Predicting future purchases with the Poisson log-normal model

The negative binomial distribution (NBD) has been widely used in marketing for modeling purchase frequency counts, particularly in packaged goods contexts. A key managerially relevant use of this model is Conditional Trend Analysis (CTA)—a method of benchmarking future sales utilizing the NBD conditional expectation. CTA allows brand managers to identify whether the sales change in a second period is accounted for by previous non-, light, or heavy buyers of the brand. Although a useful tool, the conditional prediction of the NBD suffers from a bias: it under predicts what the period-one non-buyer class will do in period two and over predicts the sales contribution of existing buyers. In addition, the NBD's assumption of a gamma-distributed mean purchase rate lacks theoretical support—it is not possible to explain why a gamma distribution should hold. This paper therefore proposes an alternative model using a log-normal distribution in place of the gamma distribution, hence creating a Poisson log-normal (PLN) distribution. The PLN distribution has a stronger theoretical grounding than the NBD as it has a natural interpretation relying on the central limit theorem. Empirical analysis of brands in multiple categories shows that the PLN distribution gives better predictions than the NBD.

An empirical study of the antecedents and consequences of brand engagement

Purpose – The purpose of this paper is to develop and empirically test a model of brand engagement. More specifically, the aim is to evaluate both antecedents and consequences of brand engagement, from a management perspective. Design/methodology/approach – A quantitative survey of 403 firms is undertaken to test the model. Structural equation modelling (SEM) is used to estimate the parameters of the model. Findings – A reliable and valid measure of brand engagement is established. The SEM model works well, in terms of goodness of fit indices. The results demonstrate that there are major brand performance benefits (consequences) of brand engagement. Additionally, and important for the practical implications, the results show that brand orientation is a major antecedent to brand engagement. Research limitations/implications – The study needs to be replicated in other countries, with scope to add other explanatory variables for influencing brand engagement. The results have considerable practical benefits for guiding the introduction of measures to enhance brand engagement. Originality/value – The study builds on earlier (mainly consumer) conceptual approaches to brand engagement, but goes further in that it provides empirical evidence about the nature, antecedents and consequences of brand engagement and further, offers a management rather than consumer perspective. Essentially, the study reveals a new perspective of factors that encourage firms to connect/engage their brands with consumers. Brand engagement is a dual concept, reflecting both a consumer and a firm perspective.

Intraday volatility interaction between the crude oil and equity markets

This paper investigates the price volatility interaction between the crude oil and equity markets in the US using 5-min data over the period 2009-2012. Our main findings can be summarised as follows. First, we find strong evidence to demonstrate that the integration of the bid-ask spread and trading volume factors leads to a better performance in predicting price volatility. Second, trading information, such as bid-ask spread, trading volume, and the price volatility from cross-markets, improves the price volatility predictability for both in-sample and out-of-sample analyses. Third, the trading strategy based on the predictive regression model that includes trading information from both markets provides significant utility gains to mean-variance investors.

Using aggregation functions to model human judgements of species diversity

In environmental ecology, diversity indices attempt to capture both the number of species in a community and the relative abundance of each. Many indices have been proposed for quantifying diversity, often based on calculations of dominance, equity and entropy from other research fields. Here we use linear fitting techniques to investigate the use of aggregation functions, both for evaluating the relative biodiversity of different ecological communities, and for understanding human tendencies when making intuitive diversity comparisons. The dataset we use was obtained from an online exercise where individuals were asked to compare hypothetical communities in terms of diversity and importance for conservation.

Role of index bonds in an optimal dynamic asset allocation model with real subsistence consumption

We investigate the role of index bonds in a dynamic consumption and asset allocation model where the rate of real consumption at any given time cannot fall below a fixed level. An explicit form of the optimal consumption and portfolio rule for a class of Constant Relative Risk Aversion (CRRA) utility functions is derived. Consumption increases above the subsistence level only when wealth exceeds a threshold value. Risky investments in equity and nominal bonds are initially proportional to the excess of wealth over a lower bound, and then increase nonlinearly with wealth. The desirability of investing in the risky assets are related to the agent’s risk preference, the equity premium, and the inflation risk premium. The demand for index bonds is also obtained. The results should be useful for the management of defined benefit pension funds, university endowments, and other portfolios which have a withdrawal pre-commitment in real terms.