scholarly journals Causality in Reversed Time Series: Reversed or Conserved?

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1067
Author(s):  
Jakub Kořenek ◽  
Jaroslav Hlinka

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.

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.


2017 ◽  
Vol 6 (2) ◽  
pp. 1
Author(s):  
Iberedem A. Iwok

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.


2001 ◽  
Vol 17 (5) ◽  
pp. 889-912 ◽  
Author(s):  
Cheng Hsiao

We show that the usual rank condition is necessary and sufficient to identify a vector autoregressive process whether the variables are I(0) or I(d) for d = 1,2,.... We then use this rank condition to demonstrate the interdependence between the identification of short-run and long-run relations of cointegrated process. We find that both the short-run and long-run relations can be identified without the existence of prior information to identify either relation. But if there exists a set of prior restrictions to identify the short-run relation, then this same set of restrictions is sufficient to identify the corresponding long-run relation. On the other hand, it is in general not possible to identify the long-run relations without information on the complete structure. The relationship between the identification of a vector autoregressive process and a Cowles Commission dynamic simultaneous equations model is also clarified.


2000 ◽  
Vol 16 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Minxian Yang

Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting” property with conventional linear stationary processes, the process offers richer short-run dynamics such as conditional heteroskedasticity, asymmetric responses, and occasional nonstationary behavior.


Author(s):  
Junhai Ma ◽  
Wandong Lou ◽  
Zongxian Wang

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.


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