Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form

Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be infinite. Both linear and nonlinear conditional mean specifications are covered. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroscedasticity and higher order time-varying moments of unknown form. They check a large number of lags, but naturally discount higher order lags, which is consistent with the stylized fact that economic behaviours are more affected by the recent past events than by the remote past events. No specific estimation method is required, and the tests have the appealing „nuisance parameter free” property that parameter estimation uncertainty has no impact on the limit distribution of the tests. A simulation study shows that it is important to take into account the impact of conditional heteroscedasticity; failure to do so will cause overrejection of a correct conditional mean model. In a horse race competition on testing linearity in mean, our tests have omnibus and robust power against a variety of alternatives relative to some existing tests. In an application, we find that after removing significant but possibly spurious autocorrelations due to nonsynchronous trading, there still exists significant predictable nonlinearity in mean for S&P 500 and NASDAQ daily returns.     

Volatility Spillovers and Contagion from Mature to Emerging Stock Markets

This paper models volatility spillovers from mature to emerging stock markets, tests for changes in the transmission mechanism during turbulences in mature markets, and examines the implications for conditional correlations between mature and emerging market returns. Tri‐variate GARCH–BEKK models of returns in mature, regional emerging, and local emerging markets are estimated for 41 emerging market economies (EMEs). Wald tests suggest that mature market volatility affects conditional variances in many emerging markets. Moreover, spillover parameters change during turbulent episodes. In the majority of the sample EMEs, conditional correlations between local and mature markets increase during these episodes. While conditional variances in local markets rise as well, volatility in mature markets rises more, and this shift is the main factor behind the increase in conditional correlations. With few exceptions, conditional beta coefficients between mature and emerging markets tend to be unchanged or lower during turbulences.     

A COMPARISON OF CONDITIONAL AND UNCONDITIONAL APPROACHES IN VALUE‐AT‐RISK ESTIMATION*

In this paper, we attempt to find the most important factor causing the differences in the performance of Value‐at‐Risk (VaR) estimation by comparing the performances of conditional and unconditional approaches. For each approach, we use various methods and models with different degrees of flexibility in their distributions including S_U‐normal distribution, which is one of the most flexible distribution functions. Our empirical results underscore the importance of the flexibility‐of‐distribution function in VaR estimation models. Even though it seems to be unclear which approach is better between conditional and unconditional approaches, it seems to be clear that the more flexible distribution we use, the better the performance, regardless of which approach we use.     

Asymmetric and Time‐Varying Causality between Inflation and Inflation Uncertainty in G‐7 Countries

We use Granger causality tests within a conditional Gaussian Markov switching vector autoregressive (MS‐VAR) model using monthly data for G‐7 countries covering the period 1959:12–2008:10 to examine the relationship between inflation and inflation‐uncertainty. The MS‐VAR model allows us to model parameter time‐variation so as to reflect changes in Granger causality, assuming that these changes are stochastic and governed by an unobservable Markov chain. Inflation uncertainty is measured as the conditional variance generated by a Fractionally Integrated Smooth Transition Autoregressive Moving Average‐Asymmetric Power ARCH (FISTARMA‐APARCH) model. The distinguishing feature of our approach from the previous studies is the determination of the sign of the Granger causality relationship between inflation and its uncertainty over time. First, using a rolling VAR model, we show that the relationship between inflation and inflation uncertainty is time varying with frequent breaks. Second, using the MS‐VAR model, we obtain strong evidence in favour of the Holland's ‘stabilizing Fed hypothesis’ for Canada, France, Germany, Japan, United Kingdom, and the United States. We also find evidence in favour of the Friedman hypothesis for Canada and the United States.     

PERSISTENCE IN CONVERGENCE AND CLUB FORMATION

In this paper, we examine the convergence hypothesis using a long memory framework that allows for structural breaks and does not rely on a benchmark country using both univariate and multivariate estimates of the long memory parameter d. Using per capita GDP gaps, we confirm the findings of non‐stationarity and long memory behavior that have been found previously in the literature using univariate tests. However, the support for these findings is much weaker when using a multivariate framework, in which case we find more evidence of stationary behavior. Based on these results, we also investigate club formation, something that would suggest the presence of conditional convergence. We describe a club formation methodology using the sequential testing criteria that we have employed in our analysis as the basis for forming clusters or clubs of countries with similar convergence characteristics.     

BAYESIAN ANALYSIS OF GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY AND STOCHASTIC VOLATILITY: MODELING LEVERAGE,JUMPS AND HEAVY‐TAILS FOR FINANCIAL TIME SERIES*

This paper develops a Bayesian model comparison of two broad major classes of varying volatility model, the generalized autoregressive conditional heteroskedasticity and stochastic volatility models, on financial time series. The leverage effect, jumps and heavy‐tailed errors are incorporated into the two models. For estimation, the efficient Markov chain Monte Carlo methods are developed and the model comparisons are examined based on the marginal likelihood. The empirical analyses are illustrated using the daily return data of US stock indices, individual securities and exchange rates of UK sterling and Japanese yen against the US dollar. The estimation results indicate that the stochastic volatility model with leverage and Student‐t errors yield the best performance among the competing models.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

We propose a generalized method of moments (GMM) estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first‐stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first‐stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first‐stage equation, we use the k‐nearest neighbour (k‐nn) non‐parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two‐stage conditional maximum likelihood estimator. Our results suggest that in the presence of heteroscedasticity in the first‐stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.     

