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This paper develops a time--varying coefficient spatial autoregressive panel data model with individual fixed effects to capture the nonlinear effects of the regressors, which vary over the time. To effectively estimate the model, we propose a method that incorporates local linear estimation and concentrated quasi-maximum likelihood estimation to obtain consistent estimators for the spatial autoregressive coefficient, variance of error term and nonparametric time-varying coefficient function. The asymptotic properties of these estimators are derived as well, showing regular the standard rate of convergence for the parametric parameters and common standard rate of convergence for the time-varying component, respectively. Monte Carlo simulations are conducted to illustrate the finite sample performance of our proposed method. Meanwhile, we apply our method to study the Chinese labor productivity to identify the spatial influences and the time--varying spillover effects among 185 Chinese cities with comparison to the results on a subregion--East China.

In proxy vector autoregressive models, the structural shocks of interest are identified by an instrument. Although heteroscedasticity is occasionally allowed for in inference, it is typically taken...

We propose an autoregressive conditional Pareto (AcP) model based on the dynamic peaks over threshold method to model a dynamic tail index in the financial markets. Unlike the score-based approach ...

We propose to exploit stochastic volatility for statistical identification of structural vector autoregressive models (SV-SVAR). We discuss full and partial identification of the model and develop efficient Expectation Maximization algorithms for Maximum Likelihood inference. Simulation evidence suggests that, compared to alternative models, the SV-SVAR works well in identifying structural parameters also under misspecification of the variance process. We apply the model to study the importance of oil supply shocks for driving oil prices. Since shocks identified by heteroskedasticity may not be economically meaningful, we exploit the framework to test instrumental variable restrictions which are overidentifying in the heteroskedastic model. Our findings suggest that conventional supply shocks are negligible drivers of oil prices, while news shocks about future supply account for almost all the variation.

Quantile autoregresive model is a useful extension to classical autoregresive models as it can capture the influences of conditioning variables on the location, scale and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this paper, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of US retail gasoline price.

We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characte...

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings.

This article proposes a new panel unit root test based on the generalized method of moments approach for panels with a possibly small number of time periods, T, and a large number of cross-sectional units, N. In the model that we consider the deterministic trend function is essentially unrestricted and the errors obey a multifactor structure that allows for rich forms of unobserved heterogeneity. In spite of these allowances, the GMM estimator considered is shown to be asymptotically unbiased, N-consistent, and asymptotically normal for all values of the autoregressive (AR) coefficient, ρ, including unity, making it a natural candidate for unit root inference. Results from our Monte Carlo study suggest that the asymptotic properties are borne out well in small samples. The implementation is illustrated by using a large sample of US banking institutions to test Gibrat’s Law.

This study considers semiparametric spatial autoregressive models that allow for endogenous regressors, as well as the heterogenous effects of these regressors across spatial units. For the model e...

This article develops a new Markov-switching vector autoregressive (VAR) model with stochastic correlation for contagion analysis on financial markets. The correlation and the log-volatility dynamics are driven by two independent Markov chains, thus allowing for different effects such as volatility spill-overs and correlation shifts with various degrees of intensity. We outline a suitable Bayesian inference procedure based on Markov chain Monte Carlo algorithms. We then apply the model to some major and Asian-Pacific cross rates against the U.S. dollar and find strong evidence supporting the existence of contagion effects and correlation drops during crises, closely in line with the stylized facts outlined in the contagion literature. A comparison of this model with its closest competitors, such as a time-varying parameter VAR, reveals that our model has a better predictive ability. Supplementary materials for this article are available online

This paper introduces a new specification for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P 500 index returns. In this modelling framework, the coefficients of the HAR are allowed to be time-varying with unspecified functional forms. The local linear method with the cross-validation (CV) bandwidth selection is applied to estimate the time-varying coefficient HAR (TVC-HAR) model, and a bootstrap method is used to construct the point-wise confidence bands for the coefficient functions. Furthermore, the asymptotic distribution of the proposed local linear estimators of the TVC-HAR model is established under some mild conditions. The results of the simulation study show that the local linear estimator with CV bandwidth selection has favorable finite sample properties. The outcomes of the conditional predictive ability test indicate that the proposed nonparametric TVC-HAR model outperforms the parametric HAR and its extension to HAR with jumps and/or GARCH in terms of multi-step out-of-sample forecasting, in particular in the post-2003 crisis and 2007 GFC periods, during which financial market volatilities were unduly high.

