster than any consumer prices (Mahdavi & Zhou, 1997). Furthermore, Gold is treated as hedging instrument against inflation and exchange rates (Hammoudeh et al., 2010). Therefore, accurate forecasting (i.e. forecasts with smaller error bands) of the gold price will serve to monetary policymakers, hedge fund managers, international portfolio managers and central banks to make accurate investment decisions in the financial market. However, forecasting of gold prices is a formidable task. This is because of the multifractal nature of the gold prices. To the best of our knowledge there is no general approach for forecasting of multifractal data.
Compared to univariate counterparts (ARFIMA), it is depicted that the consistency and performance of forecasting with multifractal time series is remarkably increased with multivariate models (VARFIMA) (Durr et al., 1997). This was also true in spite of the size of the data set chosen (Dueker & Startz, 1998) where we have used set of data from 300 daily prices up to 1100 daily prices.
EO analyzed the data with multiple wavelet coherence and multifractal de-trended fluctuation analyses and generated forecasting results using vector autoregressive fractionally integrated moving average model. GU was the supervisor in construing the results, conclusion as well as in writing the manuscript. All authors read and approved the final manuscript. The content of the manuscript has not been published or submitted for publication elsewhere.
EconPapers FAQ Archive maintainers FAQ Cookies at EconPapers Format for printing The RePEc blog The RePEc plagiarism page The Markov-switching multi-fractal model of asset returns: GMM estimation and linear forecasting of volatilityThomas LuxNo 2004-11, Economics Working Papers from Christian-Albrechts-University of Kiel, Department of EconomicsAbstract:Multi-fractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in virtually all financial data. Initial difficulties stemming from non-stationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multi-fractal model in Calvet and Fisher (2001) which allows for estimation of its parameters via maximum likelihood and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative GMM estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular Binomial and Lognormal models and that the loss incured with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.Keywords: Multifractal; Forecasting; Volatility; GMM estimation; Markov-switching (search for similar items in EconPapers)JEL-codes: C20 G12 (search for similar items in EconPapers)Date: 2004References: View references in EconPapers View complete reference list from CitEc Citations: View citations in EconPapers (2) Track citations by RSS feedDownloads: (external link) -2004-11.pdf (application/pdf)Related works:Journal Article: The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility (2008) Working Paper: The Markov-Switching Multifractal Model of asset returns: GMM estimation and linear forecasting of volatility (2006) This item may be available elsewhere in EconPapers: Search for items with the same title.Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/TextPersistent link: :zbw:cauewp:2442Access Statistics for this paperMore papers in Economics Working Papers from Christian-Albrechts-University of Kiel, Department of Economics Contact information at EDIRC.Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics (Obfuscate( 'zbw.eu', 'econstor-publish' )). var addthis_config = "data_track_clickback":true; var addthis_share = url:" :zbw:cauewp:2442"Share This site is part of RePEc and all the data displayed here is part of the RePEc data set. Is your work missing from RePEc? Here is how to contribute. Questions or problems? Check the EconPapers FAQ or send mail to Obfuscate( 'oru.se', 'econpapers' ). EconPapers is hosted by the Örebro University School of Business. 2ff7e9595c
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