Data-based ranking of realised volatility estimators

This paper presents new methods for comparing the accuracy of estimators of the quadratic variation of a price process. I provide conditions under which the relative accuracy of competing estimators can be consistently estimated (as T→∞), and show that forecast evaluation tests may be adapted to the problem of ranking these estimators. The proposed methods avoid making specific assumptions about microstructure noise, and facilitate comparisons of estimators that would be difficult using methods from the extant literature, such as those based on different sampling schemes. An application to high frequency IBM data between 1996 and 2007 illustrates the new methods.     

Least-squares forecast averaging

This paper proposes forecast combination based on the method of Mallows Model Averaging (MMA). The method selects forecast weights by minimizing a Mallows criterion. This criterion is an asymptotically unbiased estimate of both the in-sample mean-squared error (MSE) and the out-of-sample one-step-ahead mean-squared forecast error (MSFE). Furthermore, the MMA weights are asymptotically mean-square optimal in the absence of time-series dependence. We show how to compute MMA weights in forecasting settings, and investigate the performance of the method in simple but illustrative simulation environments. We find that the MMA forecasts have low MSFE and have much lower maximum regret than other feasible forecasting methods, including equal weighting, BIC selection, weighted BIC, AIC selection, weighted AIC, Bates–Granger combination, predictive least squares, and Granger–Ramanathan combination.     

Determining the MSE-optimal cross section to forecast

In this paper, we address the question of which subset of time series should be selected among a given set in order to forecast another series. We evaluate the quality of the forecasts in terms of Mean Squared Error. We propose a family of criteria to estimate the optimal subset. Consistency results are proved, both in the weak (in probability) and strong (almost sure) sense. We present the results of a Monte Carlo experiment and a real data example in which the criteria are compared to some hypothesis tests such as the ones by Diebold and Mariano (1995),  and  and Giacomini and White (2006).     

Volatility contagion: A range-based volatility approach

This article proposes a new approach to evaluate volatility contagion in financial markets. A time-varying logarithmic conditional autoregressive range model with the lognormal distribution (TVLCARR) is proposed to capture the possible smooth transition in the range process. Additionally, a smooth transition copula function is employed to detect the volatility contagion between financial markets. The approach proposed is applied to the stock markets of the G7 countries to investigate the volatility contagion due to the subprime mortgage crisis. Empirical evidence shows that volatility is contagious from the US market to several markets examined.     

Realized volatility forecasting and market microstructure noise

We extend the analytical results for reduced form realized volatility based forecasting in ABM (2004) to allow for market microstructure frictions in the observed high-frequency returns. Our results build on the eigenfunction representation of the general stochastic volatility class of models developed byMeddahi (2001). In addition to traditional realized volatility measures and the role of the underlying sampling frequencies, we also explore the forecasting performance of several alternative volatility measures designed to mitigate the impact of the microstructure noise. Our analysis is facilitated by a simple unified quadratic form representation for all these estimators. Our results suggest that the detrimental impact of the noise on forecast accuracy can be substantial. Moreover, the linear forecasts based on a simple-to-implement ‘average’ (or ‘subsampled’) estimator obtained by averaging standard sparsely sampled realized volatility measures generally perform on par with the best alternative robust measures.     

Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Levels,Differences and ECMs – Principles for Improved Econometric Forecasting*

Unit‐root testing can be a preliminary step in model development, an intermediate step, or an end in itself. Some researchers have questioned the value of any unit‐root and cointegration testing, arguing that restrictions based on theory are at least as effective. Such confusion is unsatisfactory. Needed is a set of principles that limit and define the role of the tacit knowledge of the model builders. In a forecasting context, we enumerate the various possible model selection strategies and, based on simulation and empirical evidence, recommend using these tests to improve the specification of an initial general vector autoregression model.     

How Stable is the Forecasting Performance of the Yield Curve for Output Growth?*

We provide an extensive evaluation of the predictive performance of the US yield curve for US gross domestic product growth by using new tests for forecast breakdown, in addition to a variety of in‐sample and out‐of‐sample evaluation procedures. Empirical research over the past decades has uncovered a strong predictive relationship between the yield curve and output growth, whose stability has recently been questioned. We document the existence of a forecast breakdown during the Burns–Miller and Volker monetary policy regimes, whereas during the early part of the Greenspan era the yield curve emerged as a more reliable model to predict future economic activity.     

Understanding models’ forecasting performance

We propose a new methodology to identify the sources of models’ forecasting performance. The methodology decomposes the models’ forecasting performance into asymptotically uncorrelated components that measure instabilities in the forecasting performance, predictive content, and over-fitting. The empirical application shows the usefulness of the new methodology for understanding the causes of the poor forecasting ability of economic models for exchange rate determination.     

Conditional predictive density evaluation in the presence of instabilities

We propose new methods for evaluating predictive densities. The methods include Kolmogorov–Smirnov and Cramér–von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities, even when it is time-varying. An application to density forecasts of the Survey of Professional Forecasters demonstrates the usefulness of the proposed methodologies.     