Vector autoregressive (VAR) models are frequently used for forecasting and impulse response analysis. For both applications, shrinkage priors can help improving inference. In this article, we apply the Normal-Gamma shrinkage prior to the VAR with stochastic volatility case and derive its relevant conditional posterior distributions. This framework imposes a set of normally distributed priors on the autoregressive coefficients and the covariance parameters of the VAR along with Gamma priors on a set of local and global prior scaling parameters. In a second step, we modify this prior setup by introducing another layer of shrinkage with scaling parameters that push certain regions of the parameter space to zero. Two simulation exercises show that the proposed framework yields more precise estimates of model parameters and impulse response functions. In addition, a forecasting exercise applied to U.S. data shows that this prior performs well relative to other commonly used specifications in terms of p...

This article considers a simple test for the correct specification of linear spatial autoregressive models, assuming that the choice of the weight matrix Wn is true. We derive the limiting distributions of the test under the null hypothesis of correct specification and a sequence of local alternatives. We show that the test is free of nuisance parameters asymptotically under the null and prove the consistency of our test. To improve the finite sample performance of our test, we also propose a residual-based wild bootstrap and justify its asymptotic validity. We conduct a small set of Monte Carlo simulations to investigate the finite sample properties of our tests. Finally, we apply the test to two empirical datasets: the vote cast and the economic growth rate. We reject the linear spatial autoregressive model in the vote cast example but fail to reject it in the economic growth rate example. Supplementary materials for this article are available online.

We propose an adaptive functional autoregressive (AFAR) forecast model to predict electricity price curves. With time-varying operators, the AFAR model can be safely used in both stationary and nonstationary situations. A closed-form maximum likelihood (ML) estimator is derived under stationarity. The result is further extended for nonstationarity, where the time-dependent operators are adaptively estimated under local homogeneity. We provide theoretical results of the ML estimator and the adaptive estimator. Simulation study illustrates nice finite sample performance of the AFAR modeling. The AFAR model also exhibits a superior accuracy in the forecast exercise of the California electricity daily price curves compared to several alternatives.

This article proposes a mixture double autoregressive model by introducing the flexibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed in the literature. To make it more flexible, the mixing proportions are further assumed to be time varying, and probabilistic properties including strict stationarity and higher order moments are derived. Inference tools including the maximum likelihood estimation, an expectation–maximization (EM) algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model, which has two components and is encountered more frequently in practice. Monte Carlo experiments give further support to the new models, and the analysis of an empirical example is also reported.

This article examines spatial panel autoregressive (SAR) models with dynamic, time-varying endogenous spatial weights matrices, common factors, and random coefficients. An empirical application is on the spillover effects of state Medicaid spending. Endogeneity of spatial weights matrices comes from the correlation of “economic distance” and the disturbances in the SAR equation. Common factors control for common shocks to all states and random coefficients may capture heterogeneity in responses. The Bayesian Markov chain Monte Carlo (MCMC) estimation is developed. Identification of factors and factor loadings, and model selection issues based upon the deviance information criterion (DIC) are explored. We find that a state’s Medicaid related spending is positively and significantly affected by those of its neighbors. Both welfare motivated move and yardstick competition are possible sources of strategic interactions among state governments. Welfare motivated move turns out to be more a driving force for th...

