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on Econometric Time Series |
| By: | Ivana Komunjer; Michael T. Owyang |
| Abstract: | In this paper, we propose a new family of multivariate loss functions that can be used to test the rationality of vector forecasts without assuming independence across individual variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family recently proposed by Elliott, Komunjer, and Timmermann (2005). Following their methodology, we derive a GMM test for multivariate forecast rationality that allows the forecast errors to be dependent, and takes into account forecast estimation uncertainty. We use our test to study the rationality of macroeconomic vector forecasts in the growth rate in nominal output, the CPI inflation rate, and a short-term interest rate. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2007-047&r=ets |
| By: | Gusztav Morvav; Benjamin Weiss |
| Abstract: | The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1,…,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1|X0,X1, ...Xn) can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines. |
| Keywords: | Nonparametric estimation; Stationary processes |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp464&r=ets |
| By: | Alex Novikov (School of Finance and Economics, University of Technology, Sydney); Nino Kordzakhia |
| Abstract: | Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity and use it for obtaining explicit bounds for the expectation of exit times. |
| Keywords: | first passage times; autoregressive processes; martingales; expenential boundedness |
| Date: | 2007–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:205&r=ets |
| By: | Matteo Pelagatti |
| Abstract: | The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and negative returns. In this paper we propose a process that allows the simultaneous modelling of skewed conditional returns and different dynamics in their conditional second moments. The main stochastic properties of the model are analyzed and necessary and sufficient conditions for weak and strict stationarity are derived. An application to the daily returns on the principal index of the London Stock Exchange supports our model when compared to other frequently used GARCH-type models, which are nested into ours. |
| Keywords: | Volatility, Skewness, GARCH, Asymmetric Dynamics, Stationarity |
| JEL: | C22 C53 G10 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:mis:wpaper:20071101&r=ets |
| By: | Gabriele Fiorentini (University of Florence and The Rimini Centre for Economics Analysis, Italy.); Enrique Sentana (CEMFI, Spain) |
| Abstract: | We rank the efficiency of several likelihood-based parametric and semiparametric estimators of conditional mean and variance parameters in multivariate dynamic models with i.i.d. spherical innovations, and show that Gaussian pseudo maximum likelihood estimators are inefficient except under normality. We also provide conditions for partial adaptivity of semiparametric procedures, and relate them to the consistency of distributionally misspecified maximum likelihood estimators. We propose Hausman tests that compare Gaussian pseudo maximum likelihood estimators with more efficient but less robust competitors. We also study the efficiency of sequential estimators of the shape parameters. Finally, we provide finite sample results through Monte Carlo simulations. |
| Keywords: | Adaptivity, ARCH, Elliptical Distributions, Financial Returns, Hausman tests, Semiparametric Estimators, Sequential Estimators. |
| JEL: | C13 C14 C12 C51 C52 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:38-07&r=ets |
| By: | Gabriele Fiorentini (University of Florence and The Rimini Centre for Economics Analysis, Italy.); Giorgio Calzolari (University of Florence); Enrique Sentana (CEMFI, Spain) |
| Abstract: | We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks. |
| Keywords: | ARCH, Idiosyncratic risk, Inequality constraints, Kalman filter, Sequential estimators, Simulation estimators, Volatility. |
| JEL: | C13 C15 C32 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:40-07&r=ets |
| By: | Dimitrios D. Thomakos (University of Peloponnese, Greece and The Rimini Centre for Economics Analysis, Italy.); Dimitris N. Politis (University of California, San Diego, USA) |
| Abstract: | In this paper we contribute several new results on the NoVaS transformation approach for volatility forecasting introduced by Politis (2003a,b, 2007). In particular: (a) we introduce an alternative target distribution (uniform); (b) we present a new method for volatility forecasting using NoVaS ; (c) we show that the NoVaS methodology is applicable in situations where (global) stationarity fails such as the cases of local stationarity and/or structural breaks; (d) we show how to apply the NoVaS ideas in the case of returns with asymmetric distribution; and finally (e) we discuss the application of NoVaS to the problem of estimating value at risk (VaR). The NoVaS methodology allows for a flexible approach to inference and has immediate applications in the context of short time series and series that exhibit local behavior (e.g. breaks, regime switching etc.) We conduct an extensive simulation study on the predictive ability of the NoVaS approach and find that NoVaS forecasts lead to a much ÔtighterÕ distribution of the forecasting performance measure for all data generating processes. This is especially relevant in the context of volatility predictions for risk management. We further illustrate the use of NoVaS for a number of real datasets and compare the forecasting performance of NoVaS -based volatility forecasts with realized and range-based volatility measures. |
| Keywords: | ARCH, GARCH, local stationarity, structural breaks, VaR, volatility. |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:44-07&r=ets |
| By: | Costas Milas (Keele University, UK and The Rimini Centre for Economics Analysis, Italy.); Philip Rothman (East Carolina University, USA) |
| Abstract: | In this paper we use smooth transition vector error-correction models (STVECMs) in a simulated out-of-sample forecasting experiment for the unemployment rates of the four non-Euro G-7 countries, the U.S., U.K., Canada, and Japan. For the U.S., pooled forecasts constructed by taking the median value across the point forecasts generated by the linear and STVECM forecasts appear to perform better than the linear AR(p) benchmark more so during business cycle expansions. Such pooling also tends to lead to statistically significant forecast improvement for the U.K. ÒReality checksÓ of these results suggest that they do not stem from data snooping. |
| Keywords: | nonlinear, asymmetric, STVECM, pooled forecasts, Diebold-Mariano |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:49-07&r=ets |