Pricing strategy and product substitution of bullwhip effect in dual parallel supply chain: aggravation or mitigation?

The bullwhip effect (BE) affects not only the revenue of the retailer but also the revenue of the manufacture. Thus, a lot of retailers and manufacturers aim to attenuate the negative impact of the BE. In this research, two parallel supply chains distributing two substitutable products with price-sensitive demands are considered, the order-up-to inventory policy, as well as the MMSE forecasting method, are employed by retailers in these chains. The retailer’s price-setting follows the first-order vector autoregressive process, suggesting that its pricing decision depends on its previous price as well as its rival’s price, owing to the BE. The analytical expression of the BE is calculated by the statistical method. Besides, the effects of pricing strategy and product substitution on the BE are studied through simulation. A conclusion can be drawn that the BE of the two parallel supply chains will be affected by lead time, product substitution rate, and pricing coefficient. Of particular interest is that the BE can be efficiently alleviated by adopting a price strategy with many correlations and a small coefficient of autocorrelation.

Causality in Reversed Time Series: Reversed or Conserved?

The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens—either perfectly, approximately, or not at all—using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.

Balanced Growth Approach to Tracking Recessions

In this paper, we propose a hybrid version of Dynamic Stochastic General Equilibrium models with an emphasis on parameter invariance and tracking performance at times of rapid changes (recessions). We interpret hypothetical balanced growth ratios as moving targets for economic agents that rely upon an Error Correction Mechanism to adjust to changes in target ratios driven by an underlying state Vector AutoRegressive process. Our proposal is illustrated by an application to a pilot Real Business Cycle model for the US economy from 1948 to 2019. An extensive recursive validation exercise over the last 35 years, covering 3 recessions, is used to highlight its parameters invariance, tracking and 1- to 3-step ahead forecasting performance, outperforming those of an unconstrained benchmark Vector AutoRegressive model.

Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a process is equivalent to obtaining the properties of an infinite process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

Turning a DSGE Model into a Bayesian Model

This chapter considers the turning of DSGE models into Bayesian versions by specifying a probability distribution for the innovations of the exogenous shock processes. There exists a wide variety of numerical techniques to solve DSGE models, but the chapter elaborates on a technique that involves the log-linearization of the equilibrium conditions and the solution of the resulting linear rational expectations difference equations. The approximate solution takes the form of a vector autoregressive process for the model variables, which is driven by the innovations to the exogenous shock processes, and is used as a set of state-transition equations in the state–space representation of the DSGE model. Under the assumption that these innovations are normally distributed, the log-linearized DSGE model takes the form of a linear Gaussian state–space model.