We consider an approach to analyze big data of time series. Big dependent data are first transformed into functional time series of densities via nonparametric density estimation. We then discuss some tools for exploratory data analysis of the resulting functional time series. The tools employed include K-means cluster analysis and tree-based classification. For modeling, we propose a threshold approximate-factor model and a Hellinger distance autoregressive model for functional time series of continuous densities. The latent factors of factor models are estimated by functional principal component analysis. Cross-validation and Hellinger distance are used to select the number of principal component functions. For prediction of high-dimensional time series, we use the results of cluster analysis to obtain parsimonious models. We demonstrate the proposed analysis by considering the demand of electricity, the behavior of daily U.S. stock returns, and U.S. income distributions.

This article considers tests for symmetry of the one-dimensional marginal distribution of fractionally integrated processes. The tests are implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the relevant test statistics. The sieve bootstrap allows inference on symmetry to be carried out without knowledge of either the memory parameter of the data or of the appropriate norming factor for the test statistic and its asymptotic distribution. The small-sample properties of the proposed method are examined by means of Monte Carlo experiments, and applications to real-world data are also presented.

This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the remaining parameters are asymptotically normal. Our results include the asymptotic theory of the estimator for threshold AR models with autoregressive conditional heteroscedastic (ARCH) errors and threshold ARCH models as special cases, each of which is also new in literature. Two portmanteau-type statistics are also derived for checking the adequacy of fitted model when either the error is nonnormal or the threshold is unknown. Simulation studies are conducted to assess the performance of the score-based test and the estimator in finite sa...

This article considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model is classical root-T consistent and asymptotically normal when the MA root is inside, outside, and on the unit circle. For more general models where the dependence of the cumulants on the model parameters is analytically intractable, we consider simulation-based estimators with two features. First, in addition to an autoregressive model, new auxiliary regressions that exploit information from the second and higher order moments of the data are considered. Second, the errors used to simulate the model are drawn from a flexible functional form to accommodate a large class of distributions with non-Gaussian features. The proposed simulation estimators are also asymptotically normally distributed without im...

This article proposes a novel stochastic volatility (SV) model that draws from the existing literature on autoregressive SV models, aggregation of autoregressive processes, and Bayesian nonparametric modeling to create a SV model that can capture long-range dependence. The volatility process is assumed to be the aggregate of autoregressive processes, where the distribution of the autoregressive coefficients is modeled using a flexible Bayesian approach. The model provides insight into the dynamic properties of the volatility. An efficient algorithm is defined which uses recently proposed adaptive Monte Carlo methods. The proposed model is applied to the daily returns of stocks.

In this paper we investigate the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semi-parametric specification based on the Quantile Auto-Regressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy with score functions tailored to evaluate quantile, areas of the distribution, and intervals. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at short horizons and low quantiles, while for the inflation variables the improved performance occurs mostly at the one-year horizon. We also consider an application of the distribution forecasts to predict the probability of a future decline in output and employment and illustrate their practical use at three dates during the last recession.

Applied work routinely relies on heteroscedasticity and autocorrelation consistent (HAC) standard errors when conducting inference in a time series setting. As is well known, however, these corrections perform poorly in small samples under pronounced autocorrelations. In this article, I first provide a review of popular methods to clarify the reasons for this failure. I then derive inference that remains valid under a specific form of strong dependence. In particular, I assume that the long-run properties can be approximated by a stationary Gaussian AR(1) model, with coefficient arbitrarily close to one. In this setting, I derive tests that come close to maximizing a weighted average power criterion. Small sample simulations show these tests to perform well, also in a regression context.

We propose an extension of structural fractionally integrated vector autoregressive models that avoids certain undesirable effects on the impulse responses that occur if long-run identification restrictions are imposed. We derive the model’s Granger representation and investigate the effects of long-run restrictions. Simulations illustrate that enforcing integer integration orders can have severe consequences for impulse responses. In a system of U.S. real output and aggregate prices, the effects of structural shocks strongly depend on the specification of the integration orders. In the statistically preferred fractional model, shocks that are typically interpreted as demand disturbances have a very brief influence on GDP. Supplementary materials for this article are available online.

