Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice-versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

BAYESIAN MODEL SELECTION AND FORECASTING IN NONCAUSAL AUTOREGRESSIVE MODELS

In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by‐product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high—over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models. Copyright © 2010 John Wiley & Sons, Ltd.     

Mixed causal–noncausal autoregressions with exogenous regressors

Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non-Gaussian densities. For a Student likelihood, closed-form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices.     

The nexus between exchange rates and stock markets: evidence from the euro-dollar rate and composite European stock indices using rolling analysis

Both the goods market hypothesis and the portfolio balance theory, suggest a nexus between exchange rates and stock prices, albeit with a different direction of causality. This paper, using daily data, takes up the issue of the linkages between stock prices and exchange rates in the case of the euro-dollar rate and two composite European stock market indices: the FTSE Eurotop 300 and FTSE eTX All-Share Index. It addresses the causal ordering issue between the two markets using rolling unit root, cointegration and Granger causality tests. This methodological approach allows for the emergence of a clearer picture of the possible dynamic linkages between exchange rates and stock prices. The empirical results provide evidence of time-varying causality between the two markets.     

带有结构突变的单位根检验 ——文献综述

单位根检验是时间序列分析的基础，而是否考虑结构突变对单位根检验的结论有着重要影响，因此，考虑结构突变的单位根检验已成为计量经济学界的一个前沿热点问题。本文回顾了这一问题的发展历史，总结了该领域已取得的一些重要研究成果，最后对该问题最新的发展动向加以概括。     

带有结构突变的单位根检验——文献综述

单位根检验是时间序列分析的基础,而是否考虑结构突变对单位根检验的结论有着重要影响,因此,考虑结构突变的单位根检验已成为计量经济学界的一个前沿热点问题。本文回顾了这一问题的发展历史,总结了该领域已取得的一些重要研究成果,最后对该问题最新的发展动向加以概括。     

Noncausal Bayesian Vector Autoregression

We consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by‐product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in‐sample fit and out‐of‐sample forecasting performance over its conventional causal counterpart. Economic shocks based on the noncausal model turn out to be highly anticipated in advance. We also find the GDP growth to have predictive power for future inflation, but not vice versa. Copyright © 2016 John Wiley & Sons, Ltd.     

Model identification for infinite variance autoregressive processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.     

Multivariate-based Granger causality between financial deepening and poverty: the case of Pakistan

This paper deals with the empirical investigation of causal relationship between financial deepening, economic growth and poverty reduction using quarter frequency data in case of Pakistan over the period of 1972–2011. We applied the autoregressive distributed lag model bounds testing approach by incorporating structural breaks stemming in the series. The order of integration of the variables is examined by applying structural break unit root test. Our empirical exercise indicated that the long run relationship between financial deepening, economic growth and poverty reduction exists in case of Pakistan. The causality analysis implied that causality results are sensitive with the use of proxy for poverty reduction.     

标准化与产业内贸易——基于中国机械行业的面板协整分析

本文通过对1992～2007年的机械行业中9个种类的面板数据进行实证检验,建立协整方程并对其进行误差修正,分析了我围机械行业中的标准存量与产业内贸易之间的关系。实证结果表明两者有着长期的均衡关系,机械行业中标准的使用会对该行业的产业内贸易水平产牛正的促进作用。标准的进入将在长期内改善我围的产业结构,促进产业内贸易发展。     

Market efficiency and cointegration: Some evidence in Pacific-Basin black exchange markets

This paper investigates the efficiency of the black exchange markets in Indonesia, Malaysia, the Philippines, South Korea, Taiwan, and Thailand. The study applies unit root and cointegration tests to examine black exchange market efficiency of Pacific-Basin countries. The generating process of black exchange rates appears to be a random walk. This is consistent with Gupta (1981) and other foreign exchange rate unit root test studies. Johansen cointegration tests are performed for these black exchange markets together with Japan and Singapore. The results suggest that there is at least one unit root among the black market exchange rates. Hence, black exchange markets are not collectively efficient.     

Are unemployment rates in OECD countries stationary? Evidence from univariate and panel unit root tests

This paper revisits the dynamics of unemployment rate for 29 OECD countries over the period of 1980–2013. Numerous empirical studies of the dynamics of unemployment rate are carried out within a linear framework. However, unemployment rate can show nonlinear behaviour as a result of business cycles or some idiosyncratic factors specific to labour market (Cancelo, 2007). Thus, as a testing strategy, we first perform Harvey, Leybourne, and Xiao (2008) linearity unit root test and then apply the newly ESTAR nonlinear unit root test suggested by Kruse (2011). This test has higher power than conventional unit root tests when time series exhibits nonlinear behaviour. Our empirical findings provide significant evidence in favour of unemployment rate stationarity for 25 countries. For robustness purpose, we have also used panel unit root tests without and with structural breaks. The empirical results show that unemployment hysteresis hypothesis is strongly rejected, when taking into account the cross-sectional and structural break assumptions. Thus, unemployment rate is expected to return back to their natural levels without executing any costly macroeconomic labour market policies by the OECD’s governments.     

