Generalized Nelson–Siegel term structure model: do the second slope and curvature factors improve the in-sample fit and out-of-sample forecasts?

The dynamic Nelson–Siegel (DNS) model and even the Svensson generalization of the model have trouble in fitting the short maturity yields and fail to grasp the characteristics of the Japanese government bonds yield curve, which is flat at the short end and has multiple inflection points. Therefore, a closely related generalized dynamic Nelson–Siegel (GDNS) model that has two slopes and curvatures is considered and compared empirically to the traditional DNS in terms of in-sample fit as well as out-of-sample forecasts. Furthermore, the GDNS with time-varying volatility component, modeled as standard EGARCH process, is also considered to evaluate its performance in relation to the GDNS. The GDNS model unanimously outperforms the DNS in terms of in-sample fit as well as out-of-sample forecasts. Moreover, the extended model that accounts for time-varying volatility outpace the other models for fitting the yield curve and produce relatively more accurate 6- and 12-month ahead forecasts, while the GDNS model comes with more precise forecasts for very short forecast horizons.     

The Multistep Beveridge–Nelson Decomposition

The Beveridge–Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The article introduces the multistep Beveridge–Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge–Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge–Nelson trend is more efficient than the standard one in the presence of model misspecification, and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.     

Real-Time Forecasts of the Real Price of Oil

We construct a monthly real-time dataset 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 1 year. In some cases, real-time mean squared prediction error (MSPE) reductions may be as high as 25% 1 month ahead and 24% 3 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 autoregressive (AR) and autoregressive moving average (ARMA) models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy.     

Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.     

Volatility forecasting of financial time series using wavelet based exponential generalized autoregressive conditional heteroscedasticity model

Abstract

An improved forecasting model by merging two different computational models in predicting future volatility was proposed. The model integrates wavelet and EGARCH model where the pre-processing activity based on wavelet transform is performed with de-noising technique to eliminate noise in observed signal. The denoised signal is then feed into EGARCH model to forecast the volatility. The predictive capability of the proposed model is compared with the existing EGARCH model. The results show that the hybrid model has increased the accuracy of forecasting future volatility.     

Forecast Evaluation in the Presence of Unobserved Volatility

Abstract

A number of volatility forecasting studies have led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts. In this paper we provide an analytical assessment of volatility forecasting performance. We use the volatility and log volatility framework to prove how the inherent noise in the approximation of the true- and unobservable-volatility by the squared return, results in a misleading forecast evaluation, inflating the observed mean squared forecast error and invalidating the Diebold–Mariano statistic. We analytically characterize this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram–Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.     

Quantile forecasts for financial volatilities based on parametric and asymmetric models

For financial volatilities such as realized volatility and volatility index, a new parametric quantile forecast strategy is proposed, focusing on forecast interval and value at risk (VaR) forecast. This fully addresses asymmetries in 3 parts: mean, volatility and distribution. The asymmetries are addressed by the LHAR (leverage heterogeneous autoregressive) model of McAleer and Medeiros (2008) and Corsi and Reno (2009) for the mean part, by the EGARCH model for the volatility part, and by the skew-t distribution for the error distribution part. The method is applied to the realized volatilities and the volatility indexes of the US S&P 500 index, the US NASDAQ index, the Korea KOSPI index in which significant asymmetries are identified. Considerable out-of-sample forecast improvements of the forecast interval and VaR forecast are demonstrated for the volatilities: forecast intervals of volatilities have better coverages with shorter lengths and VaR forecasts of volatility indexes have better violations if asymmetries are properly addressed rather than ignored. The proposed parametric method reveals considerably better out-of-sample performance than the recently proposed semiparametric quantile regression approach of Zikes and Barunik (2016).     

FORECASTING VOLATILITY IN THE PRESENCE OF MODEL INSTABILITY

Recent advances in financial econometrics have allowed for the construction of efficient ex post measures of daily volatility. This paper investigates the importance of instability in models of realised volatility and their corresponding forecasts. Testing for model instability is conducted with a subsampling method. We show that removing structurally unstable data of a short duration has a negligible impact on the accuracy of conditional mean forecasts of volatility. In contrast, it does provide a substantial improvement in a model's forecast density of volatility. In addition, the forecasting performance improves, often dramatically, when we evaluate models on structurally stable data.     

Forecast Evaluation in the Presence of Unobserved Volatility

A number of volatility forecasting studies have led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts. In this paper we provide an analytical assessment of volatility forecasting performance. We use the volatility and log volatility framework to prove how the inherent noise in the approximation of the true- and unobservable-volatility by the squared return, results in a misleading forecast evaluation, inflating the observed mean squared forecast error and invalidating the Diebold-Mariano statistic. We analytically characterize this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram-Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.     

Forecasting the Distribution of Economic Variables in a Data-Rich Environment

This article investigates 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 semiparametric specification based on the quantile autoregressive (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 relative to a stochastic volatility model using the quantile score. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at long horizons and in tails of the distribution, while for the inflation variables the improved performance occurs mostly at the 6-month horizon. We also illustrate the practical relevance of predicting the distribution by considering forecasts at three dates during the last recession.     

Bootstrap forecast intervals for asymmetric volatilities via EGARCH model

Bootstrap forecast intervals are developed for volatilities having asymmetric features, which are accounted for by fitting EGARCH models. A Monte-Carlo simulation compares the proposed forecast intervals with those based on GARCH fittings which ignore asymmetry. The comparison reveals substantial advantage of addressing asymmetry through EGARCH fitting over ignoring it as the conventional GARCH forecast. The EGARCH forecast intervals have empirical coverage probabilities closer to the nominal level and/or have shorter average lengths than the GARCH forecast intervals. The finding is also supported by real dataset analysis of Dow–Jones index and financial times stock exchange (FTSE) 100 index.     

