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on Econometrics |
| By: | Francesco Audrino; Fabio Trojani |
| Abstract: | 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. |
| Keywords: | Conditional mean and variance estimation, Filtered Historical Simulation, Functional Gradient Descent, Term structure; Multivariate CCC-GARCH models |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:usg:dp2007:2007-24&r=ecm |
| By: | Francesco Audrino; Fabio Trojani |
| Abstract: | 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 ÃÂïnd both threshold and GARCH structures in the conditional correlations between stock and government bond returns. In all applications, our model improves signiÃÂïcantly the in-sample and out-of-sample forecasting power for future conditional correlations with respect to other relevant multivariate GARCH models. |
| Keywords: | Multivariate GARCH models, Dynamic conditional correlations, Tree-structured GARCH models |
| JEL: | C12 C13 C51 C53 C61 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:usg:dp2007:2007-25&r=ecm |
| By: | Sergio Firpo; Nicole M. Fortin; Thomas Lemieux |
| Abstract: | We propose a new regression method to estimate the impact of explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function is a widely used tool in robust estimation that can easily be computed for each quantile of interest. We show how standard partial effects, as well as policy effects, can be estimated using our regression approach. We propose three different regression estimators based on a standard OLS regression (RIF-OLS), a logit regression (RIF-Logit), and a nonparametric logit regression (RIF-OLS). We also discuss how our approach can be generalized to other distributional statistics besides quantiles. |
| JEL: | C14 C21 J31 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberte:0339&r=ecm |
| By: | Szymon Borak; Wolfgang HÃÂärdle; Enno Mammen; Byeong U. Park |
| Abstract: | High-dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question - Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole high-dimensional system with a low-dimensional representation. We illustrate the theory with a simulation study. Also, we apply the method to a study of the dynamic behavior of implied volatilities and discuss other possible applications in finance and economics. |
| Keywords: | semiparametric models, factor models, implied volatility surface, vector autoregressive process, asymptotic inference. |
| JEL: | C14 C32 G12 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2007-023&r=ecm |
| By: | Gregor W. Smith (Department of Economics, Queen's University) |
| Abstract: | Estimating linear rational expectations models requires replacing the expectations of future, endogenous variables either with forecasts from a fully solved model, or with the instrumented actual values, or with forecast survey data. Extending the methods of McCallum (1976) and Gottfries and Persson (1988), I show how to pool these methods and also use actual, future values of these variables to improve statistical efficiency. The method is illustrated with an application using SPF survey data in the US Phillips curve, where the output gap plays a significant role but lagged inflation plays none. |
| Keywords: | rational expectations, recursive projection, Phillips curve |
| JEL: | E37 C53 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1129&r=ecm |