We construct a monthly real-time data set consisting of vintages for 1991.1-2010.12 that is suitable for generating forecasts of the real price of oil from a variety of models. We document that revisions of the data typically represent news, and we introduce backcasting and nowcasting techniques to fill gaps in the real-time data. We show that real-time forecasts of the real price of oil can be more accurate than the no-change forecast at horizons up to one year. In some cases real-time MSPE reductions may be as high as 25 percent one month ahead and 24 percent three months ahead. This result is in striking contrast to related results in the literature for asset prices. In particular, recursive vector autoregressive (VAR) forecasts based on global oil market variables tend to have lower MSPE at short horizons than forecasts based on oil futures prices, forecasts based on AR and ARMA models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy. We demonstrate how with additional identifying assumptions such VAR models may be used not only to understand historical fluctuations in the real price of oil, but to construct conditional forecasts that reflect hypothetical scenarios about future demand and supply conditions in the market for crude oil. These tools are designed to allow forecasters to interpret their oil price forecast in light of economic models and to evaluate its sensitivity to alternative assumptions., Les auteurs construisent un ensemble de données mensuelles en temps réel qui regroupe les cuvées relatives à la période allant de janvier 1991 à décembre 2010 et qui se prête à la génération de prévisions du prix réel du pétrole à partir de divers types de modèles. Ils montrent que les révisions de données correspondent le plus souvent à l’arrivée de nouvelles informations, et ils suppléent aux données en temps réel manquantes en employant des techniques de prévision pour la période précédente et la période courante. Les auteurs constatent que les prévisions en temps réel du prix réel du pétrole peuvent être plus précises que celles tirées d’une marche aléatoire à des horizons ne dépassant pas un an. Dans certains cas, la réduction de l’erreur quadratique moyenne de prévision en temps réel peut atteindre 25 % à l’horizon d’un mois et 24 % à l’horizon de trois mois, ce qui contraste fortement avec les résultats présentés dans la littérature sur les prix des actifs. Plus particulièrement, les prévisions récursives obtenues avec des modèles vectoriels autorégressifs (VAR) qui incluent des variables du marché mondial du pétrole donnent lieu en général à une réduction de l’erreur quadratique moyenne de prévision aux horizons rapprochés par rapport aux cours à terme du pétrole, aux modèles autorégressifs, aux modèles autorégressifs à moyenne mobile et à la marche aléatoire. De plus, ces modèles VAR produisent des prévisions systématiquement meilleures concernant le sens des variations. Les auteurs démontrent comment, par l’ajout d’hypothèses d’identification, ces modèles permettent non seulement de comprendre les fluctuations antérieures du prix réel du pétrole, mais aussi de construire des prévisions conditionnelles reflétant des scénarios hypothétiques au sujet de la demande et des conditions d’approvisionnement futures sur le marché du pétrole brut. Ces outils sont conçus pour que les prévisionnistes puissent interpréter leurs résultats à la lumière des modèles économiques et évaluer la sensibilité de leurs prévisions à des hypothèses différentes.

Here we assess the return fitting and option valuation performance of generalized autoregressive conditional heteroscedasticity (GARCH) models. We compare component versus GARCH(1, 1) models, affine versus nonaffine GARCH models, and conditionally normal versus nonnormal GED models. We find that nonaffine models dominate affine models in terms of both fitting returns and option valuation. For the affine models, we find strong evidence in favor of the component structure for both returns and options; for the nonaffine models, the evidence is less convincing in option valuation. The evidence in favor of the nonnormal GED models is strong when fitting daily returns, but not when valuing options.

A multivariate generalized autoregressive conditional heteroscedasticity model with dynamic conditional correlations is proposed, in which the individual conditional volatilities follow exponential generalized autoregressive conditional heteroscedasticity models and the standardized innovations follow a mixture of Gaussian distributions. Inference on the model parameters and prediction of future volatilities are addressed by both maximum likelihood and Bayesian estimation methods. Estimation of the Value at Risk of a given portfolio and selection of optimal portfolios under the proposed specification are addressed. The good performance of the proposed methodology is illustrated via Monte Carlo experiments and the analysis of the daily closing prices of the Dow Jones and NASDAQ indexes.

