Expectations equilibria with dispersed forecasts

A dispersion condition for traders' forecasts in a general equilibrium model with uncertainty and asymmetric information yields improved results for some (microeconomic) situations in which rational expectations equilibria need not exist. The hypothesis of suitably dispersed forecasts implies that consumers' aggregate excess demand is a continuous function and therefore a fixed point theorem may be applied to obtain a price vector (for each state of the world) such that markets clear. Stronger assumptions give existence of approximately rational expectations equilibria and the convergence of forecast distributions to rational expectations.     

Improving prediction market forecasts by detecting and correcting possible over-reaction to price movements

We examine the impact of price trends on the accuracy of forecasts from prediction markets. In particular, we study an electronic betting exchange market and construct independent variables from market price (odds) time series from 6058 individual markets (a dataset consisting of over 8.4 million price points). Using a conditional logit model, we find that a systematic relationship exists between trends in odds and the accuracy of odds-implied event probabilities; the relationship is consistent with participants over-reacting to price movements. In particular, in different time segments of the market, increasing and decreasing odds lead, respectively, to under- and over-estimation of odds-implied probabilities. We develop a methodology to detect and correct the erroneous forecasts associated with these trends in odds in order to considerably improve the quality of forecasts generated in prediction markets.     

Electricity price forecasting accounting for renewable energies: optimal combined forecasts

Electricity price forecasting is an interesting problem for all the agents involved in electricity market operation. For instance, every profit maximisation strategy is based on the computation of accurate one-day-ahead forecasts, which is why electricity price forecasting has been a growing field of research in recent years. In addition, the increasing concern about environmental issues has led to a high penetration of renewable energies, particularly wind. In some European countries such as Spain, Germany and Denmark, renewable energy is having a deep impact on the local power markets. In this paper, we propose an optimal model from the perspective of forecasting accuracy, and it consists of a combination of several univariate and multivariate time series methods that account for the amount of energy produced with clean energies, particularly wind and hydro, which are the most relevant renewable energy sources in the Iberian Market. This market is used to illustrate the proposed methodology, as it is one of those markets in which wind power production is more relevant in terms of its percentage of the total demand, but of course our method can be applied to any other liberalised power market. As far as our contribution is concerned, first, the methodology proposed by García-Martos et al (2007 and 2012) is generalised twofold: we allow the incorporation of wind power production and hydro reservoirs, and we do not impose the restriction of using the same model for 24?h. A computational experiment and a Design of Experiments (DOE) are performed for this purpose. Then, for those hours in which there are two or more models without statistically significant differences in terms of their forecasting accuracy, a combination of forecasts is proposed by weighting the best models (according to the DOE) and minimising the Mean Absolute Percentage Error (MAPE). The MAPE is the most popular accuracy metric for comparing electricity price forecasting models. We construct the combination of forecasts by solving several nonlinear optimisation problems that allow computation of the optimal weights for building the combination of forecasts. The results are obtained by a large computational experiment that entails calculating out-of-sample forecasts for every hour in every day in the period from January 2007 to December 2009. In addition, to reinforce the value of our methodology, we compare our results with those that appear in recent published works in the field. This comparison shows the superiority of our methodology in terms of forecasting accuracy.     

Combining ranked mean value forecasts

A methodology is developed for combining mean value forecasts using not only all the important statistics related to the past performance and the dependence of the individual forecasts, but also a rank ordering of the individual forecasts representing the belief of a decision maker about the future performance of the forecasts. The maximum likelihood combination of the forecasts turns out to be weighted linear combination of the individual forecasts, where the weights are a function of the rank order of the forecasts, correlation coefficients between the forecasts, and relative entropy information measures between the individual forecasts and the actual values. These weights are assessed once in the most general case and once in a special case where the forecasts are normally distributed. The sensitivity of the weights is also investigated. A sample application of this method for predicting U.S. hog prices is also presented.     

Expectation formation in an experimental foreign exchange market

Participants of an experimental foreign exchange market forecast an exchange rate with an unknown price reaction function. Aggregate demand is derived from their own forecasts and random shocks. Our experimental results indicate that the expectations of the subjects tend to be coordinated on a common prediction strategy. This strategy is best described as a trend-extrapolative, destabilizing expectation formation scheme. Deviations from common expectations are mainly caused by random shocks, which can be ascribed to the similarity of the subjects’ behavior within and between the different markets. The findings can be explained using insights of behavioral economics.     

The reproducible properties of correct forecasts

Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an arbitrary function from sequences of forecasts and outcomes to {0,1}. When the test returns a 0 the test is said to reject the forecasts based on the outcome sequence. When the test resturns a 1 the test is said to not reject the forecasts based on the outcome sequence. Consider any test that does not reject the truth, i.e. it does not reject when the announced forecasts are the conditional probabilities of the data generating process. Based on Fans (1953) Minimax theorem, I show that it is possible to produce forecasts that will not be rejected on any sequence of outcomes. Journal of Economic Literature Classification Number:D83 LearningI thankfully acknowledge financial support from the National Science Foundation grant SES 0109650. I also thank a referee for useful comments. All errors are mine.     