The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling

This article generalizes the popular stochastic volatility in mean model to allow for time-varying parameters in the conditional mean. The estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance, and its coefficient in the former is time-varying. We develop an efficient Markov chain Monte Carlo algorithm based on band and sparse matrix algorithms instead of the Kalman filter to estimate this more general variant. The methodology is illustrated with an application that involves U.S., U.K., and Germany inflation. The estimation results show substantial time-variation in the coefficient associated with the volatility, highlighting the empirical relevance of the proposed extension. Moreover, in a pseudo out-of-sample forecasting exercise, the proposed variant also forecasts better than various standard benchmarks.     

Estimating high-frequency foreign exchange rate volatility with nonparametric ARCH models

High-frequency foreign exchange rate (HFFX) series are analyzed on an operational time scale using models of the ARCH class. Comparison of the estimated conditional variances focuses on the asymmetry and persistence issue. Estimation results for parametric models confirm standard results for HFFX series, namely high persistence and no significance of the asymmetry coefficient in an EGARCH model. To find out whether these results are robust against alternative specifications, nonparametric models are estimated. Local linear estimation techniques are applied to a nonparametric ARCH model of order one (CHARN). The results show significant asymmetry of the volatility function. To allow for both flexibility and persistence, a higher-order multiplicative model is fitted. The results show important asymmetries in volatility. In contrast to the EGARCH specification, the news impact curves have different shapes for different lags and tend to increase slower at the boundaries.     

Cointegration and Long-Horizon Forecasting

We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box–Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures—they fail to value the maintenance of cointegrating relationships among variables—and we suggest alternatives that explicitly do so.     

Kalman filter-based modelling and forecasting of stochastic volatility with threshold

We propose a parametric nonlinear time-series model, namely the Autoregressive-Stochastic volatility with threshold (AR-SVT) model with mean equation for forecasting level and volatility. Methodology for estimation of parameters of this model is developed by first obtaining recursive Kalman filter time-update equation and then employing the unrestricted quasi-maximum likelihood method. Furthermore, optimal one-step and two-step-ahead out-of-sample forecasts formulae along with forecast error variances are derived analytically by recursive use of conditional expectation and variance. As an illustration, volatile all-India monthly spices export during the period January 2006 to January 2012 is considered. Entire data analysis is carried out using EViews and matrix laboratory (MATLAB) software packages. The AR-SVT model is fitted and interval forecasts for 10 hold-out data points are obtained. Superiority of this model for describing and forecasting over other competing models for volatility, namely AR-Generalized autoregressive conditional heteroscedastic, AR-Exponential GARCH, AR-Threshold GARCH, and AR-Stochastic volatility models is shown for the data under consideration. Finally, for the AR-SVT model, optimal out-of-sample forecasts along with forecasts of one-step-ahead variances are obtained.     

Generalized value at risk forecasting

Abstract

In this paper, using estimating function approach, a new optimal volatility estimator is introduced and based on the recursive form of the estimator a data-driven generalized EWMA model for value at risk (VaR) forecast is proposed. An appropriate data-driven model for volatility is identified by the relationship between absolute deviation and standard deviation for symmetric distributions with finite variance. It is shown that the asymptotic variance of the proposed volatility estimator is smaller than that of conventional estimators and is more appropriate for financial data with larger kurtosis. For IBM, Microsoft, Apple stocks and SP 500 index the proposed method is used to identify the model, estimate the volatility, and obtain minimum mean square error(MMSE) forecasts of VaR.     

A multivariate volatility vine copula model

This article proposes a dynamic framework for modeling and forecasting of realized covariance matrices using vine copulas to allow for more flexible dependencies between assets. Our model automatically guarantees positive definiteness of the forecast through the use of a Cholesky decomposition of the realized covariance matrix. We explicitly account for long-memory behavior by using fractionally integrated autoregressive moving average (ARFIMA) and heterogeneous autoregressive (HAR) models for the individual elements of the decomposition. Furthermore, our model incorporates non-Gaussian innovations and GARCH effects, accounting for volatility clustering and unconditional kurtosis. The dependence structure between assets is studied using vine copula constructions, which allow for nonlinearity and asymmetry without suffering from an inflexible tail behavior or symmetry restrictions as in conventional multivariate models. Further, the copulas have a direct impact on the point forecasts of the realized covariances matrices, due to being computed as a nonlinear transformation of the forecasts for the Cholesky matrix. Beside studying in-sample properties, we assess the usefulness of our method in a one-day-ahead forecasting framework, comparing recent types of models for the realized covariance matrix based on a model confidence set approach. Additionally, we find that in Value-at-Risk (VaR) forecasting, vine models require less capital requirements due to smoother and more accurate forecasts.     

ARFIMAX and ARFIMAX-TARCH realized volatility modeling

ARFIMAX models are applied in estimating the intra-day realized volatility of the CAC40 and DAX30 indices. Volatility clustering and asymmetry characterize the logarithmic realized volatility of both the indices. The ARFIMAX model with time-varying conditional heteroskedasticity is the best performing specification and, at least in the case of DAX30, provides statistically superior next trading day's realized volatility forecasts.     

A Stochastic Volatility Model With Conditional Skewness

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.     

Bayesian analysis of multivariate stochastic volatility with skew return distribution

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian modeling allows this approach to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Analyses of daily stock returns are illustrated. Empirical results show that the time-varying correlations and the sparse skew structure contribute to improved prediction performance and Value-at-Risk forecasts.