Nonlinear Vector Autoregressive Model Research Articles

The nonlinear impacts of macroeconomic shocks on the US regional housing markets

ABSTRACT This paper examines the asymmetrical impacts of aggregate macroeconomic shocks on the US regional housing markets by estimating nonlinear Vector Autoregressive models. We show how aggregate output, monetary, inflation, and credit shocks result in heterogenous impulse responses of the housing market volatilities across growing and declining housing market regimes in nine census divisions and 19 metropolitan cities. We find that output and inflation shocks cause qualitatively asymmetrical responses across regimes in majority of regions. A positive output shock and a negative inflation shock reduce (increase) housing price uncertainties when housing markets are in a declining (booming) regime in most regions. The responses of regional housing price volatilities to monetary and credit shocks are quantitatively asymmetrical across regimes in most regions. We also find that aggregate shocks have larger contributions on changing the probabilities of regime switching when a regional housing market is initially expanding than declining. Among aggregate shocks, inflation shock has the most prominent contributions across most regions. It also presents the strongest asymmetrical effects across positive and negative shocks. Our results can help regional decision makers utilize fiscal policies, regulatory measures, and regional planning to mitigate the destabilizing effects of macroeconomic shocks on regional housing markets.

Nonlinear causal network learning via Granger causality based on extreme support vector regression.

For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.

Modeling and Causality Analysis of Human Sensorimotor Control System Based on NVAR Method

Article Modeling and Causality Analysis of Human Sensorimotor Control System Based on NVAR Method Jiyu Tan 1,2, Yurong Li 1,2,*, Qiurong Xie 3, and Xiaoling Wang 3 1 College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, China 2 Fujian Key Lab of Medical Instrument and Pharmaceutical Technology, Fuzhou University, Fuzhou 350116, China 3 College of Rehabilitation Medicine, Fujian University of Traditional Chinese Medicine, Fuzhou 350122, China * Correspondence: liyurong@fzu.edu.cn Received: 2 September 2023 Accepted: 19 October 2023 Published: 21 December 2023 Abstract: Neuromuscular disorders (such as stroke and spinal cord injuries) can lead to nerve damage that profoundly affects a patient's ability to control limb movements. Analyzing and modeling the human sensorimotor control system can establish a neurophysiological foundation for both fundamental research and clinical rehabilitation assessment. Electroencephalogram (EEG) signals provide insights into how the cerebral cortex regulates limb movements, while electromyogram (EMG) signals reveal how muscles respond to motor commands. Utilizing these signals, cortical-muscular models can be developed to facilitate the quantification and assessment of the human sensorimotor control system. This study proposes a method based on the nonlinear vector autoregression model and coiflets wavelet packet decomposition to perform multivariate time-frequency Granger causality analysis. The objective of this analysis is to compute the cortical-muscular causality matrix during elbow extension in stroke patients and construct a cortical-muscular causal network. The result reveals a frequency-dependent directed information flow pattern in the cortical-muscle causality matrix during elbow extension. Specifically, the GC values of EEG→EMG (down) and EMG→EEG (up) in the alpha and beta bands are significantly higher than those in the gamma band. The cortical-muscular causal network of stroke patients does not have small-world properties. The result indicates that the proposed method is able to characterize functional connections of brain myoelectric synchronization in different frequency bands within the time-frequency domain. It also uncovers the causal association that inherently exists in the human sensorimotor control system, providing a theoretical basis for further evaluation and quantification of the human sensorimotor control system.

Forecast accuracy of the linear and nonlinear autoregressive models in macroeconomic modeling

AbstractMost nonlinear vector autoregressive methods in the econometric literature are based on specific functional forms, such as the smooth transition autoregressive model. This study proposes a general form of the nonlinear vector autoregressive model based on global approximators, such as neural networks, Volterra, and Weiner series. The simulation results of 20 linear and nonlinear multivariate time series processes indicate that nonlinear vector autoregressive methods, especially multi‐output neural networks, are more accurate based on the root mean square error and model confidence set criteria. Applying the global approximator approach to a small‐scale macroeconometric model reveals that the new approach can improve forecast accuracy compared to linear and other nonlinear vector error correction models. In addition, forecasting the relevant variables in a typical exchange rate and monetary policy models based on nonlinear specifications gives more successful results than in the linear case.

