Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts

This paper reviews recently proposed likelihood ratio tests of goodness-of-fit and independence of interval forecasts. It recasts them in the framework of Pearson chi-squared statistics, and extends them to density forecasts. Two further recent developments are also incorporated, namely a more informative decomposition of the goodness-of-fit statistic, and the calculation of exact P-values. Examples considered are the US Survey of Professional Forecasters density forecasts of inflation and the Bank of England fan charts. This first evaluation of the Bank forecasts finds that the fan charts fan out too quickly, and the excessive concern with the upside risks was not justified.

Chi-squared tests of interval and density forecasts and the Bank of England's fan charts

This paper reviews recently proposed likelihood ratio tests of goodness-of-fit and independence of interval forecasts. It recasts them in the framework of Pearson chi-squared statistics, and considers their extension to density forecasts and their exact small-sample distributions. The use of the familiar framework of contingency tables will increase the accessibility of these methods. The tests are applied to two series of density forecasts of inflation, namely the US Survey of Professional Forecasters and the Bank of England fan charts. This first evaluation of the fan chart forecasts finds that whereas the current-quarter forecasts are well-calibrated, this is less true of the one-year-ahead forecasts. The fan charts fan out too quickly, and the excessive concern with the upside risks was not justified over the period considered JEL Classification: C53, E37interval and density forecasts

In what ways do the views of parents/carers change through the participation in Multi-Family Groups in Schools?

This qualitative research examines the lived experiences of three parents who took part in a Multi-Family Group Intervention (MFGI) in School, alongside their children, in primary schools in England. The research explored any changes in parental views over the course of the intervention, with a focus on their views of family, their own wellbeing, the school and school community. The research sits within the critical realist ontological approach, which acknowledges that there is a basis of a truth that sits behind the subjective and socially located knowledge that researcher’s access. The research is based on the social constructionist and contextual epistemological view that the world is constructed through discourses and different systems of meaning. In this study, knowledge is created subjectively resulting in multiple perspectives and emerges from the different contexts the participants inhabit and their individual experiences. A systematic literature review sought to explore and present key research relevant to this study. It concluded that there is very little research in the current literature exploring Multi-Family Groups within a school context for the parents of children with special educational needs. This research adds to and expands on the current understanding of the use of Multi-Family Groups in Schools which address presenting problems in the dual context of family and home. The participants were interviewed using semi-structured interviews and a visual tool called the ‘Tree of Change’ to record views and facilitate conversations over time. Participants were interviewed at three points throughout the intervention (pre, mid-point and post) and transcripts were analysed using Interpretative Phenomenological Analysis (IPA). Four general experiential themes emerged from the analysis: Changes in Support and Coping, Changes through Observation, Changes in Identity and Self-Concept and finally Changes in Relationships with Child and School. Each theme is discussed and exemplified by quotes from the participants. Findings are discussed in relation to relevant psychological theory and research. The study is considered as relevant for Educational Psychologists, and to those working in wider educational contexts. Suggestions for future research are made in order that the findings can be extended further

Density Forecasting: A Survey

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts.

THE PROPERTIES OF SOME GOODNESS-OF-FIT TESTS

The properties of Pearson’s goodness-of-fit test, as used in density forecast evaluation, income distribution analysis and elsewhere, are analysed. The components-of-chi-squared or “Pearson analog” tests of Anderson (1994) are shown to be less generally applicable than was originally claimed. For the case of equiprobable classes, where the general components tests remain valid, a Monte Carlo study shows that tests directed towards skewness and kurtosis may have low power, due to differences between the class boundaries and the intersection points of the distributions being compared. The power of individual component tests can be increased by the use of nonequiprobable classes.Pearson’s Goodness-of-fit test ; Component tests ; Distributional assumptions ; Monte Carlo ; Normality ; Nonequiprobable partitions

Uncertainty and disagreement in economic prediction : the Bank of England Survey of External Forecasters

This article introduces a new source of survey data, namely the Bank of England Survey of External Forecasters. The survey collects point and density forecasts of inflation and GDP growth, and hence offers the opportunity of constructing direct measures of uncertainty. We present a simple statistical framework in which to define and interrelate measures of uncertainty and disagreement. The resulting measures are compared with other direct measures of uncertainty, nationally and internationally. A significant, sustained reduction in inflation uncertainty followed the 1997 granting of operational independence to the Bank of England to pursue a monetary policy of inflation targeting.Forecast surveys ; point forecasts ; density forecasts ; uncertainty ; disagreement

Chi-squared tests of interval and density forecasts and the Bank of England's fan charts

This paper reviews recently proposed likelihood ratio tests of goodness-of-fit and independence of interval forecasts. It recasts them in the framework of Pearson chi-squared statistics, and considers their extension to density forecasts and their exact small-sample distributions. The use of the familiar framework of contingency tables will increase the accessibility of these methods. The tests are applied to two series of density forecasts of inflation, namely the US Survey of Professional Forecasters and the Bank of England fan charts. This first evaluation of the fan chart forecasts finds that whereas the current-quarter forecasts are well-calibrated, this is less true of the one-year-ahead forecasts. The fan charts fan out too quickly, and the excessive concern with the upside risks was not justified over the period considere