A popular account for the demise of the U.K.’s monetary targeting regime in the 1980s blames the fluctuating predictive relationships between broad money and inflation and real output growth. Yet ex post policy analysis based on heavily revised data suggests no fluctuations in the predictive content of money. In this paper, we investigate the predictive relationships for inflation and output growth using both real-time and heavily revised data. We consider a large set of recursively estimated vector autoregressive (VAR) and vector error correction models (VECM). These models differ in terms of lag length and the number of cointegrating relationships. We use Bayesian model averaging (BMA) to demonstrate that real-time monetary policymakers faced considerable model uncertainty. The in-sample predictive content of money fluctuated during the 1980s as a result of data revisions in the presence of model uncertainty. This feature is only apparent with real-time data as heavily revised data obscure these fluctuations. Out-of-sample predictive evaluations rarely suggest that money matters for either inflation or real output. We conclude that both data revisions and model uncertainty contributed to the demise of the U.K.’s monetary targeting regime.

Implications of two concepts of asymmetry—deepness and steepness—are investigated for autoregressive processes with a Markov-switching intercept. The formulas for the skewness of these processes and the skewness of the first differences of these processes are derived. The parameter restrictions leading to nondeepness and nonsteepness are presented for the special case of a first-order autoregression and two states. It is shown that these restrictions imply that previous tests for asymmetries in autoregressive processes with a Markov-switching intercept can lead to wrong conclusions. In an empirical application of the developed tests, the U.S. unemployment rate is found to be steep.

Many macroeconomic series, such as U.S. real output growth, are sampled quarterly, although potentially useful predictors are often observed at a higher frequency. We look at whether a mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth. The MIDAS specification used in the comparison uses a novel way of including an autoregressive term. We find that the use of monthly data on the current quarter leads to significant improvement in forecasting current and next quarter output growth, and that MIDAS is an effective way to exploit monthly data compared with alternative methods.

This article proposes a simple estimator that is consistent for the fraction of a panel that has an autoregressive unit root. Given such an estimate, , we can test the null hypothesis that θ = θ0 for any value of θ0 ϵ (0, 1]. The test is asymptotically standard normal and is valid whether or not the panel is cross-sectionally correlated. The main insight is that in a panel in which some units are stationary and some have unit roots, the cross-sectional variance of the mixed panel is dominated by a linear trend that grows at rate θ, where θ is precisely the fraction of the panel with a unit root. Averaging the change in cross-sectional variance over time then gives a consistent estimate of θ as N, T → ∞. Simulations show that the estimator has good finite-sample properties when T ≥ 100, even with N as small as 30.

This article develops a generalized tree-structured (GTS) model of the short-term interest rate that accommodates regime-dependent mean reversion and regime-dependent volatility clustering and level effects in the conditional variance. The model is constructed using the idea of multivariate tree-structured thresholds and nests the popular generalized autoregressive conditional heteroscedasticity and square root processes as simple special cases. It allows us to estimate the optimal number of regimes endogenously from the data and to exploit possible additional information in the term structure and in other macroeconomic variables. We provide empirical evidence of the strong potential of the GTS model in forecasting conditional first and second moments, also in comparison with alternative models of the short rate.

Random utility models have become standard econometric tools, allowing parameter inference for individual-level categorical choice data. Such models typically presume that changes in observed choices over time can be attributed to changes in either covariates or unobservables. We study how choice dynamics can be captured more faithfully by also directly modeling temporal changes in parameters, using a vector autoregressive process and Bayesian estimation. This approach offers a number of advantages for theorists and practitioners, including improved forecasts, prediction of long-run parameter levels, and correction for potential aggregation biases. We illustrate the method using choices for a common supermarket good, where we find strong support for parameter dynamics.