Assessing the impacts of global economic policy uncertainty and the long-term bond yields on oil prices

Purpose Might the impact of the global economic policy uncertainty (GEPU) and the long-term bond yields on oil prices be asymmetric? This paper aims to consider the effects of the GEPU and the US long-term government bond yields on oil prices using quantile-based analysis and nonlinear vector autoregression (VAR) model. The author hypothesized whether the negative and positive changes in the GEPU and the long-term bond yields of the USA have different effects on oil prices. Design/methodology/approach To address this question, the author uses quantile cointegration model and the impulse response functions (IRFs) of the censored variable approach of Kilian and Vigfusson (2011). Findings The quantile cointegration test showed the existence of non-linear cointegration relationship, whereas Granger-causality analysis revealed that positive/negative variations in GEPU will have opposite effects on oil prices. This result was supported by the quantile regression model’s coefficients and nonlinear VAR model’s IRFs; more specifically, it was stressed that increasing/decreasing GEPU will deaccelerate/accelerate global economic activity and thus lead to a fall/rise in oil prices. On the other hand, the empirical models indicated that the impact of US 10-year government bond yields on oil prices is asymmetrical, while it was found that deterioration in the borrowing conditions in the USA may have an impact on oil prices by slowing down the global economic activity. Originality/value As a robustness check of the quantile-based analysis results, the slope-based Mork test is used.

Regional forecasting of COVID-19 caseload by non-parametric regression: a VAR epidemiological model.

ObjectivesThe COVID-19 pandemic (caused by SARS-CoV-2) has introduced significant challenges for accurate prediction of population morbidity and mortality by traditional variable-based methods of estimation. Challenges to modelling include inadequate viral physiology comprehension and fluctuating definitions of positivity between national-to-international data. This paper proposes that accurate forecasting of COVID-19 caseload may be best preformed non-parametrically, by vector autoregression (VAR) of verifiable data regionally.MethodsA non-linear VAR model across 7 major demographically representative New York City (NYC) metropolitan region counties was constructed using verifiable daily COVID-19 caseload data March 12–July 23, 2020. Through association of observed case trends with a series of (county-specific) data-driven dynamic interdependencies (lagged values), a systematically non-assumptive approximation of VAR representation for COVID-19 patterns to-date and prospective upcoming trends was produced.ResultsModified VAR regression of NYC area COVID-19 caseload trends proves highly significant modelling capacity of observed patterns in longitudinal disease incidence (county R2 range: 0.9221–0.9751, all p < 0.001). Predictively, VAR regression of daily caseload results at a county-wide level demonstrates considerable short-term forecasting fidelity (p < 0.001 at one-step ahead) with concurrent capacity for longer-term (tested 11-week period) inferences of consistent, reasonable upcoming patterns from latest (model data update) disease epidemiology.ConclusionsIn contrast to macroscopic variable-assumption projections, regionally-founded VAR modelling may substantially improve projection of short-term community disease burden, reduce potential for biostatistical error, as well as better model epidemiological effects resultant from intervention. Predictive VAR extrapolation of existing public health data at an interdependent regional scale may improve accuracy of current pandemic burden prognoses.

When is discretionary fiscal policy effective?

Abstract We investigate the effects of discretionary changes in government spending and taxes using a medium-scale nonlinear vector autoregressive model with policy shocks identified via sign restrictions. Tax cuts and spending increases have larger stimulative effects when there is excess slack in the economy, while they are much less effective, especially in the case of government spending increases, when the economy is close to potential. We find that contractionary shocks have larger effects than expansionary shocks across the business cycle, but this is much more pronounced during deep recessions and sluggish recoveries than in robust expansions. Notably, tax increases are highly contractionary and largely self-defeating in reducing the debt-to-GDP ratio when the economy is in a deep recession. The effectiveness of discretionary government spending, including its state dependence, appears to be almost entirely due to the response of consumption. The responses of both consumption and investment to discretionary tax changes are state dependent, but investment plays the larger quantitative role.

Nexus of Oil Price Pass-Through and Exchange Rate: Evidence from US and China

Due to technological innovation and energy consumption growth in recent years, US and China become increasingly important players in the world crude oil market and are growingly exposed to not only supply and demand shocks but also foreign exchange risks. To better understand the nexus of crude oil prices and exchange rate, we construct a nonlinear vector autoregressive model to investigate the nonlinear and asymmetric relationships among the US and China’s crude oil prices and the RMB-dollar exchange rate. This study finds that the interactions between US and China’s crude oil prices and the effect of exchange rate on oil prices are time-varying and, more importantly, dependent on oil price regimes. The reform of China’s exchange rate system has significantly impacted the dynamic relationship by enhancing China’s influence on the oil pricing in the world market.

State‐Dependent Transmission of Monetary Policy in the Euro Area

AbstractWe estimate a logit mixture vector autoregressive model describing monetary policy transmission in the euro area over the period 1999–2015. In contrast to other classes of nonlinear vector autoregressive models, regime affiliation is neither strictly binary, nor binary with a transition period, and based on multiple variables. We show that monetary policy transmission in the euro area can be described as a mixture of two states. In both states, output and prices are found to decrease after contractionary monetary policy shocks. However, the effects of monetary policy are less enduring in the “crisis state.”