Selecting a Nonlinear Time Series Model using Weighted Tests of Equal Forecast Accuracy*

Nonlinear time series models have become fashionable tools to describe and forecast a variety of economic time series. A closer look at reported empirical studies, however, reveals that these models apparently fit well in‐sample, but rarely show a substantial improvement in out‐of‐sample forecasts, at least over linear models. One of the many possible reasons for this finding is the use of inappropriate model selection criteria and forecast evaluation criteria. In this paper we therefore propose a novel criterion, which we believe does more justice to the very nature of nonlinear models. Simulations show that this criterion outperforms those criteria currently in use, in the sense that the true nonlinear model is more often found to perform better in out‐of‐sample forecasting than a benchmark linear model. An empirical illustration for US GDP emphasizes its relevance.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models

Using weekly data for stock and Forex market returns, a set of MS-GARCH models is estimated for a group of high-income (HI) countries and emerging market economies (EMEs) using algorithms proposed by Augustyniak (2014) and Ardia et al. (2018, 2019a,b), allowing for a variety of conditional variance and distribution specifications. The main results are: (i) the models selected using Ardia et al. (2018) have a better fit than those estimated by Augustyniak (2014), contain skewed distributions, and often require that the main coefficients be different in each regime; (ii) in Latam Forex markets, estimates of the heavy-tail parameter are smaller than in HI Forex and all stock markets; (iii) the persistence of the high-volatility regime is considerable and more evident in stock markets (especially in Latam EMEs); (iv) in (HI and Latam) stock markets, a single-regime GJR model (leverage effects) with skewed distributions is selected; but when using MS models, virtually no MS-GJR models are selected. However, this does not happen in Forex markets, where leverage effects are not found either in single-regime or MS-GARCH models.     

Forecasting the realized volatility of Energy Stock Market: A multimodel comparison

The realized volatility forecasting of energy sector stocks facilitates the establishment of corresponding risk warning mechanisms and investor decisions. In this paper, we collected two different energy sector indices and used different methods, namely principal component analysis (PCA) and sparse principal component analysis (SPCA), to extract features, and combined LSTM and GRU to construct 12 different models. The results show that the SPCA-LSTM model we constructed has the best forecasting performance in the realized volatility forecasting of energy indices, and SPCA has better forecasting results than PCA in the feature extraction stage. The results of the robustness test indicate that our results are robust.     

Markov-switching model selection using Kullback–Leibler divergence

In Markov-switching regression models, we use Kullback–Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. Specifically, we derive a new information criterion, Markov switching criterion (MSC), which is an estimate of KL divergence. MSC imposes an appropriate penalty to mitigate the over-retention of states in the Markov chain, and it performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. We illustrate the usefulness of MSC via applications to the U.S. business cycle and to media advertising.     

Threshold bipower variation and the impact of jumps on volatility forecasting

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent, but also scarcely plagued by small sample bias. With the aim of achieving this, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic variation in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.     

A control function approach for testing the usefulness of trending variables in forecast models and linear regression

Many predictors employed in forecasting macroeconomic and finance variables display a great deal of persistence. Tests for determining the usefulness of these predictors are typically oversized, overstating their importance. Similarly, hypothesis tests on cointegrating vectors will typically be oversized if there is not an exact unit root. This paper uses a control variable approach where adding stationary covariates with certain properties to the model can result in asymptotic normal inference for prediction regressions and cointegration vector estimates in the presence of possibly non-unit root trending covariates. The properties required for this result are derived and discussed.     

Choosing the Best Volatility Models: The Model Confidence Set Approach*

This paper applies the model confidence set (MCS) procedure of Hansen, Lunde and Nason (2003) to a set of volatility models. An MCS is analogous to the confidence interval of a parameter in the sense that it contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on 55 volatility models and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study which shows that the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, the latter delivers inferior performance.     

Variable selection, estimation and inference for multi-period forecasting problems

This paper conducts a broad-based comparison of iterated and direct multi-period forecasting approaches applied to both univariate and multivariate models in the form of parsimonious factor-augmented vector autoregressions. To account for serial correlation in the residuals of the multi-period direct forecasting models we propose a new SURE-based estimation method and modified Akaike information criteria for model selection. Empirical analysis of the 170 variables studied by Marcellino, Stock and Watson (2006) shows that information in factors helps improve forecasting performance for most types of economic variables although it can also lead to larger biases. It also shows that SURE estimation and finite-sample modifications to the Akaike information criterion can improve the performance of the direct multi-period forecasts.     

Likelihood-based scoring rules for comparing density forecasts in tails

We propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. These scoring rules can be interpreted in terms of Kullback-Leibler divergence between weighted versions of the density forecast and the true density. Existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased toward such densities. Using our novel likelihood-based scoring rules avoids this problem.