Inference With Cross-Lagged Effects - Problems in Time and New Interpretations

The interpretation of cross-effects from vector autoregressive models to infer structure and causality amongst constructs is widespread and sometimes problematic. I first explain how hypothesis testing and regularization are invalidated when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps. I then describe an alternative interpretation of cross-effect parameters that incorporates correlated random changes for a potentially more realistic view of how process are temporally coupled. Using an example based on wellbeing data, I demonstrate how some classical concerns such as sign flipping and counter intuitive effect directions can disappear when using this combined deterministic / stochastic interpretation. Models that treat processes as continuously interacting offer both a resolution to the hypothesis testing problem, and the possibility of the combined stochastic / deterministic interpretation.

Cointegration and Causality Analysis of Portuguese Tourism and Air Quality

This chapter aims to fill the knowledge gap regarding the relationship between tourism and air quality, specifically in the Portuguese tourism industry, with a focus on tourist nationality. It examines whether this relationship differs according to tourist origin. This study uses an air pollutant, PM10, with a strong impact on human health that has been highly neglected in the literature. Despite the great use of CO2 in assessing the causal relationship between tourism and the environment, this is not the best indicator of air quality (AQ). This chapter presents results by applying vector autoregressive models (VAR) with monthly data for the period of 2007-2017, considering the nationality of tourists that visit Portugal. Results suggest that PM10 levels and tourism are negatively correlated (in the Pearson sense) with a link between them in the long run. This relationship is confirmed by the four methodologies tested. The negative relation in Pearson and cointegration results suggests that tourism can be affected by AQ in Portugal and may lead to better AQ.

High-dimensional structure learning of sparse vector autoregressive models using fractional marginal pseudo-likelihood

Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the model increases. In this paper we adopt an approximate Bayesian approach to the learning problem by combining fractional marginal likelihood and pseudo-likelihood. We propose a novel method, PLVAR, that is both faster and produces more accurate estimates than the state-of-the-art methods based on penalized regression. We prove the consistency of the PLVAR estimator and demonstrate the attractive performance of the method on both simulated and real-world data.

Projection of Post-Pandemic Italian Industrial Production through Vector AutoRegressive Models

Energy system models for the analysis of future scenarios are mainly driven by the set of energy service demands that define the broad outlines of socio-economic development throughout the model time horizon. Here, the long-term effects of the COVID-19 pandemic on the drivers of the industrial production in six energy-intensive subsectors are addressed using Vector AutoRegressive models. The model results are computed either considering or not considering the effects of the pandemic. The comparison to established pre-pandemic trends allows for validating the robustness of the selected model. The anticipated effect of the pandemic to 2040 shows a long-term reduction by 3% to 10%, according to the different subsector, in the industrial energy service demand. When the computed service demands are used as input to the TIMES-Italy model, which shows good capability to reproduce the energy consumption of the industrial sectors in the period 2006–2020, the impact of the pandemic on energy consumption forecasts can be assessed in a business-as-usual scenario. The results show how the long-term effects of the shock caused by the pandemic could lead, by 2040, to a total industrial energy consumption 5% lower than what was foreseen before the pandemic, while the energy mix remains almost unchanged.

Frequency Domain Repercussions of Instantaneous Granger Causality

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Features of the vector autoregression models application in macroeconomic research

In this paper, we analyzed articles by foreign authors that use various vector autoregression models to calculate the impact of qualitative indicators on the economic processes of countries or a group of countries. In particular, the article analyzed the classical model of vector autoregression (VAR), panel model of autoregressive (PVAR), Bayesian model of autoregressive (BVAR), structural model of autoregressive (SVAR), and the global model of autoregressive (GVAR). Among the works using vector autoregressive models, the main emphasis is on financial indicators. Moreover, articles with non-trivial variables are rare. This is because financial macroeconomic variables in most cases have a direct impact on economic processes in the country. The analysis of financial indicators and the results obtained can play a significant role in the development of economic strategies in different states, since the results obtained with the help of vector autoregression models are usually quite accurate. The studied articles analyze the data of both developed and developing states or groups of states in different periods. The studied articles were classified according to several criteria, which were selected by the author to structure the work. Note that among the works using vector autoregressive models, the main emphasis is on financial indicators. Moreover, articles with non-trivial variables are rare. This is since financial macroeconomic variables in most cases have a direct impact on economic processes in the country. The analysis of financial indicators and the results obtained can play a significant role in the development of economic strategies in different states, since the results obtained with the help of vector autoregression models are usually quite accurate. In the conclusion of this study, the author presented conclusions based on the analysis of autoregressive models.

Frequency Domain Repercussions of Instantaneous Granger Causality

Using Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) in their information version, this paper extends their theoretical framework to incorporate instantaneous Granger Causality (iGC)’s frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger Connectivity where interactions mediated without delay between time series can be easily detected.