A teoria da eficiência no mercado de capitais: uma revisão da literatura e dos trabalhos empíricos: o modelos de Random walk aplicado ao índice de mercado de ações Bovespa

Durante muitos anos uma controversa questão tem ocupado tanto os discursos acadêmicos quanto os financeiros. O problema a ser resolvido diz respeito à evolução passada dos preços das ações e se tal evolução poderia ser utilizada para prever o comportamento dos preços futuros dessas ações.

Alzheimer random walk model: Two previously overlooked diffusion regimes

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Shape anisotropy of a single random-walk polymer

Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2–11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity.

The emergence of order in random walk resource discovery protocols

While others have attempted to determine, by way of mathematical formulae, optimal resource duplication strategies for random walk protocols, this paper is concerned with studying the emergent effects of dynamic resource propagation and replication. In particular, we show, via modelling and experimentation, that under any given decay (purge) rate the number of nodes that have knowledge of particular resource converges to a fixed point or a limit cycle. We also show that even for high rates of decay - that is, when few nodes have knowledge of a particular resource - the number of hops required to find that resource is small.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

A Random Walk down Main Street

US suburbs have often been characterized by their relatively low walk accessibility compared to more urban environments, and US urban environments have been characterized by low walk accessibility compared to cities in other countries. Lower overall density in the suburbs implies that activities, if spread out, would have a greater distance between them. But why should activities be spread out instead of developed contiguously? This brief research note builds a positive model for the emergence of contiguous development along “Main Street” to illustrate the trade-offs that result in the built environment we observe. It then suggests some policy interventions to place a “thumb on the scale” to choose which parcels will develop in which sequence to achieve socially preferred outcomes.

Random walk with restart over dynamic graphs

Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V|^3) time and O(|V|^2) memory to compute all (|V|^2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V|^3) to O(|delta|) time for each update without loss of accuracy, where |delta| (<<|V|^2) is the number of affected proximities. (2) To avoid O(|V|^2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V|) memory and O(|V|/l) I/O costs, where 1<=l<=|V| is a user-controlled trade-off between memory and I/O costs. (3) For bulk updates, we also devise aggregation and hashing methods, which can discard many unnecessary updates further and handle chunks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1–2 orders of magnitude faster than other competitors while securing scalability and exactness.

Essays on Risk Modeling. Applications to Portfolio and Risk Management (summary section only)

In this thesis we deal with the concept of risk. The objective is to bring together and conclude on some normative information regarding quantitative portfolio management and risk assessment. The first essay concentrates on return dependency. We propose an algorithm for classifying markets into rising and falling. Given the algorithm, we derive a statistic: the Trend Switch Probability, for detection of long-term return dependency in the first moment. The empirical results suggest that the Trend Switch Probability is robust over various volatility specifications. The serial dependency in bear and bull markets behaves however differently. It is strongly positive in rising market whereas in bear markets it is closer to a random walk. Realized volatility, a technique for estimating volatility from high frequency data, is investigated in essays two and three. In the second essay we find, when measuring realized variance on a set of German stocks, that the second moment dependency structure is highly unstable and changes randomly. Results also suggest that volatility is non-stationary from time to time. In the third essay we examine the impact from market microstructure on the error between estimated realized volatility and the volatility of the underlying process. With simulation-based techniques we show that autocorrelation in returns leads to biased variance estimates and that lower sampling frequency and non-constant volatility increases the error variation between the estimated variance and the variance of the underlying process. From these essays we can conclude that volatility is not easily estimated, even from high frequency data. It is neither very well behaved in terms of stability nor dependency over time. Based on these observations, we would recommend the use of simple, transparent methods that are likely to be more robust over differing volatility regimes than models with a complex parameter universe. In analyzing long-term return dependency in the first moment we find that the Trend Switch Probability is a robust estimator. This is an interesting area for further research, with important implications for active asset allocation.

Especificação de um modelo para explicação e projeção de retornos do IBRX-100

Neste trabalho, propomos uma especificação de modelo econométrico na forma reduzida, estimado por mínimos quadrados ordinários (MQO) e baseado em variáveis macroeconômicas, com o objetivo de explicar os retornos trimestrais do índice de ações IBRX-100, entre 2001 e 2015. Testamos ainda a eficiência preditiva do modelo e concluímos que o erro de previsão estimado em janela móvel, com re-estimação de MQO a cada rodada, e utilização de VAR auxiliar para projeção dos regressores, é significativamente inferior ao erro de previsão associado à hipótese de Random Walk para o horizonte de previsão de um trimestre a frente.