Real‐time detection of regimes of predictability in the US equity premium

We propose new real‐time monitoring procedures for the emergence of end‐of‐sample predictive regimes using sequential implementations of standard (heteroskedasticity‐robust) regression t‐statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the US equity premium at the 1‐month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the 1‐month‐ahead equity premium has temporarily been predictable, displaying so‐called “pockets of predictability,” and that these episodes of predictability could have been detected in real time by practitioners using our proposed methodology.     

Modelling multi‐period inflation uncertainty using a panel of density forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). Based on a dynamic heterogeneous panel data model, we find that the persistence in forecast uncertainty is much less than what the aggregate time series data would suggest. In addition, the strong link between past forecast errors and current forecast uncertainty, as often noted in the ARCH literature, is largely lost in a multi‐period context with varying forecast horizons. We propose a novel way of estimating ‘news’ and its variance using the Kullback‐Leibler information, and show that the latter is an important determinant of forecast uncertainty. Our evidence suggests a strong relationship of forecast uncertainty with level of inflation, but not with forecaster discord or with the volatility of a number of other macroeconomic indicators. Copyright © 2006 John Wiley & Sons, Ltd.     

Jumps in cross‐sectional rank and expected returns: a mixture model

We propose a new nonlinear time series model of expected returns based on the dynamics of the cross‐sectional rank of realized returns. We model the joint dynamics of a sharp jump in the cross‐sectional rank and the asset return by analyzing (1) the marginal probability distribution of a jump in the cross‐sectional rank within the context of a duration model, and (2) the probability distribution of the asset return conditional on a jump, for which we specify different dynamics depending upon whether or not a jump has taken place. As a result, the expected returns are generated by a mixture of normal distributions weighted by the probability of jumping. The model is estimated for the weekly returns of the constituents of the SP500 index from 1990 to 2000, and its performance is assessed in an out‐of‐sample exercise from 2001 to 2005. Based on the one‐step‐ahead forecast of the mixture model we propose a trading rule, which is evaluated according to several forecast evaluation criteria and compared to 18 alternative trading rules. We find that the proposed trading strategy is the dominant rule by providing superior risk‐adjusted mean trading returns and accurate value‐at‐risk forecasts. Copyright © 2008 John Wiley & Sons, Ltd.     

Predictability of bull and bear markets: A new look at forecasting stock market regimes (and returns) in the US

The empirical literature of stock market predictability mainly suffers from model uncertainty and parameter instability. To meet this challenge, we propose a novel approach that combines dimensionality reduction, regime-switching models, and forecast combination to predict excess returns on the S&P 500. First, we aggregate the weekly information of 146 popular macroeconomic and financial variables using different principal component analysis techniques. Second, we estimate Markov-switching models with time-varying transition probabilities using the principal components as predictors. Third, we pool the models in forecast clusters to hedge against model risk and to evaluate the usefulness of different specifications. Our weekly forecasts respond to regime changes in a timely manner to participate in recoveries or to prevent losses. This is also reflected in an improvement of risk-adjusted performance measures as compared to several benchmarks. However, when considering stock market returns, our forecasts do not outperform common benchmarks. Nevertheless, they do add statistical and, in particular, economic value during recessions or in declining markets.     

Optimal Portfolio Choice Under Decision‐Based Model Combinations

We propose a density combination approach featuring combination weights that depend on the past forecast performance of the individual models entering the combination through a utility‐based objective function. We apply this model combination scheme to forecast stock returns, both at the aggregate level and by industry, and investigate its forecasting performance relative to a host of existing combination methods, both within the class of linear and time‐varying coefficients, stochastic volatility models. Overall, we find that our combination scheme produces markedly more accurate predictions than the existing alternatives, both in terms of statistical and economic measures of out‐of‐sample predictability. Copyright © 2016 John Wiley & Sons, Ltd.     

Should I stay or should I go? A latent threshold approach to large‐scale mixture innovation models

We propose a straightforward algorithm to estimate large Bayesian time‐varying parameter vector autoregressions with mixture innovation components for each coefficient in the system. The computational burden becomes manageable by approximating the mixture indicators driving the time‐variation in the coefficients with a latent threshold process that depends on the absolute size of the shocks. Two applications illustrate the merits of our approach. First, we forecast the US term structure of interest rates and demonstrate forecast gains relative to benchmark models. Second, we apply our approach to US macroeconomic data and find significant evidence for time‐varying effects of a monetary policy tightening.     

Conditional Markov chain and its application in economic time series analysis

Motivated by the great moderation in major US macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long‐run volatility change as a recurrent structure change, while short‐run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is structure‐dependent. This formulation imposes interpretable restrictions on the Hamilton Markov switching model. Empirical studies show that this restricted model well identifies both short‐run regime switches and long‐run structure changes in the US macroeconomic data. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonparametric methods and local‐time‐based estimation for dynamic power law distributions

This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions. First, we show that any stationary distribution in a random growth setting is shaped entirely by two factors: the idiosyncratic volatilities and reversion rates (a measure of cross‐sectional mean reversion) for different ranks in the distribution. This result is valid regardless of how growth rates and volatilities vary across different economic agents, and hence applies to Gibrat's law and its extensions. Second, we present techniques to estimate these two factors using panel data. Third, we describe how our results imply predictability as higher‐ranked processes must on average grow more slowly than lower‐ranked processes. We employ our empirical methods using data on commodity prices and show that our techniques accurately describe the empirical distribution of relative commodity prices. We also show that rank‐based out‐of‐sample forecasts of future commodity prices outperform random‐walk forecasts at a 1‐month horizon.     

The quantilogram: With an application to evaluating directional predictability

We propose a new diagnostic tool for time series called the quantilogram. The tool can be used formally and we provide the inference tools to do this under general conditions, and it can also be used as a simple graphical device. We apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability. The test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to S&P500 stock index return data. The empirical results suggest some directional predictability in returns. The evidence is strongest in mid range quantiles like 5–10% and for daily data. The evidence for predictability at the median is of comparable strength to the evidence around the mean, and is strongest at the daily frequency.     

Interpoint Distance Classification of High Dimensional Discrete Observations

Classification is a multivariate technique that is concerned with allocating new observations to two or more groups. We use interpoint distances to measure the closeness of the samples and construct new rules for high dimensional classification of discrete observations. Applicable to high dimensional data, the new method is non‐parametric and uses test‐based classification with permutation testing. We propose a modification of a test‐based rule to use relative values with respect to the training samples baseline. We compare the proposed rule with parametric methods, such as likelihood ratio rule and modified linear discriminate function, and non‐parametric techniques such as support vector machine, nearest neighbour and depth‐based classification, under multivariate Bernoulli, multinomial and multivariate Poisson distributions.     

Efficient estimation of a multivariate multiplicative volatility model

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.     

Forecasting with Global Vector Autoregressive Models: a Bayesian Approach

This paper develops a Bayesian variant of global vector autoregressive (B‐GVAR) models to forecast an international set of macroeconomic and financial variables. We propose a set of hierarchical priors and compare the predictive performance of B‐GVAR models in terms of point and density forecasts for one‐quarter‐ahead and four‐quarter‐ahead forecast horizons. We find that forecasts can be improved by employing a global framework and hierarchical priors which induce country‐specific degrees of shrinkage on the coefficients of the GVAR model. Forecasts from various B‐GVAR specifications tend to outperform forecasts from a naive univariate model, a global model without shrinkage on the parameters and country‐specific vector autoregressions. Copyright © 2016 John Wiley & Sons, Ltd.     

Time series copulas for heteroskedastic data

We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first‐order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co‐movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value‐at‐risk forecasts.     

Forecasting with Bayesian Vector Autoregressions Estimated Using Professional Forecasts

We propose a Bayesian shrinkage approach for vector autoregressions (VARs) that uses short‐term survey forecasts as an additional source of information about model parameters. In particular, we augment the vector of dependent variables by their survey nowcasts, and claim that each variable modelled in the VAR and its nowcast are likely to depend in a similar way on the lagged dependent variables. In an application to macroeconomic data, we find that the forecasts obtained from a VAR fitted by our new shrinkage approach typically yield smaller mean squared forecast errors than the forecasts obtained from a range of benchmark methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Priors from Loss Matching

This paper is concerned with the construction of prior probability measures for parametric families of densities where the framework is such that only beliefs or knowledge about a single observable data point is required. We pay particular attention to the parameter which minimizes a measure of divergence to the distribution providing the data. The prior distribution reflects this attention and we discuss the application of the Bayes rule from this perspective. Our framework is fundamentally non‐parametric and we are able to interpret prior distributions on the parameter space using ideas of matching loss functions, one of which is coming from the data model and the other from the prior.     

REVERSE REGRESSIONS AND LONG‐HORIZON FORECASTING

Long‐horizon predictive regressions in finance pose formidable econometric problems when estimated using available sample sizes. Hodrick in 1992 proposed a remedy that is based on running a reverse regression of short‐horizon returns on the long‐run mean of the predictor. Unfortunately, this only allows the null of no predictability to be tested, and assumes stationary regressors. In this paper, we revisit long‐horizon forecasting from reverse regressions, and argue that reverse regression methods avoid serious size distortions in long‐horizon predictive regressions, even when there is some predictability and/or near unit roots. Meanwhile, the reverse regression methodology has the practical advantage of being easily applicable when there are many predictors. We apply these methods to forecasting excess bond returns using the term structure of forward rates, and find that there is indeed some return forecastability. However, confidence intervals for the coefficients of the predictive regressions are about twice as wide as those obtained with the conventional approach to inference. We also include an application to forecasting excess stock returns. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting commodity price indexes using macroeconomic and financial predictors

Using a long sample of commodity spot price indexes over the period 1947–2010, we examine the out-of-sample predictability of commodity prices by means of macroeconomic and financial variables. Commodity currencies are found to have some predictive power at short (monthly and quarterly) forecast horizons, while growth in industrial production and the investment–capital ratio have some predictive power at longer (yearly) horizons. Commodity price predictability is strongest when based on multivariate approaches that account for parameter estimation error. Commodity price predictability varies substantially across economic states, being strongest during economic recessions.     

Macroeconomic forecasting in times of crises

We propose a parsimonious semiparametric method for macroeconomic forecasting. Based on ideas of clustering and similarity, we partition the series into blocks, search for the closest blocks to the latest block of observations, and forecast with the matched blocks. In a real-time forecasting exercise, we show that our approach does especially well for labor market and other key macro variables. Our method outperforms parametric linear, nonlinear, time-varying, and combination forecasts for the period 1999–2015 and particularly in the Great Recession. When adding financial spreads, our method delivers further improvements for labor market variables and capacity utilization.     

Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series*

In this paper, we investigate a test for structural change in the long‐run persistence in a univariate time series. Our model has a unit root with no structural change under the null hypothesis, while under the alternative it changes from a unit‐root process to a stationary one or vice versa. We propose a Lagrange multiplier‐type test, a test with the quasi‐differencing method, and ‘demeaned versions’ of these tests. We find that the demeaned versions of these tests have better finite‐sample properties, although they are not necessarily superior in asymptotics to the other tests.