|
on Econometric Time Series |
| By: | Søren Johansen (University of Copenhagen) |
| Abstract: | There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the e¤ect of nonstationarity on inference using these methods and compare them to model based inference. Finally we analyse some data on annual mean temperature and sea level, by applying the cointegrated vector autoregressive model, which explicitly takes into account the nonstationarity of the variables. |
| Keywords: | Regression correlation cointegration, model based inference, likelihood inference, annual mean temperature, sea level |
| JEL: | C32 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:sas:wpaper:20114&r=ets |
| By: | Xibin Zhang; Maxwell L. King |
| Abstract: | This paper aims to investigate a Bayesian sampling approach to parameter estimation in the semiparametric GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviation. The proposed investigation is motivated by the lack of robustness in GARCH models with any parametric assumption of the error density for the purpose of error-density based inference such as value-at-risk (VaR) estimation. The contribution of the paper is to construct the likelihood and posterior of model and bandwidth parameters under the proposed mixture error density, and to forecast the one-step out-of-sample density of asset returns. The resulting VaR measure therefore would be distribution-free. Applying the semiparametric GARCH(1,1) model to daily stock-index returns in eight stock markets, we find that this semiparametric GARCH model is favoured against the GARCH(1,1) model with Student t errors for five indices, and that the GARCH model underestimates VaR compared to its semiparametric counterpart. We also investigate the use and benefit of localized bandwidths in the proposed mixture density of the errors. |
| Keywords: | Bayes factors, kernel-form error density, localized bandwidths, Markov chain Monte Carlo, value-at-risk |
| JEL: | C11 C14 C15 G15 |
| Date: | 2011–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2011-24&r=ets |
| By: | Rossen, Anja |
| Abstract: | This study focuses on the question whether nonlinear transformation of lagged time series values and residuals are able to systematically improve the average forecasting performance of simple Autoregressive models. Furthermore it investigates the potential superior forecasting results of a nonlinear Threshold model. For this reason, a large-scale comparison over almost 400 time series which span from 1996:3 up to 2008:12 (production indices, price indices, unemployment rates, exchange rates, money supply) from 10 European countries is made. The average forecasting performance is appraised by means of Mean Group statistics and simple t-tests. Autoregressive models are extended by transformed first lags of residuals and time series values. Whereas additional transformation of lagged time series values are able to reduce the ex-ante forecast uncertainty and provide a better directional accuracy, transformations of lagged residuals also lead to smaller forecast errors. Furthermore, the nonlinear Threshold model is able to capture certain type of economic behavior in the data and provides superior forecasting results than a simple Autoregressive model. These findings are widely independent of considered economic variables. -- |
| Keywords: | Time series modeling,forecasting comparison,nonlinear transformations,Threshold Autoregressive modeling,average forecasting performance |
| JEL: | C22 C53 C51 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:hwwirp:113&r=ets |
| By: | Charles A. Fleischman; John M. Roberts |
| Abstract: | We construct new estimates of potential output and the output gap using a multivariate approach that allows for an explicit role for measurement errors in the decomposition of real output. Because we include data on hours, output, employment, and the labor force, we are able to decompose our estimate of potential output into separate trends in labor productivity, labor-force participation, weekly hours, and the NAIRU. We find that labor-market variables—especially the unemployment rate—are the most informative individual indicators of the state of the business cycle. Conditional on including these measures, inflation is also very informative. Among measures of output, we find that although they add little to the identification for the cycle, the income-side measures of output are about as informative as the traditional product-side measures about the level of structural productivity and potential output. We also find that the output gap resulting from the recent financial crisis was very large, reaching -7 percent of output in the second half of 2009. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2011-46&r=ets |
| By: | Costantini, Mauro; Lupi, Claudio |
| Abstract: | In this paper we propose a simple extension to the panel case of the covariate- augmented Dickey Fuller (CADF) test for unit roots developed in Hansen (1995). The extension we propose is based on a p values combination approach that takes into account cross-section dependence. We show that the test is easy to compute, has good size properties and gives power gains with respect to other popular panel approaches. A procedure to compute the asymptotic p values of Hansen's CADF test is also a side-contribution of the paper. We also complement Hansen (1995) and Caporale and Pittis (1999) with some new theoretical results. Two empirical applications are carried out for illustration purposes on international data to test the PPP hypothesis and the presence of a unit root in international industrial production indices. |
| Keywords: | Unit Root, Panel data, Approximate p values, Monte Carlo |
| JEL: | C22 C23 |
| Date: | 2011–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:mol:ecsdps:esdp11062&r=ets |
| By: | J. D. Deuschel; P. K. Friz; A. Jacquier; S. Violante |
| Abstract: | Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics; cf. G. Ben Arous (1988). Our small noise expansion allows for a "second order" exponential factor. Applications include tail and implied volatility asymptotics in some correlated stochastic volatility models; in particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009). |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1111.2462&r=ets |