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We present novel, robust methods for inference on market (non-)efficiency, volatility clustering, and nonlinear dependence in financial return series. In contrast to existing methodology, our proposed methods are robust against nonlinear dynamics and tail-heaviness of returns. Specifically, our methods only rely on return processes being stationary and weakly dependent (mixing) with finite moments of a suitable order. This includes robustness against power-law distributions associated with nonlinear dynamic models such as GARCH and stochastic volatility. The methods are easy to implement and perform well in realistic settings. We revisit a recent study by Baltussen, van Bekkum, and Da (2019 , J. Financ. Econ. , 132, 26–48) on autocorrelation in major stock indexes. Using our robust methods, we document that the evidence of the presence of negative autocorrelation is weaker, compared with the conclusions of the original study. [ABSTRACT FROM AUTHOR]

We study two sources of heteroscedasticity in high-frequency financial data and estimate their contribution to overall volatility by means of a Markov switching (MS) structural VAR model. We achieve identification for all coefficients by assuming that the structural errors follow a GARCH-DCC process. Using transaction data of the EUR/USD interdealer market in 2016, we first detect three regimesof volatility. Then we show that both sources of volatility matter for the transmission of shocks, and that information is channeled to the market mostly through demand shocks. This suggests that, on the EUR/USD market, some liquidity takers (LTs) are better informed than both liquidity providers and those LTs who follow a feedback strategy. [ABSTRACT FROM AUTHOR]

Statistical inference in finance often depends on certain moment conditions such as finite or infinite variance, yet it is practically challenging to disentangle these conditions. This article develops a class of unified unit root tests for AR(1) models and a weighted least squares estimator along with robust inference for a stationary AR(r) model regardless of finite or infinite variance GARCH errors. The inferential framework applies the empirical likelihood method to some weighted score equations without estimating the GARCH errors. In contrast to extant unit root tests relying on bootstrap or subsampling methods to approximate critical values, the proposed unit root tests can be easily implemented with critical values obtained directly from a chi-squared distribution using the Wilks theorem. Extensive simulation studies confirm the good finite sample performance of the proposed methods before we illustrate them empirically with financial ratios for stock return predictability and HKD/USD exchange rate returns. [ABSTRACT FROM AUTHOR]

Many researchers seek factors that predict the cross-section of stock returns. The standard methodology sorts stocks according to their factor scores into quantiles and forms a corresponding long-short portfolio. Such a course of action ignores any information on the covariance matrix of stock returns. Historically, it has been difficult to estimate the covariance matrix for a large universe of stocks. We demonstrate that using the recent DCC-NL estimator of Engle, Ledoit, and Wolf (2017) substantially enhances the power of tests for cross-sectional anomalies: On average, "Student" t -statistics more than double. [ABSTRACT FROM AUTHOR]

Dynamic conditional beta is an approach to estimating regressions with time varying parameters. The conditional covariance matrices of the exogenous and dependent variable for each time period are used to formulate the dynamic beta. Joint estimation of the covariance matrices and other regression parameters is developed. Tests of the hypothesis that betas are constant are non-nested tests and several approaches are developed including a novel nested model. The methodology is applied to industry multifactor asset pricing and to global systemic risk estimation with non-synchronous prices. [ABSTRACT FROM AUTHOR]

It has become popular to explore the static conditional correlation structure of financial returns by using the exceedance correlations or similar measures. In this article, we propose a generalized test which is applicable to checking various conditional correlation structures in a model-free context, and apply a newly developed method to establishing a simple test for evaluating the adequacy of a model in explaining the conditional correlations. We demonstrate that our tests can generate useful alternatives to existing exceedance correlation tests, and provide a simulation study and an empirical example to show the validity and applicability of our tests. [ABSTRACT FROM AUTHOR]

Generalized auto-regressive conditional heteroskedastic model with changing parameters is specified using the sticky infinite hidden Markov-chain framework. Estimation by Bayesian inference determines the adequate number of regimes as well as the optimal specification (Markov-switching or change-point). The new provided algorithms are studied in terms of mixing properties and computational time. Applications highlight the flexibility of the model and compare it to existing parametric alternatives. [ABSTRACT FROM AUTHOR]

This article considers a GARCH process, generally named as GARCH-X, in which the additional covariate is specified as a positive fractionally integrated process. Recent work on MEM, HEAVY, and Realized GARCH models falls in this category. We investigate the asymptotic properties of this process and show how it explains stylized facts of financial time series such as the long memory property in volatility and leptokurtosis. Not surprisingly, the time series properties of the GARCH-X process with a nonstationary covariate are qualitatively different from those of the GARCH-X process with a stationary covariate. Nevertheless, if the covariate is persistent, the GARCH-X process provides adequate explanations of some stylized facts that the GARCH(1,1) model cannot capture. [ABSTRACT FROM PUBLISHER]