人民币远期市场价格发现的实证研究

通过建立向量误差修正模型并运用信息份额模型对市场间共同价格发现的贡献大小进行定量分析.借助Engle-Granger的协整检验方法对人民币外汇市场,即境外人民币NDF汇率、境内人民币远期汇率以及人民币即期汇率市场三个市场两两之间的动态关系进行探讨.研究表明,在价格发现的领域,满足协整关系的两汇率市场间确实存在着一个共同变化的趋势即共因子（common factor）,它们之间有着共同的价格发现机理过程.     

Robust pair‐copula based forecasts of realized volatility

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e‐markets poses some specific challenges. The large amount of real‐time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high‐frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair‐copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair‐copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine‐based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.     

The efficiency of financial futures markets: Tests of prediction accuracy

The prices of financial futures contracts can be interpreted as forecasts of the spot rates, which will apply at the final delivery date of that contract. Financial futures contracts have been traded daily since the early 1980s and provide a substantial bank of data to test the forecasting efficiency of such contracts. Tests are carried out to examine whether the interest rates implied by the futures price for eurodollar and short sterling contracts are cointegrated with the final settlement price over forecasting horizons of 1, 2 and 3 months. Similar analysis is carried out for the yen/dollar exchange rate futures contract. The paper then examines the forecasting performance of the three contracts over the forecasting horizons of 1, 2 and 3 months and in particular whether the forecasts implied by the futures contract provide better predictions than the naı̈ve no-change (i.e. random walk), a vector error correction model (VECM) or an ARIMA model.An examination of the relative efficiency of the markets for the three markets over the three time horizons is carried out and finally trading strategies are simulated to see whether excess profits can be achieved. In fact the results suggest that both profits and losses would be attracted.     

News-based forecasts of macroeconomic indicators: A semantic path model for interpretable predictions

The macroeconomic climate influences operations with regard to, e.g., raw material prices, financing, supply chain utilization and demand quotas. In order to adapt to the economic environment, decision-makers across the public and private sectors require accurate forecasts of the economic outlook. Existing predictive frameworks base their forecasts primarily on time series analysis, as well as the judgments of experts. As a consequence, current approaches are often biased and prone to error. In order to reduce forecast errors, this paper presents an innovative methodology that extends lag variables with unstructured data in the form of financial news: (1) we apply a variety of models from machine learning to word counts as a high-dimensional input. However, this approach suffers from low interpretability and overfitting, motivating the following remedies. (2) We follow the intuition that the economic climate is driven by general sentiments and suggest a projection of words onto latent semantic structures as a means of feature engineering. (3) We propose a semantic path model, together with estimation technique based on regularization, in order to yield full interpretability of the forecasts. We demonstrate the predictive performance of our approach by utilizing 80,813 ad hoc announcements in order to make long-term forecasts of up to 24 months ahead regarding key macroeconomic indicators. Back-testing reveals a considerable reduction in forecast errors.     

Combining forecasts

This paper reviews current theories and practice of combining forecasts from a wide perspective. The various motivations for combining are discussed, with particular attention to model credibility as well as forecast accuracy. Issues which affect the performance of composite forecasts are identified. A concluding section reflects upon the limitations of the extreme perspective of pragmatism which fosters this approach to forecasting.     

Mortality density forecasts: An analysis of six stochastic mortality models

This paper develops a framework for developing forecasts of future mortality rates. We discuss the suitability of six stochastic mortality models for forecasting future mortality and estimating the density of mortality rates at different ages. In particular, the models are assessed individually with reference to the following qualitative criteria that focus on the plausibility of their forecasts: biological reasonableness; the plausibility of predicted levels of uncertainty in forecasts at different ages; and the robustness of the forecasts relative to the sample period used to fit the model. An important, though unsurprising, conclusion is that a good fit to historical data does not guarantee sensible forecasts. We also discuss the issue of model risk, common to many modelling situations in demography and elsewhere. We find that even for those models satisfying our qualitative criteria, there are significant differences among central forecasts of mortality rates at different ages and among the distributions surrounding those central forecasts.     

Expert and novice facilitated modelling: A case of a Viable System Model workshop in a local food network

This paper provides an empirical study based on action research in which expert and novice facilitators in facilitated modelling workshops are compared. There is limited empirical research analysing the differences between expert and novice facilitators. Aiming to address this gap we study the behaviour of one expert and two novice facilitators during a Viable System Model workshop. The findings suggest common facilitation patterns in the behaviour of experts and novices. This contrasts literature claiming that experts and novices behave and use their available knowledge differently, and empirically supports the claim that facilitation skills can be taught to participants to enable them to self-facilitate workshops. Differences were also found, which led to the introduction of a new dimension—‘internal versus external’ facilitation. The implications of our findings for effective training and facilitation strategies in contexts in which external, expert facilitation is not always possible are also discussed, and limitations of this study are provided.     

