Vector Error-Correction Models in a consumer packaged goods category forecasting decision support system

A framework for developing marketing category management decision support systems (DSS) based upon the Bayesian Vector Autoregressive (BVAR) model is extended. Since the BVAR model is vulnerable to permanent and temporary shifts in purchasing patterns over time, a form that can correct for the shifts and still provide the other advantages of the BVAR is a Bayesian Vector Error-Correction Model (BVECM). We present the mechanics of extending the DSS to move from a BVAR model to the BVECM model for the category management problem. Several additional iterative steps are required in the DSS to allow the decision maker to arrive at the best forecast possible. The revised marketing DSS framework and model fitting procedures are described. Validation is conducted on a sample problem.

On the relationship between Bayesian error bars and the input data density

We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions.

Statnote 10: the two-way analysis of variance

The two-way design has been variously described as a matched-sample F-test, a simple within-subjects ANOVA, a one-way within-groups ANOVA, a simple correlated-groups ANOVA, and a one-factor repeated measures design! This confusion of terminology is likely to lead to problems in correctly identifying this analysis within commercially available software. The essential feature of the design is that each treatment is allocated by randomization to one experimental unit within each group or block. The block may be a plot of land, a single occasion in which the experiment was performed, or a human subject. The ‘blocking’ is designed to remove an aspect of the error variation and increase the ‘power’ of the experiment. If there is no significant source of variation associated with the ‘blocking’ then there is a disadvantage to the two-way design because there is a reduction in the DF of the error term compared with a fully randomised design thus reducing the ‘power’ of the analysis.

Statnote 11: the two-factor analysis of variance

Experiments combining different groups or factors are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than simply the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, in a factorial experiment, it is important to define the design of the experiment in detail because this determines the appropriate type of ANOVA. We will discuss some of the common variations of factorial ANOVA in future statnotes. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.

The use of analysis of variance (ANOVA) in applied microbiology

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the DF of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, it is important to consider the design of the experiment because this determines the appropriate ANOVA to use. Some of the most common experimental designs used in the biosciences and their relevant ANOVAs are discussed by. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Data analysis methods in optometry Part 4: an introduction to analysis of variance (ANOVA)

In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

The influence on unaided vision of age, pupil diameter and spherocylindrical refractive error

Background - The aim was to derive equations for the relationship between unaided vision and age, pupil diameter, iris colour and sphero-cylindrical refractive error. Methods - Data were collected from 663 healthy right eyes of white subjects aged 20 to 70 years. Subjective sphero-cylindrical refractive errors ranged from -6.8 to +9.4 D (mean spherical equivalent), -1.5 to +1.9 D (orthogonal component, J0) and -0.8 to 1.0 D (oblique component, J45). Cylinder axis orientation was orthogonal in 46 per cent of the eyes and oblique in 18 per cent. Unaided vision (-0.3 to +1.3 logMAR), pupil diameter (2.3 to 7.5 mm) and iris colour (67 per cent light/blue irides) was recorded. The sample included mostly females (60 per cent) and many contact lens wearers (42 per cent) and so the influences of these parameters were also investigated. Results - Decision tree analysis showed that sex, iris colour, contact lens wear and cylinder axis orientation did not influence the relationship between unaided vision and refractive error. New equations for the dependence of the minimum angle of resolution on age and pupil diameter arose from step backwards multiple linear regressions carried out separately on the myopes (2.91.scalar vector +0.51.pupil diameter -3.14 ) and hyperopes (1.55.scalar vector + 0.06.age – 3.45 ). Conclusion - The new equations may be useful in simulators designed for teaching purposes as they accounted for 81 per cent (for myopes) and 53 per cent (for hyperopes) of the variance in measured data. In comparison, previously published equations accounted for not more than 76 per cent (for myopes) and 24 per cent (for hyperopes) of the variance depending on whether they included pupil size. The new equations are, as far as is known to the authors, the first to include age. The age-related decline in accommodation is reflected in the equation for hyperopes.

