Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

Long-term dependence in financial prices: evidence from the Belgian stock market returns

This article aims to contribute to the discussion of long-term dependence, focusing on the behavior of the main Belgian stock index. Non-parametric analyzes of the general characteristics of temporal frequency show that daily returns are non-ergodic and non-stationary. Therefore, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA), under the fractional Brownian motion approach, and we found slight evidence of long-term dependence. These results refute the random walk hypothesis with i.i.d. increments, which is the basis of the EMH in its weak form, and call into question some theoretical modeling of asset pricing. Other more localized complementary study, to identify the evolution of the degree of dependence over time windows, showed that the index has become less persistent from 2010. This may mean a maturing market by the extension of the effects of current financial crisis.

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

A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.

Short-term Wind Forecasting to Support Virtual Power Player Operation

This paper proposes a wind speed forecasting model that contributes to the development and implementation of adequate methodologies for Energy Resource Man-agement in a distribution power network, with intensive use of wind based power generation. The proposed fore-casting methodology aims to support the operation in the scope of the intraday resources scheduling model, name-ly with a time horizon of 10 minutes. A case study using a real database from the meteoro-logical station installed in the GECAD renewable energy lab was used. A new wind speed forecasting model has been implemented and it estimated accuracy was evalu-ated and compared with a previous developed forecast-ing model. Using as input attributes the information of the wind speed concerning the previous 3 hours enables to obtain results with high accuracy for the wind short-term forecasting.

Short-term Load Forecasting Based on Load Profiling

Load forecasting has gradually becoming a major field of research in electricity industry. Therefore, Load forecasting is extremely important for the electric sector under deregulated environment as it provides a useful support to the power system management. Accurate power load forecasting models are required to the operation and planning of a utility company, and they have received increasing attention from researches of this field study. Many mathematical methods have been developed for load forecasting. This work aims to develop and implement a load forecasting method for short-term load forecasting (STLF), based on Holt-Winters exponential smoothing and an artificial neural network (ANN). One of the main contributions of this paper is the application of Holt-Winters exponential smoothing approach to the forecasting problem and, as an evaluation of the past forecasting work, data mining techniques are also applied to short-term Load forecasting. Both ANN and Holt-Winters exponential smoothing approaches are compared and evaluated.

Solar Intensity Forecasting using Artificial Neural Networks and Support Vector Machines

This paper presents several forecasting methodologies based on the application of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), directed to the prediction of the solar radiance intensity. The methodologies differ from each other by using different information in the training of the methods, i.e, different environmental complementary fields such as the wind speed, temperature, and humidity. Additionally, different ways of considering the data series information have been considered. Sensitivity testing has been performed on all methodologies in order to achieve the best parameterizations for the proposed approaches. Results show that the SVM approach using the exponential Radial Basis Function (eRBF) is capable of achieving the best forecasting results, and in half execution time of the ANN based approaches.

Short-term Wind Speed Forecasting using Support Vector Machines

Wind speed forecasting has been becoming an important field of research to support the electricity industry mainly due to the increasing use of distributed energy sources, largely based on renewable sources. This type of electricity generation is highly dependent on the weather conditions variability, particularly the variability of the wind speed. Therefore, accurate wind power forecasting models are required to the operation and planning of wind plants and power systems. A Support Vector Machines (SVM) model for short-term wind speed is proposed and its performance is evaluated and compared with several artificial neural network (ANN) based approaches. A case study based on a real database regarding 3 years for predicting wind speed at 5 minutes intervals is presented.

Multi-Objective and Financial Portfolio Optimization of Carrier-Sense Multiple Access Protocols with Cooperative Diversity

8th International Workshop on Multiple Access Communications (MACOM2015), Helsinki, Finland.

Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.