Using combined forecasts with changing weights for electricity demand profiling

Day-ahead half-hourly demand forecasts are required for scheduling and for calculating the daily electricity pool price. One approach predicts turning points on the demand curve and then produces half-hourly forecasts by a heuristic procedure, called profiling, which is based on a past demand curve. This paper investigates possible profiling improvements. Using a cubic smoothing spline in the heuristic leads to a slight improvement. Often, several past curves could reasonably be used in the profiling method. Consequently, there are often several demand curve forecasts available. Switching and smooth transition forecast combination models are considered. These models enable the combining weights to vary across the 48 half-hours, which is appealing as different forecasts may be more suitable for different periods. Several criteria are used to control the changing weights, including weather, and the methodology is extended to the case of more than two forecasts. Empirical analysis gives encouraging results.     

Using clustering to improve sales forecasts in retail merchandising

Given sales forecasts for a set of items along with the standard deviation associated with each forecast, we propose a new method of combining forecasts using the concepts of clustering. Clusters of items are identified based on the similarity in their sales forecasts and then a common forecast is computed for each cluster of items. On a real dataset from a national retail chain we have found that the proposed method of combining forecasts produces significantly better sales forecasts than either the individual forecasts (forecasts without combining) or an alternate method of using a single combined forecast for all items in a product line sold by this retailer.     

Bayesian multiperiod forecasts for ARX models

Bayestian muliperiod forecasts for AR models with random independent exogenous variables under normal-gamma and normal-inverted Wishart prior assumptions are investigated. By suitably arranging the integration order of the model's parameters, at-density mixture approximation is analytically derived to provide an estimator of the posterior predictive density for any future observation. In particular, a suitablet-density is proposed by a convenient closed form. The precision of the discussed methods is examined by using some simulated data and one set of real data up to lead-six-ahead forecasts. It is found that the numerical results of the discussed methods are rather close. In particular, when sample sizes are sufficiently large, it is encouraging to apply a convenientt-density in practical usage. In fact, thist-density estimator asymptotically converges to the true density.This research was supported by the National Science Council, Republic of China under contract #NSC82-0208-M-008-086.     

Using investment portfolio return to combine forecasts: A multiobjective approach

This study investigates the usefulness and efficacy of a multiobjective decision method for financial trading guided by a set of seemingly diverse analysts' forecasts. The paper proposes a goal programming (GP) approach which combines various forecasts based on the performance of their previous investment returns. In our experiment, several series of financial analysts' forecasts are generated by different forecasting techniques. Investment returns on each series of forecasts are measured and then evaluated by three performance criteria, namely, mean, variance, and skewness. Subsequently, these distributional properties of the returns are used to construct a GP model. Results of the GP model provide a set of weights to compose an investment portfolio using various forecasts. To examine its practicality, the approach is tested on several major stock market indices. The performance of the proposed GP approach is compared with those of individual forecasting techniques and a number of forecast combination models suggested by previous studies. This comparison is conducted with respect to different levels of investor preference over return, variance, and skewness. Statistical significance of the results are accessed by bootstrap re-sampling. Empirical results indicate that, for all examined investor preference functions and market indices, the GP approach is significantly better than all other models tested in this study.     

The Role of Visual Representations in Advanced Mathematical Problem Solving: An Examination of Expert-Novice Similarities and Differences

Expert mathematicians are contrasted with undergraduate students through a two-part analysis of the potential and actual use of visual representations in problem solving. In the first part, a classification task is used to indicate the extent to which visual representations are perceived as having potential utility for advanced mathematical problem solving. The analysis reveals that both experts and novices perceive visual representation use as a viable strategy. However, the two groups judge visual representations likely to be useful with different sets of problems. Novices generally indicate that visual representations would likely be useful mostly for geometry problems, whereas the experts indicate potential application to a wider variety of problems. In the second part, written solutions to problems and verbal protocols of problem-solving episodes are analyzed to determine the frequency, nature, and function of the visual representations actually used during problem solving. Experts construct visual representations more frequently than do novices and use them as dynamic objects to explore the problem space qualitatively, to develop a better understanding of the problem situation, and to guide their solution planning and enactment of problem-solving activity. In contrast, novices typically make little use of visual representations.     

The Role of Visual Representations in Advanced Mathematical Problem Solving: An Examination of Expert-Novice Similarities and Differences

Expert mathematicians are contrasted with undergraduate students through a two-part analysis of the potential and actual use of visual representations in problem solving. In the first part, a classification task is used to indicate the extent to which visual representations are perceived as having potential utility for advanced mathematical problem solving. The analysis reveals that both experts and novices perceive visual representation use as a viable strategy. However, the two groups judge visual representations likely to be useful with different sets of problems. Novices generally indicate that visual representations would likely be useful mostly for geometry problems, whereas the experts indicate potential application to a wider variety of problems. In the second part, written solutions to problems and verbal protocols of problem-solving episodes are analyzed to determine the frequency, nature, and function of the visual representations actually used during problem solving. Experts construct visual representations more frequently than do novices and use them as dynamic objects to explore the problem space qualitatively, to develop a better understanding of the problem situation, and to guide their solution planning and enactment of problem-solving activity. In contrast, novices typically make little use of visual representations.