Multivariate contemporaneous-threshold autoregressive models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex-ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific noise covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.     

Semiparametric time series regression modeling with a diverging number of parameters

Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well.     

河北省工业产业集聚与经济发展关系研究

论文基于河北省2000-2018年的相关数据,构建河北省工业产业集聚与经济发展的向量自回归模型,运用单位根检验、Johansen协整检验、脉冲响应函数等统计方法进行研究。通过研究分析发现,河北省工业产业集聚与经济发展之间存在互相促进的正面效应。在数据分析的基础上,对河北省工业产业集聚与经济增长提出了有针对性的、合理化的对策建议。     

Diagnostic analysis for a vector autoregressive model under Student′s t‐distributions

In this paper, we use the local influence method to study a vector autoregressive model under Student^′s t‐distributions. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature diagnostics for the vector autoregressive model under three usual perturbation schemes for identifying possible influential observations. The effectiveness of the proposed diagnostics is examined by a simulation study, followed by our data analysis using the model to fit the weekly log returns of Chevron stock and the Standard & Poor's 500 Index as an application.     

Does Output Gap,Labour's Share or Unemployment Rate Drive Inflation?

We propose a new methodology for ranking in probability the commonly proposed drivers of inflation in the new Keynesian model. The approach is based on Bayesian model selection among restricted vector autoregressive (VAR) models, each of which embodies only one or none of the candidate variables as the driver. Simulation experiments suggest that our procedure is superior to the previously used conventional pairwise Granger causality tests in detecting the true driver. Empirical results lend little support to labour share, output gap or unemployment rate as the driver of US inflation.     

The contagion effect of jump risk across Asian stock markets during the Covid-19 pandemic

This paper tests the market jump contagion hypothesis in the context of the Covid-19 pandemic. We first use a nonparametric approach to identify jumps by decomposing the realized volatility into continuous and jump components, and we use the threshold autoregressive model to describe the jump interdependency structure between different markets. We empirically investigate the contagion effect across several major Asian equity markets (Mainland China, Hong Kong, Japan, South Korea, Singapore, Thailand, and Taiwan) using the 5-minute high frequency data. Some key findings emerge: jump behaviors occur frequently and make an important contribution to the total realized volatility; jump dynamics exhibit significant nonlinearity, asymmetry, and the feature of structural breaks, which can be effectively captured by the threshold autoregressive model; jump contagion effects are obviously detected and this effect varies depending on the regime.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

Unit root tests for panel MTAR model with cross-sectionally dependent error

Unit root tests are constructed for dynamic panels whose component series are momentum threshold autoregressive processes. Gaussian null asymptotics are established for the proposed tests. A Monte–Carlo experiment is conducted to compare finite sample properties of the proposed tests. The tests are illustrated by a real data set.     

Sources of volatility persistence: A case study of the U.K. pound/U.S. dollar exchange rate returns

This paper utilizes a new approach to examine the inherent nonlinear dynamics of the exchange rate returns volatility. Specifically, we utilize a regime switching threshold (i) generalized autoregressive conditional heteroskedasticity (RS-TGARCH) and (ii) a fractional generalized autoregressive conditional heteroskedasticity (RS-TFIGARCH) model. The RS-TGARCH model is found to be adequate in analyzing the first two moments of the U.K. pound/U.S. dollar monthly exchange rate returns series. The RS-TFIGARCH is found to be adequate for the daily returns series. The volatility persistence and leverage effects associated with exchange rate returns series are jointly tested by means of a Wald Chi-square test.     

Structural evolution of the postwar U.S. economy

We consider a time-varying parameter vector autoregressive model with stochastic volatility and mixture innovations to study the empirical relevance of the Lucas critique for the postwar U.S. economy. The model allows blocks of parameters to change at endogenously estimated points of time. Contrary to the Lucas critique, there are large changes at certain points of time in the parameters associated with monetary policy that do not correspond to changes in “reduced-form” parameters for inflation or the unemployment rate. However, the structure of the U.S. economy has evolved considerably over the postwar period, with an apparent reduction in the late 1980s in the impact of monetary policy shocks on inflation, though not on the unemployment rate. Related, we find changes in the Phillips curve tradeoff between inflation and cyclical unemployment (measured as the deviation from the time-varying steady-state unemployment rate implied by the model) in the 1970s and especially since the mid-1990s.     

The ACR Model: A Multivariate Dynamic Mixture Autoregression*

This paper proposes and analyses the autoregressive conditional root (ACR) time‐series model. This multivariate dynamic mixture autoregression allows for non‐stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis.     