Effects of Monetary Policy during Financial Market Crises and Regime Changes: An Empirical Evaluation Using a Nonlinear Vector Autoregression Model

Using monthly data for Korea, this study examines nonlinear effects of monetary policy in association with financial market distress. The study uses a nonlinear vector autoregression model and finds that monetary policy becomes ineffective for addressing huge demand contractions in times of financial market turmoil or severe economic downturn, implying a structural change from a non‐Keynesian to a Keynesian regime, such as a liquidity trap. Monetary contractions have stronger output effects than monetary expansions, particularly in times of financial distress. We found no evidence in favor of asymmetric effects of monetary shocks of different sizes. Finally, we also found financial shocks to have stronger effects on the real economy in times of financial distress than in normal times. The results have important policy implications for periods of financial turmoil or economic crisis.

MONETARY SHOCKS AND STOCK MARKET FLUCTUATIONS: WITH AN APPLICATION TO THE CHINESE STOCK MARKET

Using a simple theoretical model, this paper provides a micro-foundation of applying vector auto-regressive (VAR) models to explore the effects of monetary shocks on stock market fluctuations. We analytically show that, when monetary shocks change investors’ wealth and portfolio liquidity, their degree of risk aversion associated with wealth and liquidity changes accordingly, which is then channeled to their investment decision and finally to the stock market fluctuations. Both the wealth effect and liquidity effect of monetary shocks have inter-temporal impacts on stock pricing. Therefore, monetary shocks and stock price fluctuations should be treated as a unified vector system that is auto-correlated. Based on the theoretical analysis, this paper further studies the impacts of different forms of monetary shocks on the Chinese stock market over the period 2005 to 2012 with a non-linear VAR model. We find that monetary shocks in China have significant and asymmetric effects on the stock market performance over different market cycles. Our estimation suggests that changes in monetary policy may increase stock market volatility, even though these monetary policies are often aimed at stabilizing the Chinese macro-economic activities.

Reconstruction of Complex Directional Networks with Group Lasso Nonlinear Conditional Granger Causality

Reconstruction of networks underlying complex systems is one of the most crucial problems in many areas of engineering and science. In this paper, rather than identifying parameters of complex systems governed by pre-defined models or taking some polynomial and rational functions as a prior information for subsequent model selection, we put forward a general framework for nonlinear causal network reconstruction from time-series with limited observations. With obtaining multi-source datasets based on the data-fusion strategy, we propose a novel method to handle nonlinearity and directionality of complex networked systems, namely group lasso nonlinear conditional granger causality. Specially, our method can exploit different sets of radial basis functions to approximate the nonlinear interactions between each pair of nodes and integrate sparsity into grouped variables selection. The performance characteristic of our approach is firstly assessed with two types of simulated datasets from nonlinear vector autoregressive model and nonlinear dynamic models, and then verified based on the benchmark datasets from DREAM3 Challenge4. Effects of data size and noise intensity are also discussed. All of the results demonstrate that the proposed method performs better in terms of higher area under precision-recall curve.

When Do Discretionary Changes in Government Spending or Taxes Have Larger Effects?

We investigate the effects of discretionary changes in government spending and taxes using a medium-scale nonlinear vector autoregressive model with policy shocks identified via sign restrictions. Tax cuts and spending increases have larger stimulative effects when there is excess slack in the economy, while they are much less effective, especially in the case of government spending increases, when the economy is close to potential. We find that contractionary shocks have larger effects than expansionary shocks across the business cycle, but this is much more pronounced during deep recessions and sluggish recoveries than in robust expansions. Notably, tax increases are highly contractionary and largely self-defeating in reducing the debt-to-GDP ratio when the economy is in a deep recession. The effectiveness of discretionary government spending, including its state dependence, appears to be almost entirely due to the response of consumption. The responses of both consumption and investment to discretionary tax changes are state dependent, but investment plays the larger quantitative role.

The cycle of violence in the Second Intifada: Causality in nonlinear vector autoregressive models

SummaryWe contest Jaeger and Paserman's claim (Jaeger and Paserman , 2008. The cycle of violence? An empirical analysis of fatalities in the Palestinian–Israeli conflict. American Economic Review 98(4): 1591–1604) that Palestinians did not react to Israeli aggression during Intifada 2. We address the differences between the two sides in terms of the timing and intensity of violence, estimate nonlinear vector autoregression models that are suitable when the linear vector autoregression innovations are not normally distributed, identify causal effects rather than Granger causality using the principle of weak exogeneity, and introduce the “kill‐ratio” as a concept for testing hypotheses about the cycle of violence. The Israelis killed 1.28 Palestinians for every killed Israeli, whereas the Palestinians killed only 0.09 Israelis for every killed Palestinian.

