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Small-scale VARs are widely used in macroeconomics for forecasting US output, prices, and interest rates. However, recent work suggests these models may exhibit instabilities. As such, a variety of estimation or forecasting methods might be used to improve their forecast accuracy. These include using different observation windows for estimation, intercept correction, time-varying parameters, break dating, Bayesian shrinkage, model averaging, etc. This paper compares the effectiveness of such methods in real-time forecasting. We use forecasts from univariate time series models, the Survey of Professional Forecasters, and the Federal Reserve Board's Greenbook as benchmarks.

A state space representation of a linearized DSGE model implies a VAR in terms of observable variables. The model is said be non-invertible if there exists no linear rotation of the VAR innovations which can recover the economic shocks. Non-invertibility arises when the observed variables fail to perfectly reveal the state variables of the model. The imperfect observation of the state drives a wedge between the VAR innovations and the deep shocks, potentially invalidating conclusions drawn from structural impulse response analysis in the VAR. The principal contribution of this chapter is to show that non-invertibility should not be thought of as an “either/or” proposition – even when a model has a non-invertibility, the wedge between VAR innovations and economic shocks may be small, and structural VARs may nonetheless perform reliably. As an increasingly popular example, so-called “news shocks” generate foresight about changes in future fundamentals – such as productivity, taxes, or government spending – and lead to an unassailable missing state variable problem and hence non-invertible VAR representations. Simulation evidence from a medium scale DSGE model augmented with news shocks about future productivity reveals that structural VAR methods often perform well in practice, in spite of a known non-invertibility. Impulse responses obtained from VARs closely correspond to the theoretical responses from the model, and the estimated VAR responses are successful in discriminating between alternative, nested specifications of the underlying DSGE model. Since the non-invertibility problem is, at its core, one of missing information, conditioning on more information, for example through factor augmented VARs, is shown to either ameliorate or eliminate invertibility problems altogether.

This article surveys recent developments in the evaluation of point and density forecasts in the context of forecasts made by vector autoregressions. Specific emphasis is placed on highlighting those parts of the existing literature that are applicable to direct multistep forecasts and those parts that are applicable to iterated multistep forecasts. This literature includes advancements in the evaluation of forecasts in population (based on true, unknown model coefficients) and the evaluation of forecasts in the finite sample (based on estimated model coefficients). The article then examines in Monte Carlo experiments the finite-sample properties of some tests of equal forecast accuracy, focusing on the comparison of VAR forecasts to AR forecasts. These experiments show the tests to behave as should be expected given the theory. For example, using critical values obtained by bootstrap methods, tests of equal accuracy in population have empirical size about equal to nominal size.

This article proposes a new approach to detecting the presence of common cyclical features when several time series are sampled at different frequencies. We generalize the common-frequency approach introduced by Engle and Kozicki (1993) and Vahid and Engle (1993). We start with the mixed-frequency VAR representation investigated in Ghysels (2012) for stationary time series. For non-stationary time series in levels, we show that one has to account for the presence of two sets of long-run relationships. The first set is implied by identities stemming from the fact that the differences of the high-frequency I (1) regressors are stationary. The second set comes from possible additional long-run relationships between one of the high-frequency series and the low-frequency variables. Our transformed vector error-correction model (VECM) representations extend the results of Ghysels (2012) and are important for determining the correct set of variables to be used in a subsequent common cycle investigation. This fact has implications for the distribution of test statistics and for forecasting. Empirical analyses with quarterly real gross national product (GNP) and monthly industrial production indices for, respectively, the United States and Germany illustrate our new approach. We also conduct a Monte Carlo study which compares our proposed mixed-frequency models with models stemming from classical temporal aggregation methods.

This article reviews the literature on the econometric relationship between DSGE and VAR models from the point of view of estimation and model validation. The mapping between DSGE and VAR models is broken down into three stages: (1) from DSGE to state-space model; (2) from state-space model to VAR( ∞ ); (3) from VAR( ∞ ) to finite-order VAR. The focus is on discussing what can go wrong at each step of this mapping and on critically highlighting the hidden assumptions. I also point out some open research questions and interesting new research directions in the literature on the econometrics of DSGE models. These include, in no particular order: understanding the effects of log-linearization on estimation and identification; dealing with multiplicity of equilibria; estimating nonlinear DSGE models; incorporating into DSGE models information from atheoretical models and from survey data; adopting flexible modeling approaches that combine the theoretical rigor of DSGE models and the econometric model’s ability to fit the data.

In this chapter, we investigate the effect of long memory in volatility on the accuracy of emerging stock markets risk estimation during the period of the recent global financial crisis. For this purpose, we use a short (GJR-GARCH) and long (FIAPARCH) memory volatility models to compute in-sample and out-of-sample one-day-ahead VaR. Using six emerging stock markets index, we show that taking into account the long memory property in volatility modelling generally provides a more accurate VaR estimation and prediction. Therefore, conservative risk managers may adopt long memory models using GARCH-type models to assess the emerging market risks, especially when incorporating crisis periods.

This paper aims to better jointly estimate Value at Risk (VaR) and expected shortfall (ES) by using the joint regression combined forecasting (JRCF) model.

