A consistent characteristic function-based test for conditional independence

Y is conditionally independent of Z given X   if Pr{f(y|X,Z)=f(y|X)}=1$\{f(y|X,Z)=f(y|X)\}=1$ for all y on its support, where f(·|·)$f(·|·)$ denotes the conditional density of Y   given (X,Z)$(X,Z)$ or X.$X.$ This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We extend the test of Su and White (2005. A Hellinger-metric nonparametric test for conditional independence. Discussion Paper, Department of Economics, UCSD) in two directions: (1) our test is less sensitive to the choice of bandwidth sequences; (2) our test has power against deviations on the full support of the density of (X,Y,Z$X,Y,Z$). We establish asymptotic normality for our test statistic under weak data dependence conditions. Simulation results suggest that the test is well behaved in finite samples. Applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear Granger causality test fails to detect.     

A consistent nonparametric test for nonlinear causality—Specification in time series regression

Since the pioneering work by Granger (1969), many authors have proposed tests of causality between economic time series. Most of them are concerned only with “linear causality in mean”, or if a series linearly affects the (conditional) mean of the other series. It is no doubt of primary interest, but dependence between series may be nonlinear, and/or not only through the conditional mean. Indeed conditional heteroskedastic models are widely studied recently. The purpose of this paper is to propose a nonparametric test for possibly nonlinear causality. Taking into account that dependence in higher order moments are becoming an important issue especially in financial time series, we also consider a test for causality up to the Kth conditional moment. Statistically, we can also view this test as a nonparametric omitted variable test in time series regression. A desirable property of the test is that it has nontrivial power against T^1/2-local alternatives, where T is the sample size. Also, we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis. Furthermore, we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically. The null asymptotic distribution is not normal, but we can easily calculate the critical regions by simulation. Monte Carlo experiments show that the proposed test has good size and power properties.     

Do business strategies vary across firms in the banking industry? New perspectives from the bank size–profitability nexus

This study examines the roles of interdependence and policy variations across firms in the causality between bank size and profitability in Nigeria, using second-generation estimators and the Dumitrescu–Hurlin panel Granger non-causality test. The findings support different business strategies and policy variances across banks. Causality is found non-existent in the cases of 11 banks. A unidirectional causality from size to profitability is established in two banks while evidence of a unidirectional causality is established from profitability to bank size in the other two banks. This study concludes that cross-sectional dependence and policy variations across firms matter in the bank size–profitability nexus.     

Modeling and forecasting of stock index volatility with APARCH models under ordered restriction

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student's t and skewed Student's t‐distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron) tests, co‐integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500 daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student's t‐distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.     

Non-causality in bivariate binary time series

In this paper we develop a dynamic discrete-time bivariate probit model, in which the conditions for Granger non-causality can be represented and tested. The conditions for simultaneous independence are also worked out. The model is extended in order to allow for covariates, representing individual as well as time heterogeneity. The proposed model can be estimated by Maximum Likelihood. Granger non-causality and simultaneous independence can be tested by Likelihood Ratio or Wald tests. A specialized version of the model, aimed at testing Granger non-causality with bivariate discrete-time survival data is also discussed. The proposed tests are illustrated in two empirical applications.     

GARCH models,tail indexes and error distributions: An empirical investigation

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns and compare these to the tail indexes produced by simulating GARCH models. Our results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which underestimate the tail risk. By contrast, the GARCH models with Student's t conditional distributions capture the tail shape more accurately, with GARCH and GJR-GARCH being the top performers.     

Are Google searches making the Bitcoin market run amok? A tail event analysis

This paper aims at detecting extreme value spillover between the large co-movements of Bitcoin returns and the rate of change in investor attention (for which Google search is used as a proxy). For this purpose, we use the concept of the Granger causality in tail event. Thus, we test whether positive, or negative, extreme values of rate of change in Google searches have a significant predictive power for negative, or positive, large values of Bitcoin returns, and vice versa . Our results shed light on a unidirectional causality effect from the returns to investor attention in the first place, before becoming bidirectional when the time delay increases.     

Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity

In this paper, we propose a fixed design wild bootstrap procedure to test parameter restrictions in vector autoregressive models, which is robust in cases of conditionally heteroskedastic error terms. The wild bootstrap does not require any parametric specification of the volatility process and takes contemporaneous error correlation implicitly into account. Via a Monte Carlo investigation, empirical size and power properties of the method are illustrated for the case of white noise under the null hypothesis. We compare the bootstrap approach with standard ordinary least squares (OLS)-based, weighted least squares (WLS) and quasi-maximum likelihood (QML) approaches. In terms of empirical size, the proposed method outperforms competing approaches and achieves size-adjusted power close to WLS or QML inference. A White correction of standard OLS inference is satisfactory only in large samples. We investigate the case of Granger causality in a bivariate system of inflation expectations in France and the United Kingdom. Our evidence suggests that the former are Granger causal for the latter while for the reverse relation Granger non-causality cannot be rejected.     

On economic uncertainty,stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.     

On testing for independence against right tail increasing in bivariate models

A random variableY is right tail increasing (RTI) inX if the failure rate of the conditional distribution ofX givenY>y is uniformly smaller than that of the marginal distribution ofX for everyy0. This concept of positive dependence is not symmetric inX andY and is stronger than the notion of positive quadrant dependence. In this paper we consider the problem of testing for independence against the alternative thatY is RTI inX. We propose two distribution-free tests and obtain their limiting null distributions. The proposed tests are compared to Kendall's and Spearman's tests in terms of Pitman asymptotic relative efficiency. We have also conducted a Monte Carlo study to compare the powers of these tests.Research supported by an NSERC Canada operating grant at the University of Alberta.Part of this research was done while visiting the University of Alberta supported by the NSERC Canada grant of the first author.     

OPEC news and predictability of oil futures returns and volatility: Evidence from a nonparametric causality-in-quantiles approach

This paper provides a novel perspective to the predictive ability of OPEC meeting dates and production announcements for (Brent Crude and West Texas Intermediate) oil futures market returns and GARCH-based volatility using a nonparametric quantile-based methodology. We show a nonlinear relationship between oil futures returns and OPEC-based predictors; hence, linear Granger causality tests are misspecified and the linear model results of non-predictability are unreliable. When the quantile-causality test is implemented, we observe that the impact of OPEC variables is restricted to Brent Crude futures only (with no effect observed for the WTI market). Specifically, OPEC production announcements, and meeting dates predict only lower quantiles of the conditional distribution of Brent futures market returns. While, predictability of volatility covers the majority of the quantile distribution, barring extreme ends.     

Testing conditional independence via empirical likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.     

Local indirect least squares and average marginal effects in nonseparable structural systems

We study the scope of local indirect least squares (LILS) methods for nonparametrically estimating average marginal effects of an endogenous cause X on a response Y in triangular structural systems that need not exhibit linearity, separability, or monotonicity in scalar unobservables. One main finding is negative: in the fully nonseparable case, LILS methods cannot recover the average marginal effect. LILS methods can nevertheless test the hypothesis of no effect in the general nonseparable case. We provide new nonparametric asymptotic theory, treating both the traditional case of observed exogenous instruments Z and the case where one observes only error-laden proxies for Z.     

Causality in temporal systems: Characterization and a survey

A time series {Y_t} ‘causes’ another time series {Y_t}, in the sense defined by C.W.J. Granger, if present Y can be predicted better by using past values of X than by not doing so, other relevant information (including the past of Y) being used in either case. In this paper we (1) classify the possible causality relationships between two series X and Y, using an analogy to events in a sample space; (2) review existing work and present some new results on alternative characterizations of the more important causality events; and (3) compare several recent procedures for the empirical detection of causality.     