In maximum likelihood estimation, the real but unknown innovation distribution is often replaced by a nonparametric estimate, and thus the estimation procedure becomes semiparametric. These semiparametric approaches generally involve two steps: the first step that incorporate an initial estimate of the model parameterto produce a residual sample, and the second step that uses the residuals to estimate the likelihood, which is subsequently maximized to obtain the final estimate of the model parameter. Therefore, the characteristics of the initial input estimator may be carried over to the final semiparametric estimator, and the performance of the semiparametric estimator will be impaired if the input estimate is deficient. In this article we have studied a one-step semiparametric estimator where no initial input is necessary. The estimation procedure is illustrated via a generalized autoregressive conditional heteroskedasticity (GARCH) model. Asymptotic properties of the estimator are established, and finite sample performance of the estimator is evaluated via simulation. The results suggest that the proposed one-step semiparametric estimator avoids significant drawbacks of its two-step counterparts. [ABSTRACT FROM AUTHOR]

Variance targeting estimation (VTE) is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood estimation (QMLE) of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining parameters are estimated by quasi maximum likelihood (QML) in a second step. This paper establishes the asymptotic distribution of the estimators obtained by this method in univariate GARCH models. Comparisons with the standard QML are provided and the merits of the variance targeting method are discussed. In particular, it is shown that when the model is misspecified, the VTE can be superior to the QMLE for long-term prediction or value-at-risk calculation. An empirical application based on stock market indices is proposed. [ABSTRACT FROM AUTHOR]

Financial risk management has generally focused on short-term risks rather than long-term risks, and arguably this was an important component of the recent financial crisis. Econometric approaches to measuring long-term risk are developed in order to estimate the term structure of value at risk and expected shortfall. Long-term negative skewness increases the downside risk and is a consequence of asymmetric volatility models. A test is developed for long-term skewness. In a Merton style structural default model, bankruptcies are accompanied by substantial drops in equity prices. Thus, skewness in a market factor implies high defaults and default correlations even far in the future corroborating the systemic importance of long-term skewness. Investors concerned about long-term risks may hedge exposure as in the Intertemporal Capital Asset Pricing Model (ICAPM). As a consequence, the aggregate wealth portfolio should have asymmetric volatility and hedge portfolios should have reversed asymmetric volatility. Using estimates from VLAB, reversed asymmetric volatility is found for many possible hedge portfolios such as volatility products, long- and short-term treasuries, some exchange rates, and gold. JEL: G01 [ABSTRACT FROM AUTHOR]

In this paper we address the issue of forecasting Value–at–Risk (VaR) using different volatility measures: realized volatility, bipower realized volatility, two-scales realized volatility, realized kernel, as well as the daily range. We propose a dynamic model with a flexible trend specification bonded with a penalized maximum likelihood estimation strategy: the P-spline multiplicative error model. Exploiting ultra-high-frequency data (UHFD) volatility measures, VaR predictive ability is considerably improved upon relative to a baseline GARCH but not so relative to the range; there are gains from modeling volatility trends and from using realized kernels that are robust to dependent microstructure noise. [ABSTRACT FROM PUBLISHER]

Constructed from high-frequency data, realized volatility (RV) provides an accurate estimate of the unobserved volatility of financial markets. This paper uses a Bayesian approach to investigate the evidence for structural breaks in reduced form time-series models of RV. We focus on the popular heterogeneous autoregressive (HAR) models of the logarithm of realized volatility. Using Monte Carlo simulations we demonstrate that our estimation approach is effective in identifying and dating structural breaks. Applied to daily S&P 500 data from 1993-2004, we find strong evidence of a structural break in early 1997. The main effect of the break is a reduction in the variance of log-volatility. The evidence of a break is robust to different models including a GARCH specification for the conditional variance of log(RV). [ABSTRACT FROM AUTHOR]

GARCH models and Stochastic Volatility (SV) models can both be used to describe unobserved volatility in asset returns. We consider the issue of testing a GARCH model against an SV model. For that purpose, we propose a new and parsimonious GARCH-t model with an additional restricted moving average term, which can capture SV model properties. We discuss model representation, parameter estimation, and our simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate our model and test for nine daily stock-return series. [ABSTRACT FROM AUTHOR]

Engles ARCH test has become the standard test for ARCH effects in applied work. Under non-normality the true rejection probability of this test can differ substantially from the nominal level, however. Bootstrap and Monte Carlo versions of the test may then be used instead. This paper proposes an alternative test procedure. The new test exploits the empirical distribution of the data and an extended probability integral transformation. The test is compared with the former tests in Monte Carlo experiments. Under normality, the new test works as well as the conventional Monte Carlo test and the bootstrap. Under non-normality, the test tends to be more accurate and more powerful than the bootstrapped ARCH test. The procedure is then used to test for ARCH effects in S&P 500 returns sampled at different frequencies. In contrast to the standard and the bootstrapped ARCH tests, the new test detects ARCH effects in the transformed low-frequency returns. [ABSTRACT FROM AUTHOR]

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series. [ABSTRACT FROM AUTHOR]

