Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

A real time pricing approach to deal with excessive wind power situations

The introduction of wind power generation in several countries around the world, including in European countries, where energy policy directives have encouraged the use of renewables, led to several changes in market and power systems operation. The intensive integration of these sources has led to situations in which the demand is lower than the available renewable resources. In these situations a part of the available generation is wasted if not used for storage or to supply additional demand. This paper proposes a real time demand response methodology based on changing the electricity price for the consumers expecting an increase in the demand in the periods in which that demand is lower than the available renewable generation. The consumers response to the changes in electricity price is characterized by their price elasticity of demand considered distinct for each consumer type. The proposed methodology is applied to the Portuguese power system, in the context of the Iberian electricity market (MIBEL). The renewable-based producers are considered as special producers, with special tariffs, and so it is important to use the energy available as it will be paid anyway. In this context, consumers are entities actively participating in the operation of the market.

Virtual power players dealing with excessive wind power situations using real time pricing

The increasing importance given by environmental policies to the dissemination and use of wind power has led to its fast and large integration in power systems. In most cases, this integration has been done in an intensive way, causing several impacts and challenges in current and future power systems operation and planning. One of these challenges is dealing with the system conditions in which the available wind power is higher than the system demand. This is one of the possible applications of demand response, which is a very promising resource in the context of competitive environments that integrates even more amounts of distributed energy resources, as well as new players. The methodology proposed aims the maximization of the social welfare in a smart grid operated by a virtual power player that manages the available energy resources. When facing excessive wind power generation availability, real time pricing is applied in order to induce the increase of consumption so that wind curtailment is minimized. The proposed method is especially useful when actual and day-ahead wind forecast differ significantly. The proposed method has been computationally implemented in GAMS optimization tool and its application is illustrated in this paper using a real 937-bus distribution network with 20310 consumers and 548 distributed generators, some of them with must take contracts.

Demand response in electrical energy supply: an optimal real time pricing approach

In competitive electricity markets with deep concerns for the efficiency level, demand response programs gain considerable significance. As demand response levels have decreased after the introduction of competition in the power industry, new approaches are required to take full advantage of demand response opportunities. This paper presents DemSi, a demand response simulator that allows studying demand response actions and schemes in distribution networks. It undertakes the technical validation of the solution using realistic network simulation based on PSCAD. The use of DemSi by a retailer in a situation of energy shortage, is presented. Load reduction is obtained using a consumer based price elasticity approach supported by real time pricing. Non-linear programming is used to maximize the retailer’s profit, determining the optimal solution for each envisaged load reduction. The solution determines the price variations considering two different approaches, price variations determined for each individual consumer or for each consumer type, allowing to prove that the approach used does not significantly influence the retailer’s profit. The paper presents a case study in a 33 bus distribution network with 5 distinct consumer types. The obtained results and conclusions show the adequacy of the used methodology and its importance for supporting retailers’ decision making.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Contextual Intelligent Load Management Considering Real-Time Pricing in a Smart Grid Environment

The use of demand response programs enables the adequate use of resources of small and medium players, bringing high benefits to the smart grid, and increasing its efficiency. One of the difficulties to proceed with this paradigm is the lack of intelligence in the management of small and medium size players. In order to make demand response programs a feasible solution, it is essential that small and medium players have an efficient energy management and a fair optimization mechanism to decrease the consumption without heavy loss of comfort, making it acceptable for the users. This paper addresses the application of real-time pricing in a house that uses an intelligent optimization module involving artificial neural networks.

Real Time Pricing Approaches to Deal With Unexpected Wind Power Variations

The use of renewables have been increased I several countries around the world, namely in Europe. The wind power is generally the larger renewable resource with very specific characteristics in what concerns its variability and the inherent impacts in the power systems and electricity markets operation. This paper focuses on the Portuguese context of renewables use, including wind power. The work here presented includes the use of a real time pricing methodology developed by the authors aiming the reduction of electricity consumption in the moments of unexpected low wind power. A more specific example of application of real time pricing is demonstrated for the minimization of the operation costs in a distribution network. When facing lower wind power generation than expected from day ahead forecast, demand response is used in order to minimize the impacts of such wind availability change. In this way, consumers actively participate in regulation up and spinning reserve ancillary services through demand response programs.

Real-Time Simulation of Real-Time Pricing Demand Response to Meet Wind Variations

Recent changes of paradigm in power systems opened the opportunity to the active participation of new players. The small and medium players gain new opportunities while participating in demand response programs. This paper explores the optimal resources scheduling in two distinct levels. First, the network operator facing large wind power variations makes use of real time pricing to induce consumers to meet wind power variations. Then, at the consumer level, each load is managed according to the consumer preferences. The two-level resources schedule has been implemented in a real-time simulation platform, which uses hardware for consumer’ loads control. The illustrative example includes a situation of large lack of wind power and focuses on a consumer with 18 loads.

How realistic is the mixed-criticality real-time system model?

