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on Econometric Time Series |
| By: | Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT); Davide La Torre (Department of Economics, Business and Statistics, University of Milan, IT) |
| Abstract: | Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L^2 decomposition like the Kac-Siegert/Karnounen-Loeve series.In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations. |
| Keywords: | iterated function systems, Brownian motion, simulation of stochastic differential equations, |
| Date: | 2006–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:bep:unimip:1016&r=ets |
| By: | Helena Veiga |
| Abstract: | This paper compares empirically the forecasting performance of a continuous time stochastic volatility model with two volatility factors (SV2F) to a set of alternative models (GARCH, FIGARCH, HYGARCH, FIEGARCH and Component GARCH). We use two loss functions and two out-of-sample periods in the forecasting evaluation. The two out-of-sample periods are characterized by different patterns of volatility. The volatility is rather low and constant over the first period but shows a significant increase over the second out-of-sample period. The empirical results evidence that the performance of the alternative models depends on the characteristics of the out-ofsample periods and on the forecasting horizons. Contrarily, the SV2F forecasting performance seems to be unaffected by these two facts, since the model provides the most accurate volatility forecasts according to the loss functions we consider. |
| Date: | 2006–04 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws062509&r=ets |
| By: | Lokshin Boris (METEOR) |
| Abstract: | This paper compares the performance of three recently proposed estimators for dynamic panel data models (LSDV bias-corrected, MLE and MDE) along with GMM. Using Monte-Carlo, we find that MLE and biascorrected estimators have the smallest bias and are good alternatives for the GMM. System-GMM outperforms the rest in ‘difficult’ designs. Unfortunately, bias-corrected estimator is not reliable in these designs which may limit its applicability. |
| Keywords: | econometrics; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006012&r=ets |
| By: | Palm Franz C.; Smeekes Stephan; Urbain Jean-Pierre (METEOR) |
| Abstract: | In this paper we study and compare the properties of several bootstrap unit root tests recently proposed in the literature. The tests are Dickey-Fuller or Augmented DF-tests, either based on residuals from an autoregression and the use of the block bootstrap (Paparoditis & Politis, 2003) or on first differenced data and the use of the stationary bootstrap (Swensen, 2003a) or sieve bootstrap (Psaradakis, 2001; Chang & Park, 2003). We extend the analysis by interchanging the data transformations (differences versus residuals), the types of bootstrap and the presence or absence of a correction for autocorrelation in the tests. We prove that two sieve bootstrap tests based on residuals remain asymptotically valid, thereby completing the proofs of validity for all the types of DF bootstrap tests. In contrast to the literature which basically focuses on a comparison of the bootstrap tests with an asymptotic test, we compare the bootstrap tests among them using response surfaces for their size and power in a simulation study. We also investigate how the tests behave when accounting for a deterministic trend, even in the absence of such a trend in the data. This study leads to the following conclusions: (i) augmented DF-tests are always preferred to standard DF-tests; (ii) the sieve bootstrap performs slightly better than the block bootstrap; (iii) difference-based and residual-based tests behave similarly in terms of size although the latter appear more powerful. The results for the response surfaces allow us to make statements about the behaviour of the bootstrap tests as sample size increases. |
| Keywords: | Economics ; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006014&r=ets |
| By: | Erik Hjalmarsson |
| Abstract: | This paper considers the estimation of average autoregressive roots-near-unity in panels where the time-series have heterogenous local-to-unity parameters. The pooled estimator is shown to have a potentially severe bias and a robust median based procedure is proposed instead. This median estimator has a small asymptotic bias that can be eliminated almost completely by a bias correction procedure. The asymptotic normality of the estimator is proved. The methods proposed in the paper provide a useful way of summarizing the persistence in a panel data set, as well as a complement to more traditional panel unit root tests. |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:852&r=ets |
| By: | Erik Hjalmarsson |
| Abstract: | I develop new asymptotic results for long-horizon regressions with overlapping observations. I show that rather than using auto-correlation robust standard errors, the standard t-statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data. Further, when the regressors are persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and similar corrections and test procedures as those proposed for the short-run case should also be used in the long-run. In addition, I show that under an alternative of predictability, long-horizon estimators have a slower rate of convergence than short-run estimators and their limiting distributions are non-standard and fundamentally different from those under the null hypothesis. These asymptotic results are supported by simulation evidence and suggest that under standard econometric specifications, short-run inference is generally preferable to long-run inference. The theoretical results are illustrated with an application to long-run stock-return predictability. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:853&r=ets |