Influence diagnostics have become important tools for statistical analysis since the seminal work by Cook. In this article we present a curvature-based directional diagnostic, set up based on the slope-based diagnostic to assess the local influence of minor perturbations on influence graph in a regression model. Using both slope- and curvature-based diagnostics, we examine local influence in the generalized autoregressive conditional heteroscedasticity (GARCH) model under two perturbation schemes that involve model perturbation and data perturbation. We present a Monte Carlo study to obtain the approximate benchmark for determining the significance of a directional diagnostic, as well as the threshold for locating influential observations. An empirical study involving GARCH modeling of the continuously compounded daily return of the New York Stock Exchange composite index illustrates the effectiveness of the proposed diagnostics. The empirical study also shows that the curvature-based diagnostic can find ...

We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable assumptions. Second, we derive analytically the asymptotic distribution of our unit-root test under the null. Using monthly real exchange rate data, our test rejects the null of unit-root against a threshold process for five European series.

We provide a comprehensive analysis of the out-of-sample performance of a wide variety of spot rate models in forecasting the probability density of future interest rates. Although the most parsimonious models perform best in forecasting the conditional mean of many financial time series, we find that the spot rate models that incorporate conditional heteroscedasticity and excess kurtosis or heavy tails have better density forecasts. Generalized autoregressive conditional heteroscedasticity significantly improves the modeling of the conditional variance and kurtosis, whereas regime switching and jumps improve the modeling of the marginal density of interest rates. Our analysis shows that the sophisticated spot rate models in the existing literature are important for applications involving density forecasts of interest rates.

This article studies time series dependence in the direction of stock prices by modeling the (instantaneous) probability that a bull or bear market terminates as a function of its age and a set of underlying state variables, such as interest rates. A random walk model is rejected both for bull and bear markets. Although it . ts the data better, a generalized autoregressive conditional heteroscedasticity model is also found to be inconsistent with the very long bull markets observed in the data. The strongest effect of increasing interest rates is found to be a lower bear market hazard rate and hence a higher likelihood of continued declines in stock prices. Udgivelsesdato: JUL This article studies time series dependence in the direction of stock prices by modeling the (instantaneous) probability that a bull or bear market terminates as a function of its age and a set of underlying state variables, such as interest rates. A random walk model is rejected both for bull and bear markets. Although it . ts the data better, a generalized autoregressive conditional heteroscedasticity model is also found to be inconsistent with the very long bull markets observed in the data. The strongest effect of increasing interest rates is found to be a lower bear market hazard rate and hence a higher likelihood of continued declines in stock prices.

A semiparametric efficient estimation procedure is developed for the parameters of multivariate generalized autoregressive conditional heteroscedasticity-in-mean models when the disturbances have a conditional distribution assumed to be elliptically symmetric but otherwise unrestricted. Under high-level assumptions, the resulting estimator achieves the asymptotic semiparametric efficiency bound. The elliptical symmetry assumption allows us to avert the curse of dimensionality problem that would otherwise arise in estimating the unknown error distribution. This framework is suitable for the estimation and testing of conditional asset-pricing models, such as the conditional capital asset-pricing model. We apply our procedure in an empirical study of stock prices, with Monte Carlo simulation results also reported.

We develop Bayesian methods of analysis for a new class of threshold autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions.

This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramer–von Mises and the Kolmogorov–Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically use...

There has recently been renewed research interest in the development of tests of the rank of a matrix. This article evaluates the performance of some asymptotic tests of rank determination in reduced rank regression models together with bootstrapped versions through simulation experiments. The bootstrapped procedures significantly improve on the performance of the corresponding asymptotic tests. The article also presents a Monte Carlo exercise comparing the forecasting performance of reduced rank and unrestricted vector autoregressive (VAR) models in which the former appear superior. The tests of rank considered here are then applied to construct reduced rank VAR models for leading indicators of U.K. economic activity. These more parsimonious multivariate representations display an improvement in forecasting performance over that of unrestricted VAR models.