Heterogeneity dependence between oil prices and exchange rate: Evidence from a parametric test of Granger causality in quantiles

This paper re-examines the nexus between crude oil price and exchange rate by investigating their heterogeneity dependence structure within the framework of Granger causality in quantiles for a sample of developed and emerging economies (namely UK, Canada, Brazil, Russia, Mexico, Norway, India, Japan, South Africa, South Korea and European Union (EU)). The results indicate no distinct causality between the crude oil price changes and the real exchange rate returns for all countries besides Russia at the median of the conditional distribution. Besides, the crude oil price changes influence the exchange rate returns in all countries, except Norway and EU, particularly around the tails of the conditional distributions of exchange rate returns. This suggests that the oil price changes influence the real exchange rate returns when the real exchange rate returns are either in extreme appreciation or depreciation. Moreover, the crude oil price movement can be explained by the exchange rate returns for most oil importers only when the crude oil market is bearish or bullish. By contrast, the real exchange rate can permanently affect the crude oil price for most oil-importing countries irrespective of the crude oil market's state. Finally, our findings provide an essential reference for managing the extreme risk dependence between the exchange rate market and the crude oil market.     

Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory,structural breaks,asymmetry, and fat-tails matter?

This paper addresses the question whether dual long memory (LM), asymmetry and structural breaks in stock market returns matter when forecasting the value at risk (VaR) and expected shortfall (ES) for short and long trading positions. We answer this question for the Gulf Cooperation Council (GCC) stock markets. Empirically, we test the occurrence of structural breaks in the GCC return data using the Inclan and Tiao (1994)’s algorithm and we check the relevance of LM using Shimotsu (2006) procedure before estimating the ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with different innovations’ distributions and computing VaR and ES. Our results show that all the GCC market's volatilities exhibit significant structural breaks matching mainly with the 2008–2009 global financial crises and the Arab spring. Also, they are governed by LM process either in the mean or in the conditional variance which cannot be due to the occurrence of structural breaks. Furthermore, the forecasting ability analysis shows that the FIAPARCH model under skewed Student-t distribution turn out to improve substantially the VaR and the ES forecasts.     

Performance of conditional Wald tests in IV regression with weak instruments

We compare the powers of five tests of the coefficient on a single endogenous regressor in instrumental variables regression. Following Moreira [2003, A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048], all tests are implemented using critical values that depend on a statistic which is sufficient under the null hypothesis for the (unknown) concentration parameter, so these conditional tests are asymptotically valid under weak instrument asymptotics. Four of the tests are based on k-class Wald statistics (two-stage least squares, LIML, Fuller's [Some properties of a modification of the limited information estimator. Econometrica 45, 939–953], and bias-adjusted TSLS); the fifth is Moreira's (2003) conditional likelihood ratio (CLR) test. The heretofore unstudied conditional Wald (CW) tests are found to perform poorly, compared to the CLR test: in many cases, the CW tests have almost no power against a wide range of alternatives. Our analysis is facilitated by a new algorithm, presented here, for the computation of the asymptotic conditional p-value of the CLR test.     

Density estimates of low bias

Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(h ^p ) for any given p, where h = h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared errors than classical kernel density estimates and those due to Jones et al. (Biometrika 82:327–338, 1995).     

Modelling the conditional volatility of commodity index futures as a regime switching process

Commodity index futures offer a versatile tool for gaining different forms of exposure to commodity markets. Volatility is a critical input in many of these applications. This paper examines issues in modelling the conditional variance of futures returns based on the Goldman Sachs Commodity Index (GSCI). Given that commodity markets tend to be ‘choppy’ (Webb, 1987 ), a general econometric model is proposed that allows for abrupt changes or regime shifts in volatility, transition probabilities which vary explicitly with observable fundamentals such as the basis, GARCH dynamics, seasonal variations and conditional leptokurtosis. The model is applied to daily futures returns on the GSCI over 1992–1997. The results show clear evidence of regime shifts in conditional mean and volatility. Once regime shifts are accounted for, GARCH effects are minimal. Consistent with the theory of storage, returns are more likely to switch to the high‐variance state when the basis is negative than when the basis is positive. The regime switching model also performs well in forecasting the daily volatility compared to standard GARCH models without regime switches. The model should be of interest to sophisticated traders who base their trading strategies on short‐term volatility movements, managed commodity funds interested in hedging an underlying diversified portfolio of commodities and investors of options and other derivatives tied to GSCI futures contracts. Copyright © 2001 John Wiley & Sons, Ltd.