Adaptive learning in multiagent systems: a forecasting methodology based on error analysis

Electricity markets are complex environments, involving a large number of different entities, playing in a dynamic scene to obtain the best advantages and profits. MASCEM is a multi-agent electricity market simu-lator to model market players and simulate their operation in the market. Market players are entities with specific characteristics and objectives, making their decisions and interacting with other players. MASCEM pro-vides several dynamic strategies for agents’ behaviour. This paper presents a method that aims to provide market players strategic bidding capabilities, allowing them to obtain the higher possible gains out of the market. This method uses an auxiliary forecasting tool, e.g. an Artificial Neural Net-work, to predict the electricity market prices, and analyses its forecasting error patterns. Through the recognition of such patterns occurrence, the method predicts the expected error for the next forecast, and uses it to adapt the actual forecast. The goal is to approximate the forecast to the real value, reducing the forecasting error.

Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadística de Catalunya) with the Chambers of Commerce (Cámaras de Comercio) of Sabadell and Terrassa.

Use of Two-Part Regression Calibration Model to Correct for Measurement Error in Episodically Consumed Foods in a Single-Replicate Study Design: EPIC Case Study.

In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis

This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treatments, obtained from the analysis with recovery of interblock information, having as mean square of the error the mean effective variance of this same analysis with recovery of inter-block information. For the four alternatives of analysis, the estimators and estimates were obtained for the variance components and heritability coefficients. The classification of material was also studied. The present study suggests that for each experiment and depending of the objectives of the analysis, one should observe which alternative of analysis is preferable, mainly in cases where a negative estimate is obtained for the variance component due to effects of blocks within adjusted repetitions.

Looking for Validity or Testing It? The Perils of Stepwise Regression, Extreme-Scores Analysis, Heteroscedasticity, and Measurement Error

When researchers introduce a new test they have to demonstrate that it is valid, using unbiased designs and suitable statistical procedures. In this article we use Monte Carlo analyses to highlight how incorrect statistical procedures (i.e., stepwise regression, extreme scores analyses) or ignoring regression assumptions (e.g., heteroscedasticity) contribute to wrong validity estimates. Beyond these demonstrations, and as an example, we re-examined the results reported by Warwick, Nettelbeck, and Ward (2010) concerning the validity of the Ability Emotional Intelligence Measure (AEIM). Warwick et al. used the wrong statistical procedures to conclude that the AEIM was incrementally valid beyond intelligence and personality traits in predicting various outcomes. In our re-analysis, we found that the reliability-corrected multiple correlation of their measures with personality and intelligence was up to .69. Using robust statistical procedures and appropriate controls, we also found that the AEIM did not predict incremental variance in GPA, stress, loneliness, or well-being, demonstrating the importance for testing validity instead of looking for it.

Quantitative market and sales forecast accuracy analysis

The main objective of this master’s thesis was to quantitatively study the reliability of market and sales forecasts of a certain company by measuring bias, precision and accuracy of these forecasts by comparing forecasts against actual values. Secondly, the differences of bias, precision and accuracy between markets were explained by various macroeconomic variables and market characteristics. Accuracy and precision of the forecasts seems to vary significantly depending on the market that is being forecasted, the variable that is being forecasted, the estimation period, the length of the estimated period, the forecast horizon and the granularity of the data. High inflation, low income level and high year-on-year market volatility seems to be related with higher annual market forecast uncertainty and high year-on-year sales volatility with higher sales forecast uncertainty. When quarterly market size is forecasted, correlation between macroeconomic variables and forecast errors reduces. Uncertainty of the sales forecasts cannot be explained with macroeconomic variables. Longer forecasts are more uncertain, shorter estimated period leads to higher uncertainty, and usually more recent market forecasts are less uncertain. Sales forecasts seem to be more uncertain than market forecasts, because they incorporate both market size and market share risks. When lead time is more than one year, forecast risk seems to grow as a function of root forecast horizon. When lead time is less than year, sequential error terms are typically correlated, and therefore forecast errors are trending or mean-reverting. The bias of forecasts seems to change in cycles, and therefore the future forecasts cannot be systematically adjusted with it. The MASE cannot be used to measure whether the forecast can anticipate year-on-year volatility. Instead, we constructed a new relative accuracy measure to cope with this particular situation.

Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Estimation de la variance en présence de données imputées pour des plans de sondage à grande entropie

Les travaux portent sur l’estimation de la variance dans le cas d’une non- réponse partielle traitée par une procédure d’imputation. Traiter les valeurs imputées comme si elles avaient été observées peut mener à une sous-estimation substantielle de la variance des estimateurs ponctuels. Les estimateurs de variance usuels reposent sur la disponibilité des probabilités d’inclusion d’ordre deux, qui sont parfois difficiles (voire impossibles) à calculer. Nous proposons d’examiner les propriétés d’estimateurs de variance obtenus au moyen d’approximations des probabilités d’inclusion d’ordre deux. Ces approximations s’expriment comme une fonction des probabilités d’inclusion d’ordre un et sont généralement valides pour des plans à grande entropie. Les résultats d’une étude de simulation, évaluant les propriétés des estimateurs de variance proposés en termes de biais et d’erreur quadratique moyenne, seront présentés.

Short-Term Load Forecast Of A Low Loadfactor Power System For Optimization Of Merit Order Dispatch Using Adaptive Learning Algorithm

Short term load forecasting is one of the key inputs to optimize the management of power system. Almost 60-65% of revenue expenditure of a distribution company is against power purchase. Cost of power depends on source of power. Hence any optimization strategy involves optimization in scheduling power from various sources. As the scheduling involves many technical and commercial considerations and constraints, the efficiency in scheduling depends on the accuracy of load forecast. Load forecasting is a topic much visited in research world and a number of papers using different techniques are already presented. The accuracy of forecast for the purpose of merit order dispatch decisions depends on the extent of the permissible variation in generation limits. For a system with low load factor, the peak and the off peak trough are prominent and the forecast should be able to identify these points to more accuracy rather than minimizing the error in the energy content. In this paper an attempt is made to apply Artificial Neural Network (ANN) with supervised learning based approach to make short term load forecasting for a power system with comparatively low load factor. Such power systems are usual in tropical areas with concentrated rainy season for a considerable period of the year

Using the R-MAPE index as a resistant measure of forecast accuracy

Resumen tomado de la publicación

Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

Forecast calibration and combination: a simple Bayesian approach for ENSO

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Niño-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Niño-3.4 index values over the period 1950–2001. Coupled model ensemble forecasts for the period 1987–99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987–99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.