| By: | Erik Hjalmarsson |
| Abstract: | I show that the test procedure derived by Campbell and Yogo (2005, Journal of Financial Economics, forthcoming) for regressions with nearly integrated variables can be interpreted as the natural t-test resulting from a fully modified estimation with near-unit-root regressors. This clearly establishes the methods of Campbell and Yogo as an extension of previous unit-root results. |
| Keywords: | Regression analysis |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:854&r=ets |
| By: | Erik Hjalmarsson |
| Abstract: | Using Monte Carlo simulations, I show that typical out-of-sample forecast exercises for stock returns are unlikely to produce any evidence of predictability, even when there is in fact predictability and the correct model is estimated. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:855&r=ets |
| By: | Hui Guo; Robert Savickas |
| Abstract: | Finance theory, e.g., Campbell's (1993) ICAPM, indicates that the expected equity premium is a linear function of stock market volatility and the volatility of shocks to investment opportunities. We show that one can use average CAPM-based idiosyncratic volatility as a proxy for the latter. In particular, over the period 1927:Q1 to 2005:Q4, stock market volatility and idiosyncratic volatility jointly forecast stock market returns both in sample and out of sample. This finding is robust to alternative measures of idiosyncratic volatility; subsamples; the log transformation of volatility measures; and control for various predictive variables commonly used by early authors. Our results suggest that stock market returns are predictable. |
| Keywords: | Stock exchanges ; Stock - Prices |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2006-019&r=ets |
| By: | Høg, Espen P. (Department of Accounting, Aarhus School of Business); Frederiksen, Per H. (Jyske Bank) |
| Abstract: | The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable <p> instead of the standard Brownian motion. This is a new direction in pricing non defaultable bonds with offspring in the arbitrage free pricing of weather derivatives based on fractional Brownian motions. By applying fractional Itˆo calculus and a fractional version of the Girsanov transform, <p> a no arbitrage price of the bond is recovered by solving a fractional version of the fundamental bond pricing equation. Besides this theoretical contribution, the paper proposes an estimation methodology based on the Kalman filter approach, which is applied to the US term structure of <p> interest rates. |
| Keywords: | Fractional bond pricing equation; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; long memory; Kalman filter |
| Date: | 2006–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:hhb:aaracc:06-001&r=ets |
| By: | Katsumi Shimotsu (Queen's University) |
| Abstract: | This paper analyzes the semiparametric estimation of multivariate long-range dependent processes. The class of spectral densities considered is motivated by and includes those of multivariate fractionally integrated processes. The paper establishes the consistency of the multivariate Gaussian semiparametric estimator (GSE), which has not been shown in other work, and the asymptotic normality of the GSE estimator. The proposed GSE estimator is shown to have a smaller limiting variance than the two-step GSE estimator studied by Lobato (1999). Gaussianity is not assumed in the asymptotic theory. Some simulations confirm the relevance of the asymptotic results in samples of the size used in practical work. |
| Keywords: | fractional integration, long memory, semiparametric estimation |
| JEL: | C22 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1062&r=ets |
| By: | Hiroyuki Kasahara (University of Western Ontario); Katsumi Shimotsu (Queen's University) |
| Abstract: | This paper analyzes the higher-order properties of nested pseudo-likelihood (NPL) estimators and their practical implementation for parametric discrete Markov decision models in which the probability distribution is defined as a fixed point. We propose a new NPL estimator that can achieve quadratic convergence without fully solving the fixed point problem in every iteration. We then extend the NPL estimators to develop one-step NPL bootstrap procedures for discrete Markov decision models and provide some Monte Carlo evidence based on a machine replacement model of Rust (1987). The proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations. Improvements are particularly noticeable when analyzing the dynamic impacts of counterfactual policies. |
| Keywords: | Edgeworth expansion, k-step bootstrap, maximum pseudo-likelihood estimators, nested fixed point algorithm, Newton-Raphson method, policy iteration |
| JEL: | C12 C13 C14 C15 C44 C63 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1063&r=ets |