23rd International Conference on Real-Time Networks and Systems (RTNS 2015). 4 to 6, Nov, 2015, Main Track. Lille, France. Best Paper Award Nominee

Using demand response to deal with unexpected low wind power generation in the context of smart grid

Demand response is assumed an essential resource to fully achieve the smart grids operating benefits, namely in the context of competitive markets. Some advantages of Demand Response (DR) programs and of smart grids can only be achieved through the implementation of Real Time Pricing (RTP). The integration of the expected increasing amounts of distributed energy resources, as well as new players, requires new approaches for the changing operation of power systems. The methodology proposed aims the minimization of the operation costs in a smart grid operated by a virtual power player. It is especially useful when actual and day ahead wind forecast differ significantly. When facing lower wind power generation than expected, RTP is used in order to minimize the impacts of such wind availability change. The proposed model application is here illustrated using the scenario of a special wind availability reduction day in the Portuguese power system (8th February 2012).

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

Long-term memory in financial prices: evidence from the Dutch stock market returns

Prepared for presentation at the Portuguese Finance Network International Conference 2014, Vilamoura, Portugal, June 18-20

An optimal boundary fair scheduling

Nowadays, many real-time operating systems discretize the time relying on a system time unit. To take this behavior into account, real-time scheduling algorithms must adopt a discrete-time model in which both timing requirements of tasks and their time allocations have to be integer multiples of the system time unit. That is, tasks cannot be executed for less than one time unit, which implies that they always have to achieve a minimum amount of work before they can be preempted. Assuming such a discrete-time model, the authors of Zhu et al. (Proceedings of the 24th IEEE international real-time systems symposium (RTSS 2003), 2003, J Parallel Distrib Comput 71(10):1411–1425, 2011) proposed an efficient “boundary fair” algorithm (named BF) and proved its optimality for the scheduling of periodic tasks while achieving full system utilization. However, BF cannot handle sporadic tasks due to their inherent irregular and unpredictable job release patterns. In this paper, we propose an optimal boundary-fair scheduling algorithm for sporadic tasks (named BF TeX ), which follows the same principle as BF by making scheduling decisions only at the job arrival times and (expected) task deadlines. This new algorithm was implemented in Linux and we show through experiments conducted upon a multicore machine that BF TeX outperforms the state-of-the-art discrete-time optimal scheduler (PD TeX ), benefiting from much less scheduling overheads. Furthermore, it appears from these experimental results that BF TeX is barely dependent on the length of the system time unit while PD TeX —the only other existing solution for the scheduling of sporadic tasks in discrete-time systems—sees its number of preemptions, migrations and the time spent to take scheduling decisions increasing linearly when improving the time resolution of the system.

Virtual Power Player Using Demand Response to Deal with Unexpected Low Wind Power Generation

Demand response is assumed as an essential resource to fully achieve the smart grids operating benefits, namely in the context of competitive markets and of the increasing use of renewable-based energy sources. Some advantages of Demand Response (DR) programs and of smart grids can only be achieved through the implementation of Real Time Pricing (RTP). The integration of the expected increasing amounts of distributed energy resources, as well as new players, requires new approaches for the changing operation of power systems. The methodology proposed in this paper aims the minimization of the operation costs in a distribution network operated by a virtual power player that manages the available energy resources focusing on hour ahead re-scheduling. When facing lower wind power generation than expected from day ahead forecast, demand response is used in order to minimize the impacts of such wind availability change. In this way, consumers actively participate in regulation up and spinning reserve ancillary services through demand response programs. Real time pricing is also applied. The proposed model is especially useful when actual and day ahead wind forecast differ significantly. Its application is illustrated in this paper implementing the characteristics of a real resources conditions scenario in a 33 bus distribution network with 32 consumers and 66 distributed generators.

Maximizing the Social Welfare of Virtual Power Players Operation in Case of Excessive Wind Power

The integration of growing amounts of distributed generation in power systems, namely at distribution networks level, has been fostered by energy policies in several countries around the world, including in Europe. This intensive integration of distributed, non-dispatchable, and natural sources based generation (including wind power) has caused several changes in the operation and planning of power systems and of electricity markets. Sometimes the available non-dispatchable generation is higher than the demand. This generation must be used; otherwise it is wasted if not stored or used to supply additional demand. New policies and market rules, as well as new players, are needed in order to competitively integrate all the resources. The methodology proposed in this paper aims at the maximization of the social welfare in a distribution network operated by a virtual power player that aggregates and manages the available energy resources. When facing a situation of excessive non-dispatchable generation, including wind power, real time pricing is applied in order to induce the increase of consumption so that wind curtailment is minimized. This method is especially useful when actual and day-ahead resources forecast differ significantly. The distribution network characteristics and concerns are addressed by including the network constraints in the optimization model. The proposed methodology has been implemented in GAMS optimization tool and its application is illustrated in this paper using a real 937-bus distribution network with 20.310 consumers and 548 distributed generators, some of them non-dispatchable and with must take contracts. The implemented scenario corresponds to a real day in Portuguese power system.