Given the growing need for managing financial risk, risk prediction plays an increasing role in banking and finance. In this study we compare the out-of-sample performance of existing methods and some new models for predicting value at risk (VaR) in a univariate context. Using more than 30 years of the daily return data on the NASDAQ Composite Index, we find that most approaches perform inadequately, although several models are acceptable under current regulatory assessment rules for model adequacy. A hybrid method, combining a heavy-tailed generalized autoregressive conditionally heteroskedastic (GARCH) filter with an extreme value theory-based approach, performs best overall, closely followed by a variant on a filtered historical simulation, and a new model based on heteroskedastic mixture distributions. Conditional autoregressive VaR (CAViaR) models perform inadequately, though an extension to a particular CAViaR model is shown to outperform the others. [ABSTRACT FROM AUTHOR]

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student's t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric. [ABSTRACT FROM AUTHOR]

This article addresses some empirical problems in the term structure of interest rates using a threshold autoregressive framework with GARCH errors. This framework provides a parsimonious representation of some stylized features of interest rate data and facilitates statistical inference in the presence of high persistence and conditional heteroskedasticity. We propose a bootstrap-based LM test for linearity in the conditional mean and variance functions. The empirical results indicate a presence of threshold nonlinearities in the AR and GARCH representations of the conditional moments of short-term rate. The explicit modeling of these nonlinearities appears to improve the stability properties of the process for spot rate. The article also reports that allowing for threshold nonlinearities in conditional mean and variance leads to significant forecast improvements. The economic significance of these findings is evaluated by the term structure implications of the estimated TAR-GARCH model. [ABSTRACT FROM AUTHOR]

A key component of managing international interest rate portfolios is forecasts of the covariances between national interest rates and accompanying exchange rates. How should portfolio managers choose among the large number of covariance forecasting models available? We find that covariance matrix forecasts generated by models incorporating interest-rate level volatility effects perform best with respect to statistical loss functions. However, within a value-at-risk (VaR) framework the relative performance of the covariance matrix forecasts depends greatly on the VaR distributional assumption, and forecasts based just on weighted averages of past observations perform best. In addition, portfolio variance forecasts that ignore the covariance matrix generate the lowest regulatory capital charge, a key economic decision variable for commercial banks. Our results provide empirical support for the commonly used VaR models based on simple covariance matrix forecasts and distributional assumptions. [ABSTRACT FROM AUTHOR]

The article evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for β-mixing processes and EDF-based tests for the residuals of such nonlinear dependent processes. Hence the tests apply to the class of ARCH- and SV-type processes as well as data-driven volatility estimators using high-frequency data. It is shown that some of the high-frequency volatility estimators substantially improve the power of the structural break tests, especially for detecting changes in the tail of the conditional distribution. Similarly certain types of filtering and transformation of the returns process can improve the power of CUSUM statistics. We also explore the impact of sampling frequency on each of the test statistics. [ABSTRACT FROM PUBLISHER]

Both unconditional mixed normal distributions and GARCH models with fat-tailed conditional distributions have been employed in the literature for modeling financial data. We consider a mixed normal distribution coupled with a GARCH-type structure (termed MN-GARCH) which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. For the empirically most relevant GARCH(1,1) case, the conditions for existence of arbitrary integer moments are given and analytic expressions of the unconditional skewness, kurtosis, and autocorrelations of the squared process are derived. Finally, employing daily return data on the NASDAQ index, we provide a detailed empirical analysis and compare both the in-sample fit and out-of-sample forecasting performance of the MN-GARCH as well as recently proposed Markov-switching models. We show that the MN-GARCH approach can generate a plausible disaggregation of the conditional variance process in which the components' volatility dynamics have a clearly distinct behavior, which is, for example, compatible with the well-known leverage effect. [ABSTRACT FROM PUBLISHER]

Financial risk model evaluation or backtesting is a key part of the internal model's approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests. [ABSTRACT FROM PUBLISHER]

We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled conditions and then we use daily currency and equity index returns to evaluate how the models perform in a risk management application. Although the GARCH models produce less precise forecasts than the SARV models in the simulations, it is not clear that the performance differences are large enough to be economically meaningful. Consistent with this view, we find that the GARCH and SARV models perform comparably in tests of conditional value-at-risk estimates using the actual data. [ABSTRACT FROM PUBLISHER]

In this paper, we show the effects that outliers have on estimation and inference for autoregressive conditional heteroskedasticity (ARCH) models. We propose for a wide class of ARCH models commonly estimated, an empirically tractable solution to this problem by replacing outliers with their conditional expectations (optimal forecasts) in the likelihood function. This solution works well in both simulations and applications, as opposed to dummy variables which can lead to multimodality in the ARCH likelihood and invalid inference. We demonstrate the accuracy of our procedure for parameter estimation and forecasting. The empirical examples include U.S. interest rate, foreign exchange rate, and stock index data. In addition, we suggest a robust bootstrap test for outliers and evaluate this against the Andrews (2003) S test. (JEL: C120, C130, C510) [ABSTRACT FROM AUTHOR]