Asymmetric effects of monetary policy shocks on economic performance: empirical evidence from Turkey

ABSTRACTThis study investigates the asymmetric effects of monetary policy shocks on the macroeconomic variables of exchange rate, output and inflation for an emerging economy ‒ Turkey ‒ by using monthly data between 1990 and 2014. We employ the innovative nonlinear vector autoregressive model of Kilian and Vigfusson (2011), which allows us to observe the effect of different stances (tight or loose) and different sizes (small or large) of monetary policy actions. Our empirical evidence reveals that tight monetary policy, which, in this case, is captured with a positive shock to interest rate, decreases exchange rate, output and prices, as economic theory suggests. Loose monetary policy, which is captured with a negative shock to interest rate, has the opposite effect on these variables. However, the effects of loose monetary policy are weaker than the effects of tight monetary policy because loose monetary policy shocks are less effective than tight monetary policy shocks. Moreover, as the magnitude of a shock increases, the difference between the effects of tight and loose monetary policy policies also increases.

Evaluating forecasts of political conflict dynamics

There is considerable interest today in the forecasting of conflict dynamics. Commonly, the root mean square error and other point metrics are used to evaluate the forecasts from such models. However, conflict processes are non-linear, so these point metrics often do not produce adequate evaluations of the calibration and sharpness of the forecast models. Forecast density evaluation improves the model evaluation. We review tools for density evaluation, including continuous rank probability scores, verification rank histograms, and sharpness plots. The usefulness of these tools for evaluating conflict forecasting models is explained. We illustrate this, first, in a comparison of several time series models’ forecasts of simulated data from a Markov-switching process, and second, in a comparison of several models’ abilities to forecast conflict dynamics in the Cross Straits. These applications show the pitfalls of relying on point metrics alone for evaluating the quality of conflict forecasting models. As in other fields, it is more useful to employ a suite of tools. A non-linear vector autoregressive model emerges as the model which is best able to forecast conflict dynamics between China and Taiwan.

Financial regulation policy uncertainty and credit spreads in the US

This paper investigates the linear and nonlinear effects of financial regulation policy uncertainty shocks on US macroeconomic aggregates within a Vector Autoregressive (VAR) framework. Financial regulation policy uncertainty (FRPU) is quantified with a news-based index developed by Baker et al. (2013). Particular attention is paid to the reaction of corporate credit spreads to FRPU shocks. The linear VAR results suggest that exogenous increases in the FRPU index trigger increases in the cost of external finance as well as a persistent negative impact on the real economy. By using a nonlinear (Smooth-Transition) VAR model, I then show that these effects are asymmetric over the business cycle, i.e., credit spreads are estimated to rise three times more during recessions than in non-recessionary periods. Importantly, in both the linear and nonlinear models, FRPU shocks account for large shares of the variability of unemployment and credit spreads. My findings are supported by various robustness checks.

A tutorial to identify nonlinear associations in gene expression time series data.

The study of gene regulatory networks is the basis to understand the biological complexity of several diseases and/or cell states. It has become the core of research in the field of systems biology. Several mathematical methods have been developed in the last decade, especially in the analysis of time series gene expression data derived from microarrays and sequencing-based methods. Most of the models available in the literature assumes linear associations among genes and do not infer directionality in these connections or uses a priori biological knowledge to set the directionality. However, in several cases, a priori biological information is not available. In this context, we describe a statistical method, namely nonlinear vector autoregressive model to estimate nonlinear relationships and also to infer directionality at the edges of the network by using the temporal information of the time series gene expression data without a priori biological information.

Identification of nonlinear VAR models using general conditional independence graphs

The general conditional independence graphs are proposed for identifying nonlinear vector autoregressive model, which extend the graphical modeling approach for linear structure VAR. The conditional independence relations between time series variables and their lags can be tested efficiently and consistently using conditional mutual information statistics and a permutation procedure. Furthermore, a statistic resulted from the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity of the dependence. A bootstrap method based on surrogate data is used to determine the significance of the nonlinear test statistic. The finite sample behavior of the procedure through simulation time series with different linear and nonlinear dependence relations is investigated.

Stability results for nonlinear error correction models

This paper studies analogs of Granger's representation theorem in the context of a general nonlinear vector autoregressive error correction model. The model allows for nonlinear autoregressive conditional heteroskedasticity and the conditional distribution involved can be a mixture distribution of a rather general type. Mixture models of this kind can be thought of as generalizations of threshold models and they have attracted attention in the recent time series and econometrics literature. The paper develops a useful transformation which shows how the nonlinear error correction model can be transformed to a nonlinear vector autoregressive model so that available results on the stationarity or nonstationarity of the latter can be used for the former. The most satisfactory results are obtained in a model in which a specific structural relation between the nonlinearity and equilibrium correction prevails. Without this structural relation only a lower bound for the number of long-run equilibrium relations can explicitly be determined because the exact number depends on properties of the first and second moments of a nonlinear stationary component of the process.