Cross-sectional dependence robust block bootstrap panel unit root tests

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the group-mean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data, originally proposed for a setting of no cross-sectional dependence beyond a common time effect. The tests, suited for testing for unit roots in the observed data, can be easily implemented as no specification or estimation of the dependence structure is required. Asymptotic properties of the tests are derived for T going to infinity and N finite. Asymptotic validity of the bootstrap tests is established in very general settings, including the presence of common factors and cointegration across units. Properties under the alternative hypothesis are also considered. In a Monte Carlo simulation, the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests. The power properties of the bootstrap tests appear to be similar to those of the asymptotic tests.     

IDENTIFYING CAUSAL MECHANISMS (PRIMARILY) BASED ON INVERSE PROBABILITY WEIGHTING

This paper demonstrates the identification of causal mechanisms of a binary treatment under selection on observables, (primarily) based on inverse probability weighting; i.e. we consider the average indirect effect of the treatment, which operates through an intermediate variable (or mediator) that is situated on the causal path between the treatment and the outcome, as well as the (unmediated) direct effect. Even under random treatment assignment, subsequent selection into the mediator is generally non‐random such that causal mechanisms are only identified when controlling for confounders of the mediator and the outcome. To tackle this issue, units are weighted by the inverse of their conditional treatment propensity given the mediator and observed confounders. We show that the form and applicability of weighting depend on whether some confounders are themselves influenced by the treatment or not. A simulation study gives the intuition for these results and an empirical application to the direct and indirect health effects (through employment) of the US Job Corps program is also provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Unit Root Testing Using Covariates: Some Theory and Evidence

This paper analyzes the conditions under which power gains can be achieved using the Covariate Augmented Dickey-Fuller test (CADF) rather than the conventional Augmented Dickey-Fuller (ADF), and argues that this method has the advantage, relative to univariate unit root tests, of increasing power without suffering from the large size distortions affecting the latter. The inclusion of covariates affects unit root testing by: (a) reducing the standard error of the estimate of the autoregressive parameter without affecting the estimate itself, and/or (b) reducing both the standard error and the absolute value of the estimate itself. Conditions in terms of contemporaneous correlation and Granger causality are derived for case (a) or (b) to arise. As an illustration, it is shown that applying the more powerful CADF (rather than the ADF) test reverses the finding of a unit root for many US macroeconomic series.     

Nonresponse in dynamic panel data models

To verify whether data are missing at random (MAR) we need to observe the missing data. There are only two exceptions: when the relationship between the probability of responding and the missing variables is either imposed by introducing untestable assumptions or recovered using additional data sources. In this paper, we briefly review the estimation and test procedures for selectivity in panel data. Furthermore, by extending the MAR definition from a static setting to the case of dynamic panel data models, we prove that some tests for selectivity are not verifying the MAR condition.     

Additional critical values and asymptotic representations for seasonal unit root tests

This paper is concerned with tests for seasonal unit roots in a univariate time series process. The paper extends the procedures and tables of critical values due to Hylleberg et al. (1990) and Ghysels et al. (1994) to obtain tests which are similar (exactly and asymptotically) with respect to both the initial values of the process and the possibility of differential seasonal drift under the null hypothesis of a seasonal unit root. Representations are derived for the limiting distributions of the test statistics in this and other cases of interest. These representations provide an explanation for the similarity between critical values for the statistics in different scenarios. The seasonal unit root properties of real seasonally unadjusted UK non-durable consumption expenditure are re-examined.     

Testing for a unit root in a random coefficient panel data model

This paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples.     

Electricity consumption and economic growth empirical evidence from Pakistan

The present article uses the Autoregressive Distributed Lag (ARDL) bounds testing procedure to identify the long run equilibrium relationship between electricity consumption and economic growth. Toda Yamamoto and Wald-test causality tests have identified the direction of the causal relationship between these two variables in the case of Pakistan in the period between 1971 and 2008. Ng-Perron and Clement-Montanes-Reyes unit root tests are used to handle the problem of integrating orders for variables. The results suggest that the two variables are in a long run equilibrium relationship and economic growth leads to electricity consumption and not vice versa.     

On Bayesian routes to unit roots

This paper is a comment on P. C. B. Phillips, ‘To criticise the critics: an objective Bayesian analysis of stochastic trends’ [Phillips, (1991)]. Departing from the likelihood of an univariate autoregressive model different routes that lead to a posterior odds analysis of the unit root hypothesis are explored, where the differences in routes are due to the different choices of the prior. Improper priors like the uniform and the Jeffreys prior are less suited for Bayesian inference on a sharp null hypothesis as the unit root. A proper normal prior on the mean of the process is analysed and empirical results using extended Nelson-Plosser data are presented.