Accounting & Finance

We propose a simple modification to the error backpropagation procedure which takes into account gradually changing input-output relations. The procedure is based on the principle of Discounted least squares whereby learning is biased towards more recent observations with long term effects experiencing exponential decay through time. This is particularly important in systems in which the structural relationship between input and response vectors changes gradually over time but certain elements of long term memory are still retained. The procedure is implemented by a simple modification of the least-squares cost function commonly used in error backpropagation. We compare the performance of the two cost functions using both a controlled simulation experiment and a non-trivial application in estimating stock returns on the basis of multiple factor exposures. We show that in both cases the DLS procedure gives significantly better results. Typically, there is an average improvement of above 30% (in MSE terms) for the stock return modelling problem.

The scope of this study is to present a complete statistical framework for model identification of wavelet neural networks (WN). In each step in WN construction we test various methods already proposed in literature. In the first part we compare four different methods for the initialization and construction of the WN. Next various information criteria as well as sampling techniques proposed in previous works were compared to derive an algorithm for selecting the correct topology of a WN. Finally, in variable significance testing the performance of various sensitivity and model-fitness criteria were examined and an algorithm for selecting the significant explanatory variables is presented.

Abstract. In this paper, we use wavelet analysis to localize in Paris, France, a mean-reverting Ornstein-Uhlenbeck process with seasonality in the level and volatility. Wavelet analysis is an extension of the Fourier transform, which is very well suited to the analysis of ...

Neural networks are a consistent example of non-parametric estimation, with powerful universal approximation properties. However, the effective development and deployment of neural network applications, has to be based on established procedures for estimating confidence and ...

In this paper, we try to investigate the factors that affect crude oil price for the period 1988-2008 comparing a linear and a non-linear approach. We studied the dynamics of the West Texas Intermediate crude oil price time series as well as the relation of crude oil price and returns to various explanatory variables. First we use wavelet analysis to extract the driving forces and dynamics of the crude oil price and returns processes. Wavelet analysis brought out events and breaks of the time series that were not originally visible. Moreover examining the wavelet transform of past events we can make assumptions about the future behavior of oil prices. Moreover we examine if a wavelet neural network estimator can provide some incremental value in understanding the crude oil price process. Unlike the linear model wavelet network findings are in line with those of economic analysts. Wavelet networks not only have better predictive power in forecasting crude oil returns, but can also model correctly the dynamics of returns. In addition the sensitivity of crude oil prices and returns were examined and the time evolution of the affection of each predictor to the crude oil returns presented. Finally, forecasted values of crude oil returns were presented under various scenarios.

Wind is considered to be a free, renewable and environmentally friendly source of energy. However, wind farms are exposed to excessive weather risk since the power production depends on the wind speed, the wind direction and the wind duration. This risk can be successfully hedged using a financial instrument called weather derivatives. In this study the dynamics of the wind generating process are modeled using a non-parametric non-linear wavelet network. Our model is validated in New York. The proposed methodology is compared against alternative methods, proposed in prior studies. Our results indicate that wavelet networks can model the wind process very well and consequently they constitute an accurate and efficient tool for wind derivatives pricing. Finally, we provide the pricing equations for wind futures written on two indices, the cumulative average wind speed index and the Nordix wind speed index.

A step-by-step introduction to modeling, training, and forecasting using wavelet networks Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification presents the statistical model identification framework that is needed to successfully apply wavelet networks as well as extensive comparisons of alternate methods. Providing a concise and rigorous treatment for constructing optimal wavelet networks, the book links mathematical aspects of wavelet network construction to statistical modeling and forecasting applications in areas such as finance, chaos, and classification.

According to International Energy Outlook 2007 the total world demand of energy is projected to increase through 2030 about 95% for the non-OECD region and 24% for OECD nations. Crude oil is one of the most critical energy commodities while with coal and natural gas are projected to provide roughly the 86% share of the total US primary energy supply in 2030. In this paper, we use wavelet neural networks to forecast monthly West Texas Intermediate (WTI) crude oil spot prices. As explanatory variables we consider price lags, the producer price index for petroleum and the world production of crude oil. The data are provided by the Energy Information Administration (EIA). The proposed model is used to forecast in-sample and out-of-sample. We forecast one, three and six month future prices of crude oil and we compare our estimates with the EIA's STEO econometric forecasting model.

The scope of this study is to present a complete statistical framework for model identification of wavelet neural networks (WN). In each step in WN construction we test various methods already proposed in literature. In the first part we compare four different methods for the initialization and construction of the WN. Next various information criteria as well as sampling techniques proposed in previous works were compared to derive an algorithm for selecting the correct topology of a WN. Finally, in variable significance testing the performance of various sensitivity and model-fitness criteria were examined and an algorithm for selecting the significant explanatory variables is presented.

This study examines the conditional relationship between beta and return for stocks traded on S&P 500 for the period from July 2001 to June 2011. The portfolios formed based on the Book value per share and betas using monthly data. A novel approach for capturing time variation in betas whose pattern is treated as a function of market returns is developed and presented. The estimated coefficients of a nonlinear regression constitute the basis of creating a two factor model. Our results indicate that the proposed specification surpasses alternative models in explaining the cross-section of returns.

We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we "learn" the induced nonlinear mapping using a local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its eAectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.

A step-by-step introduction to modeling, training, and forecasting using wavelet networks Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification presents the statistical model identification framework that is needed to successfully apply wavelet networks as well as extensive comparisons of alternate methods. Providing a concise and rigorous treatment for constructing optimal wavelet networks, the book links mathematical aspects of wavelet network construction to statistical modeling and forecasting applications in areas such as finance, chaos, and classification.