International risk‐sharing in the short run and in the long run

Abstract International risk‐sharing has far‐reaching implications both for economic policy and for basic research in economics. When countries do not share consumption risk, individuals experience consumption fluctuations that are undesirable and possibly unnecessary. We investigate bilateral risk‐sharing at short vs. long horizons. We find substantial cross‐country consumption correlations at trend and business‐cycle frequencies. Correlations are particularly high within Europe. Prior research focused on first‐difference correlations, which are typically quite low. We argue that this reflects measurement error. At all horizons, we find that consumption correlations are not significantly different from output correlations, implying a lack of deliberate consumption risk‐sharing.     

Stock market comovements in Central Europe: Evidence from the asymmetric DCC model

We examine time-varying stock market comovements in Central Europe employing the asymmetric dynamic conditional correlation multivariate GARCH model. Using daily data from 2001 to 2011, we find that the correlations among stock markets in Central Europe and between Central Europe vis-à-vis the euro area are strong. The correlations increased over time, particularly after their EU entry and largely remained at these levels during the financial crisis. The stock markets exhibit asymmetry in the conditional variances and to a certain extent in the conditional correlations as well, pointing to the importance of applying a sufficiently flexible econometric framework. The conditional variances and correlations are positively related, suggesting that the diversification benefits decrease disproportionally during volatile periods.     

SEMINONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS*

This article studies estimation of a conditional moment restriction model with the seminonparametric maximum likelihood approach proposed by Gallant and Nychka (Econometrica 55 (March 1987), 363–90). Under some sufficient conditions, we show that the estimator of the finite dimensional parameter θ is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function is consistent under L₂ norm. Some results on the convergence rate of the estimated density function are derived. An easy to compute covariance matrix for the asymptotic covariance of the θ estimator is presented.     

Data-dependent selection of the lag truncation parameter in unit root tests of the Phillips-Perron type

The Andrews (Econometrica, 1991, 59, 817–858) plug-in method of heteroscedastic and autocovariance consistent covariance matrix estimation is used to construct estimators of the long-run variance parameter for use in Phillips-Perron unit root tests. This allows the lag truncation parameter to be data dependent. Monte Carlo size and power estimates are obtained suggesting that this apparently natural approach does not provide significant improvements in test performance.     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

NONPARAMETRIC BOOTSTRAP PROCEDURES FOR PREDICTIVE INFERENCE BASED ON RECURSIVE ESTIMATION SCHEMES*

We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out‐of‐sample nonlinear Granger causality, and in the other we outline a test for selecting among multiple alternative forecasting models, all of which are possibly misspecified. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (Journal of Applied Econometrics 14 (1999), 491–510), within the context of encompassing and predictive accuracy tests. In the empirical illustration, it is found that unemployment has nonlinear marginal predictive content for inflation.     

Diversification into Emerging Markets – An Australian and the US Perspective Using a Time‐varying Approach

Over the past two decades, a number of studies have examined the benefits of diversifying equity investments internationally, particularly into emerging markets. In the portfolio construction process, many researchers have criticised Markowitz's Portfolio Theory because of its inherent assumptions such as symmetric and constant correlations. In this study, we use a conditional copula model to estimate the time‐varying asymmetric correlations of stock markets and construct optimal portfolios by using estimated correlations. We find that optimised portfolios provide significant benefits for both Australian and the US investors. Out‐of‐sample results show Copula model provides results closer to the in‐sample‐estimated benefits of diversification. The results have important implications for portfolio managers who seek to diversify into emerging markets.     

Labor Market Dynamics and the Business Cycle: Structural Evidence for the United States*

We use a 12‐dimensional VAR to examine the aggregate effects of two structural technology shocks and two policy shocks. For each shock, we examine the dynamic effects on the labor market, the importance of the shock for labor market volatility, and the comovement between labor market variables and other key aggregate variables in response to the shock. We document that labor market indicators display “hump‐shaped” responses to the identified shocks. Technology shocks and monetary policy shocks are important for labor market volatility but the ranking of their importance is sensitive to the VAR specification. The conditional correlations at business cycle frequencies are similar in response to the four shocks, apart from the correlations between hours worked, labor productivity and real wages. To account for the unconditional correlations between these variables, a mixture of shocks is required.     

Efficient Estimation of Additive Partially Linear Models

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite-dimensional parameter is identified under weak conditions. I establish the root-n-normality result for the finite-dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite-dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.     

should Transfers To Poor Families Be Conditional On School Attendance? A Household Bargaining Perspective*

This article considers the welfare implications of transfers to poor families that are conditional on school attendance and other forms of investment in children's human capital. Family decisions are assumed to be the result of (generalized) Nash bargaining between the two parents. We show that, as long as bequests are zero, conditional transfers are better for children than unconditional transfers. The mother's welfare may also be improved by conditional transfers. Thus, conditioning transfers to bequest‐constrained families have potentially desirable intergenerational and intragenerational welfare effects. Conditioning transfers to unconstrained families make every family member worse off.     

Finite Sample Limited Information Inference Methods for Structural Equations and Models With Generated Regressors

We propose exact tests and confidence sets for various structural models typically estimated by IV methods, such as models with unobserved regressors, which remain valid despite the presence of identification problems or weak instruments. Two approaches are considered: (1) an instrument substitution method, which generalizes the Anderson–Rubin procedure, and (2) a sample‐split method, that allows the use of “generated regressors.” Projection techniques are also proposed for inference on general parameter transformations. The asymptotic theory of the tests under weaker assumptions is discussed. Simulation results are presented. The suggested techniques are applied to a model of Tobin's q and to a model of academic performance.     

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.