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on Econometric Time Series |
| By: | Michel Fliess (LIX - Laboratoire d'informatique de l'école polytechnique - CNRS : UMR7161 - Polytechnique - X, INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - CNRS : UMR - Ecole Centrale de Lille); Cédric Join (INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - CNRS : UMR - Ecole Centrale de Lille, CRAN - Centre de recherche en automatique de Nancy - CNRS : UMR7039 - Université Henri Poincaré - Nancy I - Institut National Polytechnique de Lorraine - INPL) |
| Abstract: | We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the rôle of probability theory. |
| Keywords: | Financial time series; mathematical finance; technical analysis; trends; random walks; efficient markets; forecasting; volatility; heteroscedasticity; quickly fluctuating functions; low-pass filters; nonstandard analysis; operational calculus. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:inria-00352834_v1&r=ets |
| By: | Alastair Cunningham (Bank of England); Jana Eklund (Bank of England); Chris Jeffery (Bank of England); George Kapetanios (Queen Mary, University of London and Bank of England); Vincent Labhard (European Central Bank) |
| Abstract: | Most macroeconomic data are uncertain - they are estimates rather than perfect measures of underlying economic variables. One symptom of that uncertainty is the propensity of statistical agencies to revise their estimates in the light of new information or methodological advances. This paper sets out an approach for extracting the signal from uncertain data. It describes a two-step estimation procedure in which the history of past revisions are first used to estimate the parameters of a measurement equation describing the official published estimates. These parameters are then imposed in a maximum likelihood estimation of a state space model for the macroeconomic variable. |
| Keywords: | Real-time data analysis, State space models, Data uncertainty, Data revisions |
| JEL: | C32 C53 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp637&r=ets |
| By: | Luis A. Gil-Alana (Facultad de Ciencias Económicas y Empresariales, Universidad de Navarra); Antonio Moreno (Facultad de Ciencias Económicas y Empresariales, Universidad de Navarra) |
| Abstract: | This paper identifies structural breaks in the post-World War II joint dynamics of U.S. inflation, unemployment and the short-term interest rate. We derive a structural break-date procedure which allows for long-memory behavior in all three series and perform the analysis for alternative data frequencies. Both long-memory and short-run coefficients are relevant for characterizing the changing patterns of U.S. macroeconomic dynamics. We provide an economic interpretation of those changes by examining the link between macroeconomic events and structural breaks. |
| Keywords: | Fractional integration, structural breaks, multivariate analysis, inflation dynamics |
| JEL: | C32 C51 E31 E32 E52 |
| Date: | 2009–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:una:unccee:wp0209&r=ets |
| By: | Kunst, Robert M. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria, and Department of Economics, University of Vienna, Vienna, Austria) |
| Abstract: | We consider a nonparametric test for the null of seasonal unit roots in quarterly time series that builds on the RUR (records unit root) test by Aparicio, Escribano, and Sipols. We find that the test concept is more promising than a formalization of visual aids such as plots by quarter. In order to cope with the sensitivity of the original RUR test to autocorrelation under its null of a unit root, we suggest an augmentation step by autoregression. We present some evidence on the size and power of our procedure and we illustrate it by applications to a commodity price and to an unemployment rate. |
| Keywords: | Seasonality, Nonparametric test, Unit roots |
| JEL: | C12 C14 C22 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:233&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear processes, involving only the autocorrelation function of the observed process. The second term, which is specific to nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of the linear innovation process and the autocorrelation function of its square. This formula is obtained under a symmetry assumption on the linear innovation process. An application to GARCH models is proposed. |
| Keywords: | Bartlett's formula; nonlinear time series model; sample autocorrelation; GARCH model; weak white noise |
| JEL: | C13 C12 C22 |
| Date: | 2009–02–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:13224&r=ets |
| By: | Andrle, Michal |
| Abstract: | The paper discusses the role of stochastic trends in DSGE models and effects of stochastic detrending. We argue that explicit structural assumptions on trend behavior is convenient, namely for emerging countries. In emerging countries permanent shocks are an important part of business cycle dynamics. The reason is that permanent shocks spill over the whole frequency range, potentially, including business cycle frequencies. Applying high- or band-pass filter to obtain business cycle dynamics, however, does not eliminate the influence of permanent shocks on comovements of time series. The contribution of the paper is to provide a way how to calculate the role of permanent shocks on the detrended/ filtered business cycle population dynamics in a DSGE model laboratory using the frequency domain methods. |
| Keywords: | detrending; band-pass filter; spectral density; DSGE. |
| JEL: | E32 C53 D58 |
| Date: | 2008–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:13289&r=ets |