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

In this article we propose a new multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. Whereas each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analog. Our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and Baba–Engle–Kraft–Kroner models. We report some Monte Carlo results on the finite-sample distributions of the maximum likelihood estimate of the varying-correlation MGARCH model. The new model is applied to some real data sets.

This article develops a new conditional jump model to study jump dynamics in stock market returns. We propose a simple filter to infer ex post the distribution of jumps. This permits construction of the shock affecting the time t conditional jump intensity and is the main input into an autoregressive conditional jump intensity model. The model allows the conditional jump intensity to be time-varying and follows an approximate autoregressive moving average (ARMA) form. The time series characteristics of 72 years of daily stock returns are analyzed using the jump model coupled with a generalized autoregressive conditional heteroscedasticity (GARCH) specification of volatility. We find significant time variation in the conditional jump intensity and evidence of time variation in the jump size distribution. The conditional jump dynamics contribute to good in-sample and out-of-sample fits to stock market volatility and capture the rally often observed in equity markets following a significant downturn.

Estimators for the parameters of autoregressive time series are compared, emphasizing processes with a unit root or a root close to 1. The approximate bias of the sum of the autoregressive coefficients is expressed as a function of the test for a unit root. This expression is used to construct an estimator that is nearly unbiased for the parameter of the first-order scalar process. The estimator for the first-order process has a mean squared error that is about 40% of that of ordinary least squares for the process with a unit root and a constant mean, and the mean squared error is smaller than that of ordinary least squares for about half of the parameter space. The maximum loss of efficiency is 6n-1 in the remainder of the parameter space. The estimation procedure is extended to higher-order processes by modifying the estimator of the sum of the autoregressive coefficients. Limiting results are derived for the autoregressive process with a mean that is a linear trend.

Federal-funds rate-forecast errors from vector autoregressive (VAR) models used for monetary policy analysis and fitted by ordinary least squares (OLS) are large relative to those from the futures market. Using three different structural VAR models, we show that forecasts based on a shrinkage estimator dominate the OLS-based forecasts—even after restricting the lag length and/or imposing exact unit-root restrictions—and are broadly comparable to the futures-market forecasts. Our results refute the perception that VAR models forecast the funds rate poorly in general and suggest that using stochastic prior restrictions can provide an effective way of improving forecast accuracy without sacrificing structural interpretation.

This article considers the problem of testing for a nonstochastic seasonal unit root in a seasonally observed time series process against the alternative of a randomized seasonal root with mean unity; that is, the process displays heteroscedastic seasonal integration. The alternative hypothesis allows for potentially frequently occurring changes of regime in the process under investigation, allowing for more volatile forms of seasonal nonstationarity. We discuss a family of models that allow for a potentially smooth transition between the explosive and stationary phases of the seasonal model. To test this hypothesis we consider extensions to existing approaches developed to test against nonseasonal stochastic unit roots. Asymptotic representations of the test statistics are derived. An empirical application to a variety of quarterly measures of U.K. consumer's expenditure is also considered.

Tests for asymmetric adjustment in possibly nonstationary, nearly nonstationary, or stationary time series data are developed. The asymmetry is modeled by the momentum threshold autoregressive model of Enders and Granger and an extension of it. The tests are t-type tests and Wald tests based on instrumental-variable estimators and are asymptotically normal or chi-squared regardless of stationarity/nonstationarity of data-generating processes. This is in contrast to the fact that the ttests and the Wald tests based on the ordinary least squares estimator (OLSE) are asymptotically normal and chisquared, respectively, only under stationarity and are thus statistically invalid under nonstationarity. A Monte Carlo simulation shows that the proposed tests have stable sizes. Powers of the proposed tests against stationary alternatives are comparable to those of the OLSE-based tests. The Monte Carlo study also shows that the new estimators are less biased than the OLSE when data-generating processes are random wa...