Nonstationary brand variables in category management: A cointegration perspective

Category-management models serve to assist in the development of plans for pricing and promotions of individual brands. Techniques to solve the models can have problems of accuracy and interpretability because they are susceptible to spurious regression problems due to nonstationary time-series data. Improperly stated nonstationary systems can reduce the accuracy of the forecasts and undermine the interpretation of the results. This is problematic because recent studies indicate that sales are often a nonstationary time-series. Newly developed correction techniques can account for nonstationarity by incorporating error-correction terms into the model when using a Bayesian Vector Error-Correction Model. The benefit of using such a technique is that shocks to control variates can be separated into permanent and temporary effects and allow cointegration of series for analysis purposes. Analysis of a brand data set indicates that this is important even at the brand level. Thus, additional information is generated that allows a decision maker to examine controllable variables in terms of whether they influence sales over a short or long duration. Only products that are nonstationary in sales volume can be manipulated for long-term profit gain, and promotions must be cointegrated with brand sales volume. The brand data set is used to explore the capabilities and interpretation of cointegration.

Motor unit synchronization between medial and lateral vasti muscles

Objective: Accurate neuromuscular control of the patellofemoral joint is important in knee joint mechanics. Strategies to coordinate the vasti muscles, such as motor unit synchronization, may simplify control of patellar tracking. This study investigated motor unit synchronization between vastus medialis (VM) and lateralis (VL). Methods: Electromyographic (EMG) recordings of single motor unit action potentials (MUAPs) were made from VM and single- and multi-unit recordings were made from VL. Synchronization was quantified from peaks in the cross-correlogram generated from single MUAP pairs in VL and VM. The proportion of motor units in VM with synchronized firing in VL was also quantified from peaks in averages of multiunit VL EMG triggered from the VM MUAP. Results: A high degree of synchronization of motor unit firing between VM and VL was identified. Results were similar for cross-correlation (similar to 45% of cases) and triggered averages (similar to 41% of cases). Conclusions: The data suggest that synchronization between VM and VL is higher than expected. Agreement between traditional cross-correlation and triggered averaging methods suggest that this new technique may provide a more clinically viable method to quantify synchronization. Significance: High synchronization between VM and VL may provide a solution to simplify control of the mechanically unstable patellofemoral joint. (c) 2005 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.