Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950-2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling pa-rameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “con-trarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur.Gaussian Processes; Mixed Fractional Brownian Motion; Hurst Exponent; Local Self-similarity, Persistence; Anti-persistence; Definiteness of covariance Functions; Dissipative dynamic systems

Evaluating the efficiency of Latin American banks

Latin American banking sector has undergone tremendous changes over the years as a result of changes in regulation, globalization and developments in Telecommunications and Information Technology. A very important development has been financial liberalization where Latin America opened its doors to foreign banks. An important issue that needs to be addressed is whether the local commercial banks are efficient enough in their operations to be economically viable in a highly competitive environment. The objective of this study is to examine the factors behind bank profitability, following financial liberalization in five countries, Honduras, Mexico, Paraguay, Peru, and Venezuela, using 2004 financial data.Banking efficiency; financial liberalization; Latin American banking

Dollarization in El Salvador: Revisited

The economic crisis in different parts of Latin America has given rise to consideration of dollarization as an option for many of these countries. Those countries that seek to replace their domestic currencies with the US dollar do so with the hope of achieving both growth and economic stability. At the beginning of 2001, El Salvador began a bold experiment of with dollarization. According to many economists, dollarization does nothing to resolve structural and institutional problems which, in many cases, give rise to economic problems. The purpose of this paper is to address the dollarization in El Salvador. This paper will address both the costs and benefits facing the path that El Salvador has chose

The Impact of the Adoption of the Euro: Evidence From Portugal

The purpose of this paper is to analyze the impact of the adoption of the Euro on trade within the Euro-zone, in particular on how it specifically affects the Iberian Peninsula, more specifically the country of Portugal. The literature on monetary unions has argued that there are benefits and costs for those countries in entering a monetary union and adopting a single currency other than their own and who give up their monetary policy. The primary benefits from following this course of action are the uncertainties associated with exchange rate fluctuations and the elimination of transaction costs. Other benefits include 1) a single European market, 2) a single financial market, which benefits both investors and savers, 3) political integration, which benefits the entire process of integration, and 4) practical benefits, such as facilitating travel within the Euro area. Included among the costs are the loss of seignorage and the loss of an independent monetary polic

Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index

In extant financial market models, including the Black-Scholes’ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of ‘independent price fluctuations’ and the existence of some ‘fixed-point equilibrium’. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a ‘black noise’ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the ‘value at risk’.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk

Mixed Fractional Brownian Motion, Short and Long-Term Dependence and Economic Conditions: The Case of the S&P-500 Index

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950- 2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling parameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “contrarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur.Key words: Gaussian processes; Mixed fractional Brownian motion; Hurst exponent; Local self-similarity; Persistence; Anti-persistence; Definiteness of covariance functions; Dissipative dynamic system

Mixed Fractional Brownian Motion, Short and Long-Term Dependence and Economic Conditions: The Case of the S&P-500 Index

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950- 2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling parameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “contrarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur.Key words: Gaussian processes; Mixed fractional Brownian motion; Hurst exponent; Local self-similarity; Persistence; Anti-persistence; Definiteness of covariance functions; Dissipative dynamic system

The dynamics of market share’s growth and competition in quadratic mappings

This paper shows that the observed output of any market, placed within the confine of a quadratic map, can characterize the state of that market. Such an approach explains the process of market share’s growth and its pitfalls, the consequences of broken symmetry of scaling, as well as the limits of firms’ competition for market share

Could Investors’ Expectations Explain Temporal Variations in Hurst’s Exponent, Loci of Multifractal Spectra, and Statistical Prediction Errors? The Case of the S&P 500 Index

Over the periods 1998-2002 and 2009-2011, the S&P-500 Index went from persistence to anti-persistence mode, as measured by the Hurst index H. To uncover the reasons that characterize such a change, this paper uses a simple method that consists in treating quasi self-similar segments of the Index as initiators, and then finding appropriate generators with two intervals each to asymptotically model the strange attractor. The multifractal formalism shows that the change in persistence implies a corresponding change in the multifractal spectrum, and an enlargement of the invariant equilibrium set, making a market crash more likely, most probably due to a collapse of investors’ expectations. This also means that all statistical predictions made in one mode would have been off by an amount proportional to change in any element of the generalized set of dimensions in the other

Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950-2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling pa-rameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “con-trarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur