Forecasting correlations during the late-2000s financial crisis: short-run component, long-run component, and structural breaks

We empirically investigate the predictive power of the various components affecting correlations that have been recently introduced in the literature. We focus on models allowing for a flexible specification of the short-run component of correlations as well as the long-run component. Moreover, we also allow the correlation dynamics to be subjected to regime-shift caused by threshold-based structural breaks of a different nature. Our results indicate that in some cases there may be a superimposition of the long- and short-term movements in correlations. Therefore, care is called for in interpretations when estimating the two components. Testing the forecasting accuracy of correlations during the late-2000s financial crisis yields mixed results. In general component models allowing for a richer correlation specification possess a (marginally) increased predictive accuracy. Economically speaking, no relevant gains are found by allowing for more flexibility in the correlation dynamics.Correlation forecasting; Component models; Threshold regime-switching models; Mixed data sampling; Performance evaluation

Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model

Accurate Yield Curve Scenarios Generation using Functional Gradient Descent

We propose a multivariate nonparametric technique for generating reliable historical yield curve scenarios and confidence intervals. The approach is based on a Functional Gradient Descent (FGD) estimation of the conditional mean vector and volatility matrix of a multivariate interest rate series. It is computationally feasible in large dimensions and it can account for non-linearities in the dependence of interest rates at all available maturities. Based on FGD we apply filtered historical simulation to compute reliable out-of-sample yield curve scenarios and confidence intervals. We back-test our methodology on daily USD bond data for forecasting horizons from 1 to 10 days. Based on several statistical performance measures we find significant evidence of a higher predictive power of our method when compared to scenarios generating techniques based on (i) factor analysis, (ii) a multivariate CCC-GARCH model, or (iii) an exponential smoothing volatility estimators as in the RiskMetrics approachConditional mean and volatility estimation; Filtered Historical Simulation; Functional Gradient Descent; Term structure; Multivariate CCC-GARCH models

Volatility Forecasting: Downside Risk, Jumps and Leverage Effect

We provide new empirical evidence on volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Leverage and volatility feedback effects among continuous and jump components of the S&P500 price and volatility dynamics are examined using recently developed methodologies to detect jumps and to disentangle their size from continuous return and continuous volatility. Granted that jumps in both return and volatility are important components for generating the two effects, we find jumps in return can improve forecasts of volatility, while jumps in volatility improve volatility forecasts to a lesser extent. Moreover, disentangling jump and continuous variations into signed semivariances further improve the out-of-sample performance of volatility forecasting models, with negative jump semivariance being highly more informative then positive jump semivariance. The model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of number of parameters to be estimated.High frequency data, Realized volatility forecasting, Downside risk, Leverage effect

Realized Correlation Tick-by-Tick

We propose the Heterogeneous Autoregressive (HAR) model for the estimation and prediction of realized correlations. We construct a realized correlation measure where both the volatilities and the covariances are computed from tick-by-tick data. As for the realized volatility, the presence of market microstructure can induce significant bias in standard realized covariance measure computed with artificially regularly spaced returns. Contrary to these standard approaches we analyse a simple and unbiased realized covariance estimator that does not resort to the construction of a regular grid, but directly and efficiently employs the raw tick-by-tick returns of the two series. Montecarlo simulations calibrated on realistic market microstructure conditions show that this simple tick-by-tick covariance possesses no bias and the smallest dispersion among the covariance estimators considered in the study. In an empirical analysis on S&P 500 and US bond data we find that realized correlations show significant regime changes in reaction to financial crises. Such regimes must be taken into account to get reliable estimates and forecasts.High frequency data, Realized Correlation, Market Microstructure, Bias correction, HAR, Regimes