Combining different forecasting models in financial risk measurement can improve their prediction accuracy by integrating the individual models’ information. This paper applies the JRCF model to measure VaR and ES at 5%, 2.5% and 1% probability levels in the Chinese stock market. While ES is not elicitable on its own, the joint elicitability property of VaR and ES is established by the joint consistent scoring functions, which further refines the ES’s backtest. In addition, a variety of backtesting and evaluation methods are used to analyze and compare the alternative risk measurement models.

The empirical results show that the JRCF model outperforms the competing models. Based on the evaluation results of the joint scoring functions, the proposed model obtains the minimum scoring function value compared to the individual forecasting models and the average combined forecasting model overall. Moreover, Murphy diagrams’ results further reveal that this model has consistent comparative advantages among all considered models.

The JRCF model of risk measures is proposed, and the application of the joint scoring functions of VaR and ES is expanded. Additionally, this paper comprehensively backtests and evaluates the competing risk models and examines the characteristics of Chinese financial market risks.

This paper aims to propose a scenario-based approach for measuring interest rate risks. Many regulatory capital standards in banking and insurance make use of similar approaches. The authors provide a theoretical justification and extensive backtesting of our approach.

The authors theoretically derive a scenario-based value-at-risk for interest rate risks based on a principal component analysis. The authors calibrate their approach based on the Nelson–Siegel model, which is modified to account for lower bounds for interest rates. The authors backtest the model outcomes against historical yield curve changes for a large number of generated asset–liability portfolios. In addition, the authors backtest the scenario-based value-at-risk against the stochastic model.

The backtesting results of the adjusted Nelson–Siegel model (accounting for a lower bound) are similar to those of the traditional Nelson–Siegel model. The suitability of the scenario-based value-at-risk can be substantially improved by allowing for correlation parameters in the aggregation of the scenario outcomes. Implementing those parameters is straightforward with the replacement of Pearson correlations by value-at-risk-implied tail correlations in situations where risk factors are not elliptically distributed.

The paper assumes deterministic cash flow patterns. The authors discuss the applicability of their approach, e.g. for insurance companies.

The authors’ approach can be used to better communicate interest rate risks using scenarios. Discussing risk measurement results with decision makers can help to backtest stochastic-term structure models.

The authors’ adjustment of the Nelson–Siegel model to account for lower bounds makes the model more useful in the current low-yield environment when unjustifiably high negative interest rates need to be avoided. The proposed scenario-based value-at-risk allows for a pragmatic measurement of interest rate risks, which nevertheless closely approximates the value-at-risk according to the stochastic model.

The purpose of this study is to investigate the performance of Value-at-Risk (VaR) models for nine Middle East and North Africa Islamic indices using RiskMetrics and VaR parametric models.

The authors test the performance of several VaR models using Kupiec and Engle and Manganelli tests at 95 and 99 per cent levels for long and short trading positions, respectively, for the period from August 10, 2006 to December 14, 2014.

The authors’ findings show that the VaR under Student and skewed Student distribution are preferred at a 99 per cent level VaR. However, at 95 per cent level, the VaR forecasts obtained under normal distribution are more accurate than those generated using models with fat-tailed distributions. These results suggest that VaR is a good tool for measuring market risk. The authors support the use of RiskMetrics during calm periods and the asymmetric models (Generalized Autoregressive Conditional Heteroskedastic and the Asymmetric Power ARCH model) during stressed periods.

These results will be useful to investors and risk managers operating in Islamic markets, because their success depends on the ability to forecast stock price movements. Therefore, because a few Islamic financial institutions use internal models for their capital calculations, the regulatory committee should enhance market risk disclosure.

This study contributes to the knowledge in this area by improving our understanding of market risk management for Islamic assets during the stress periods. Then, it highlights important implications regarding financial risk management. Finally, this study fills a gap in the literature, as most empirical studies dealing with evaluating VaR prediction models have focused on quantifying the model risk in the conventional market.

The paper aims to model multiple-period market risk forecasts under long memory persistence in market volatility.

The paper proposes volatility forecasts based on a combination of the GARCH(1,1)-model with potentially fat-tailed and skewed innovations and a long memory specification of the slowly declining influence of past volatility shocks. As the square-root-of-time rule is known to be mis-specified, the GARCH setting of Drost and Nijman is used as benchmark model. The empirical study of equity market risk is based on daily returns during the period January 1975 to December 2010. The out-of-sample accuracy of VaR predictions is studied for 5, 10, 20 and 60 trading days.

The long memory scaling approach remarkably improves VaR forecasts for the longer horizons. This result is only in part due to higher predicted risk levels. Ex post calibration to equal unconditional VaR levels illustrates that the approach also enhances efficiency in allocating VaR capital through time.

The improved VaR forecasts show that one should account for long memory when calibrating risk models.

The paper models single-period returns rather than choosing the simpler approach of modeling lower-frequency multiple-period returns for long-run volatility forecasting. The approach considers long memory in volatility and has two main advantages: it yields a consistent set of volatility predictions for various horizons and VaR forecasting accuracy is improved.