Discussing Anthropogenic Global Warming from an Econometric Perspective: A Change in Forecasting Based on the ARIMA Paleoclimate Time Series Model

Global warming has divided the scientific community worldwide with predominance for anthropogenic alarmism. This article aims to project a climate change scenario using a stochastic model of paleotemperature time series and compare it with the dominant thesis. The ARIMA model – an integrated autoregressive process of moving averages, known as Box-Jenkins - was used for this purpose. The results showed that the estimates of the model parameters were below 1°C for a scenario of 100 years which suggests a period of temperature reduction and a probable cooling, contrary to the prediction of the IPCC and the anthropogenic current of an increase in 1.50° C to 2.0° C by the end of this century. Thus, we hope with this study to contribute to the discussion by adding a statistical element of paleoclimate in counterpoint to the current consensus and to placing the debate in a long-term historical dimension, in line with other research present in climate sciences and statistics.

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.

Performance assessment of a low-complexity autoregressive Kalman filter for GNSS carrier tracking using real scintillation time series

Ionospheric scintillation is one of the most challenging sources of errors in global navigation satellite systems (GNSS). It is an effect of space weather that introduces rapid amplitude and phase fluctuations to transionospheric signals and, as a result, it severely degrades the tracking performance of receivers, particularly carrier tracking. It can occur anywhere on the earth during intense solar activity, but the problem aggravates in equatorial and high-latitude regions, thus posing serious concerns to the widespread deployment of GNSS in those areas. One of the most promising approaches to address this problem is the use of Kalman filter-based techniques at the carrier tracking level, incorporating some a priori knowledge about the statistics of the scintillation to be dealt with. These techniques aim at dissociating the carrier phase dynamics of interest from phase scintillation by modeling the latter through some correlated Gaussian function, such as the case of autoregressive processes. However, besides the fact that the optimality of these techniques is still to be reached, their applicability for dealing with scintillation in real-world environments also remains to be confirmed. We carry out an extensive analysis and experimentation campaign on the suitability of these techniques by processing real data captures of scintillation at low and high latitudes. We first evaluate how well phase scintillation can be modeled through an autoregressive process. Then, we propose a novel adaptive, low-complexity autoregressive Kalman filter intended to facilitate the implementation of the approach in practice. Last, we provide an analysis of the operational region of the proposed technique and the limits at which a performance gain over conventional tracking architectures is obtained. The results validate the excellence of the proposed approach for GNSS carrier tracking under scintillation conditions.

Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process

In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets.

Lagrangian Integro-Difference Equation Model for Precipitation Nowcasting

Delivering reliable nowcasts (short-range forecasts) of severe rainfall and the resulting flash floods is important in densely populated urban areas. The conventional method is advection-based extrapolation of radar echoes. However, during rapidly evolving convective rainfall this so-called Lagrangian persistence (LP) approach is limited to deterministic and very short-range nowcasts. To address these limitations in the one-hour time range, a novel extension of LP, called Lagrangian INtegro-Difference equation model withAutoregression (LINDA), is proposed. The model consists of five components: 1) identification of rain cells, 2) advection, 3) autoregressive process describing growth and decay of the cells, 4) convolution describing loss of predictability at small scales and 5) stochastic perturbations to simulate forecast uncertainty. Advection is separated from the other components that are applied in the Lagrangian coordinates. The reliability of LINDA is evaluated using the NEXRAD WSR-88D radar that covers the Dallas-Fort Worth metropolitan area, as well as the NEXRAD mosaic covering the continental United States. This is done with two different configurations: LINDA-D for deterministic and LINDA-P for probabilistic nowcasts. The validation dataset consists of 11 rainfall events during 2018-2020. For predicting moderate to heavy rainfall (5-20 mm/h), LINDA outperforms the previously proposed LP-based approaches. The most significant improvement is seen for the ETS and POD statistics with the 5 mm/h threshold. For 30-minute nowcasts, they show 15% and 16% increase, respectively, to the second-best method and 48% and 34% increase compared to LP. For the 5 mm/h threshold, the increase in the ROC skill score of 30-minute nowcasts from the second-best method is 10%.

On the generalization of the central limit theorem for the least-squares estimator of the unknown parameter in the autoregressive process of order one (AR(1))

In this work it is proved central limit theorem for the least-squares estimator of the unknown parameter in the generalization autoregressive process of order one (AR(1)).

Probabilistic Projection of Subnational Life Expectancy

Projecting mortality for subnational units, or regions, is of great interest to practicing demographers. We seek a probabilistic method for projecting subnational life expectancy that is based on the national Bayesian hierarchical model used by the United Nations, and at the same time is easy to use. We propose three methods of this kind. Two of them are variants of simple scaling methods. The third method models life expectancy for a region as equal to national life expectancy plus a region-specific stochastic process which is a heteroskedastic first-order autoregressive process (AR(1)), with a variance that declines to a constant as life expectancy increases. We apply our models to data from 29 countries. In an out-of-sample comparison, the proposed methods outperformed other comparative methods and were well calibrated for individual regions. The AR (1) method performed best in terms of crossover patterns between regions. Although the methods work well for individual regions, there are some limitations when evaluating within-country variation. We identified four countries for which the AR(1) method either underestimated or overestimated the predictive between-region within-country standard deviation. However, none of the competing methods work better in this regard than the AR(1) method. In addition to providing the full distribution of subnational life expectancy, the methods can be used to obtain probabilistic forecasts of age-specific mortality rates.

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.