Accurate Short-Term Yield Curve Forecasting using Functional Gradient Descent

We propose a multivariate nonparametric technique for generating reliable shortterm historical yield curve scenarios and confidence intervals. The approach is based on a Functional Gradient Descent (FGD) estimation of the conditional mean vector and covariance matrix of a multivariate interest rate series. It is computationally feasible in large dimensions and it can account for non-linearities in the dependence of interest rates at all available maturities. Based on FGD we apply filtered historical simulation to compute reliable out-of-sample yield curve scenarios and confidence intervals. We back-test our methodology on daily USD bond data for forecasting horizons from 1 to 10 days. Based on several statistical performance measures we find significant evidence of a higher predictive power of our method when compared to scenarios generating techniques based on (i) factor analysis, (ii) a multivariate CCC-GARCH model, or (iii) an exponential smoothing covariances estimator as in the RiskMetricsTM approach.Conditional mean and variance estimation, Filtered Historical Simulation, Functional Gradient Descent, Term structure; Multivariate CCC-GARCH models

A general multivariate threshold GARCH model with dynamic conditional correlations

We propose a new multivariate GARCH model with Dynamic Conditional Correlations that extends previous models by admitting multivariate thresholds in conditional volatilities and correlations. The model estimation is feasible in large dimensions and the positive deniteness of the conditional covariance matrix is easily ensured by the structure of the model. Thresholds in conditional volatilities and correlations are estimated from the data, together with all other model parameters. We study the performance of our model in three distinct applications to US stock and bond market data. Even if the conditional volatility functions of stock returns exhibit pronounced GARCH and threshold features, their conditional correlation dynamics depends on a very simple threshold structure with no local GARCH features. We obtain a similar result for the conditional correlations between government and corporate bond returns. On the contrary, we ¯nd both threshold and GARCH structures in the conditional correlations between stock and government bond returns. In all applications, our model improves signi¯cantly the in-sample and out-of-sample forecasting power for future conditional correlations with respect to other relevant multivariate GARCH models.Multivariate GARCH models, Dynamic conditional correlations, Tree-structured GARCH models

What Drives Short Rate Dynamics? A Functional Gradient Descent Approach

Functional gradient descent (FGD), a recent technique coming from computational statistics, is applied to the estimation of the conditional moments of the short rate process with the goal of finding the main drivers of the drift and volatility dynamics. FGD can improve the accuracy of some reasonable starting estimates obtained using classical short rate models introduced in the literature. It exploits the predictive information of an enlarged set of variables, including yields at other maturities, time, and macroeconomic indicators. Fitting this methodology to the time series of monthly US 3-month Treasury bill rates, we find that the drift dynamics react mostly in a non-linear way to changes in macroeconomic variables, whereas volatility dynamics are subjected to time-dependent regime-switches. Finally we show the superior performance of the final predictions obtained by applying FGD in a forecasting exercis

Yield Curve Predictability, Regimes, and Macroeconomic Information: A Data-Driven Approach

We propose an empirical approach to determine the various economic sources driving the US yield curve. We allow the conditional dynamics of the yield at different maturities to change in reaction to past information coming from several relevant predictor variables. We consider both endogenous, yield curve factors and exogenous, macroeconomic factors as predictors in our model, letting the data themselves choose the most important variables. We find clear, different economic patterns in the local dynamics and regime specification of the yields depending on the maturity. Moreover, we present strong empirical evidence for the accuracy of the model in fitting in-sample and predicting out-of-sample the yield curve in comparison to several alternative approaches.Yield curve modeling and forecasting; Macroeconomic variables; Tree-structured models; Threshold regimes; GARCH; Bagging

Modeling and Forecasting Short-term Interest Rates: The Benefits of Smooth Regimes, Macroeconomic Variables, and Bagging

In this paper we propose a smooth transition tree model for both the conditional mean and variance of the short-term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi-maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short-term interest rate we find (1) leading indicators for inflation and real activity are the most relevant predictors in characterizing the multiple regimes’ structure; (2) the optimal model has three limiting regimes. Moreover, we provide empirical evidence of the power of the model in forecasting the first two conditional moments when it is used in connection with bootstrap aggregation (bagging).short-term interest rate, regression tree, smooth transition, conditional variance, bagging, asymptotic theory