Tourism time series forecast

In this chapter four combinations of input features and the feedforward, cascade forward and recurrent architectures are compared for the task of forecast tourism time series. The input features of the ANNs consist in the combination of the previous 12 months, the index time modeled by two nodes used to the year and month and one input with the daily hours of sunshine (insolation duration). The index time features associated to the previous twelve values of the time series proved its relevance in this forecast task. The insolation variable can improved results with some architectures, namely the cascade forward architecture. Finally, the experimented ANN models/architectures produced a mean absolute percentage error between 4 and 6%, proving the ability of the ANN models based to forecast this time series. Besides, the feedforward architecture behaved better considering validation and test sets, with 4.2% percentage error in test set.

INFLACIÓN E INCERTIDUMBRE INFLACIONARIA: EVIDENCIA PARA COSTA RICA

En este documento se estima una medida de la incertidumbre inflacionaria. Un modelo de inflación señala incertidumbre cuando los errores de pronóstico son heteroscedásticos. Por medio de la especificación de una ecuación GARCH (Generalized Autoregressive Conditional Heteroscedasticity), para la varianza del término de error de un modelo de inflación, es posible estimar una proxy de incertidumbre inflacionaria. La estimación simultánea del modelo de inflación y de la ecuación GARCH, produce un nuevo modelo de inflación en el cual los errores de pronóstico son homocedásticos. Existe consenso en la literatura económica en que hay una correlación positiva entre incertidumbre inflacionaria y la magnitud de la tasa de inflación, lo cual, como lo señaló Friedman (1977), representa uno de los costos asociados con la persistencia inflacionaria. Esto es porque tal incertidumbre dificulta la toma de decisiones óptimas por parte de los agentes económicos.La evidencia empírica, para el periodo 1954:01-2002:08, apoya la hipótesis de que para el caso de Costa Rica mientras mayor es la inflación mayor es la incertidumbre respecto a esta variable. En los últimos siete años (1997-2002) la incertidumbre presenta la variación media más baja de todo el periodo. Además, se identifica un efecto asimétrico de la inflación sobre la incertidumbre inflacionaria, es decir, la incertidumbre inflacionaria tiende a incrementarse más para el siguiente periodo cuando la inflación pronosticada está por debajo de la inflación actual, que cuando la inflación pronosticada está por arriba de la tasa observada de inflación. Estos resultados tienen una clara implicación para la política monetaria. Para minimizar la dificultad que la inflación causa en la toma óptima de decisiones de los agentes económicos es necesario perseguir no solamente un nivel bajo de inflación sino que también sea estable.AbstractThis paper estimates a measure of inflationary uncertainty. An inflation model signals uncertainty when the forecast errors are heteroskedastic. By the specification of a GARCH (Generalized Autoregressive Conditional Heteroscedasticity) equation, for the variance of the error term of the inflation model, it is possible to estimate a proxy for inflationary uncertainty. By the simultaneous estimation of the inflation model and the GARCH equation, a new inflation model is obtained in which the forecast errors are homocedastic. Most economists agree that there is a positive correlation between inflationary uncertainty and the magnitude of the inflation rate, which, as was pointed out by Friedman (1977), represents one of costs associated with the persistence of inflation. This is because such uncertainty clouds the decision-making process of consumers and investors.The empirical evidence for the period 1954:01-2002:08 confirms that in the case of Costa Rica inflationary uncertainty increases as inflation rises. In the last seven years(1997-2002) the uncertainty present the mean variation most small of the period. In addition, inflation has an asymmetric effect on inflationary uncertainty. That is, when the inflation forecast is below the actual inflation, inflationary uncertainty increases for the next period. The opposite happens when the inflation forecast is above the observed rate of inflation. Besides, the absolute value of the change on uncertainty is greater in the first case than the second. These results have a clear implication for monetary policy. To minimize the disruptions that inflation causes to the economic decision-making process, it is necessary to pursue, not only a low level of inflation, but a stable one as well.

Testing the random walk hypothesis with variance ratio statistics

Mestrado em Finanças

Refractive Error In School Children In Campinas, Brazil.

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Analise do processo de rastreamento automatico de jogadores em esportes coletivos

Universidade Estadual de Campinas . Faculdade de Educação Física

Tempo de reação, tempo de movimento e aquisição de timing antecipatorio em idosos

Universidade Estadual de Campinas. Faculdade de Educação Física