Fractional Integration and the Dynamics of UK Unemployment*

This article is concerned with estimating the dynamic behaviour of UK unemployment using fractional integration methods. The question it considers is whether an unemployment model using a relatively small set of determinants of unemployment is consistent with the persistence which estimates an integrated model yield, or the much long‐lasting estimates obtained from fractional integration. Our empirical tests favour the latter version. The results show that when accounting for UK unemployment in terms of lagged values of the real oil price and the real interest rate, unemployment appears fractionally integrated. This finding means that although unemployment is mean reverting, once it is shocked it may take a very long time to recover, and our estimates of the response times are considerably in excess of those previously reported in the literature.     

Nonlinearities and Fractional Integration in the US Unemployment Rate*

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange multiplier procedure with a standard null‐limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some nonlinear functions of labour‐demand variables such as real oil prices and real interest rates. We also find evidence of a long‐memory component. Our results are consistent with a hysteresis model with path dependency rather than a non‐accelerating inflation rate of unemployment (NAIRU) model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilization policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy‐making.     

Bayesian Variable Selection in Spatial Autoregressive Models

This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. It presents two alternative approaches that can be implemented using Gibbs sampling methods in a straightforward way and which allow one to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. A simulation study shows that the variable selection approaches tend to outperform existing Bayesian model averaging techniques in terms of both in-sample predictive performance and computational efficiency. The alternative approaches are compared in an empirical application using data on economic growth for European NUTS-2 regions.     

人民币汇率波动对我国HS分类商品出口的影响

本文以1997~2006年HS分类商品出口的月度数据为样本,采用边限检验方法判别长期协整关系,并采用自回归多元滞后分布-误差修正模型(ARDL-ECM)分析人民币实际有效汇率波动,对不同类别商品出口的长期和短期影响。估计结果显示,不同类别商品出口受人民币汇率水平和波动率变化的影响有较大差异。     

The geographic distribution of unemployment rates in the U.S.: A spatial-time series analysis

This paper presents estimates of the time series and spatial pattern of unemployment rate fluctuations in the U.S. over the period 1977.I–1983.IV. Spatial and time series autocorrelations over a regular lattice are estimated using both simultaneous (SAR) and conditional (CAR) autoregressive models of spatial series. The empirical results indicate that a temporary unemployment rate shock has a significant effect on unemployment rates in adjacent areas contemporaneously, but virtually no impact on neighboring unemployment rates after six quarters. A permanent change in an area's unemployment rate has a strong and persistent impact on unemployment rates in labor markets within 250 miles of the initial shock.     

The (un)importance of unemployment fluctuations for the welfare cost of business cycles

This paper studies the cost of business cycles within a real business cycle model with search and matching frictions in the labor market. We endogenously link both the cyclical fluctuations and the mean level of unemployment to the aggregate business cycle risk. The key result of the paper is that business cycles are costly: fluctuations over the cycle induce a higher average unemployment rate since employment is nonlinear in the job-finding rate and the past unemployment rate. We show this analytically for a special case of the model. We then calibrate the model to U.S. data. For the calibrated model, too, business cycles cause higher average unemployment; the welfare cost of business cycles can easily be an order of magnitude larger than Lucas's (1987) estimate. The cost of business cycles is the higher the lower the value of nonemployment is, or, equivalently, the lower is the disutility of work. The ensuing cost of business cycles rises further when workers' skills depreciate during unemployment.     

Efficient tests of long‐run causation in trivariate VAR processes with a rolling window study of the money–income relationship

This paper develops a simple sequential multiple‐horizon non‐causation test strategy for trivariate VAR models (with one auxiliary variable). We apply the test strategy to a rolling window study of money supply and real income, with the price of oil, the unemployment rate and the spread between the Treasury bill and commercial paper rates as auxiliary processes. Ours is the first study to control simultaneously for common stochastic trends, sensitivity of test statistics to the chosen sample period, null hypothesis over‐rejection, sequential test size bounds, and the possibility of causal delays. Evidence suggests highly significant direct or indirect causality from M1 to real income, in particular through the unemployment rate and M2 once we control for cointegration. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of cointegrated VARMA processes

VARMA (vector autoregressive moving average) processes are proposed for modelling cointegrated variables. For this purpose the echelon form is combined with the error correction form. Procedures for estimating the Kronecker indices which characterize the echelon form and for specifying the cointegration rank are discussed. The asymptotic distribution of the coefficient estimators is given. An example based o n US macroeconomic data illustrates the procedure and demonstrates its feasibility in practice.