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on Econometric Time Series |
| By: | Theis Lange (Department of Economics, University of Copenhagen & CREATES) |
| Abstract: | This paper studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The regime process is assumed to depend on the lagged disequilibrium, as measured by the norm of linear stable or cointegrating relations. The main contributions of the paper are: i) conditions ensuring geometric ergodicity and nite second order moment of linear long run equilibrium relations and differenced observations, ii) a representation theorem similar to Granger's representations theorem and a functional central limit theorem for the common trends, iii) to establish that the usual reduced rank regression estimator of the cointegrating vector is consistent even in this highly extended model, and iv) asymptotic normality of the parameters for xed cointegration vector and regime parameters. Finally, an application of the model to US term structure data illustrates the empirical relevance of the model. |
| Keywords: | Cointegration, Non-linear adjustment, Regime switching, Multivariate ARCH. |
| JEL: | C13 C32 C51 |
| Date: | 2009–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-04&r=ets |
| By: | Andrés González (Banco de la República, Bogotá and CREATES, University of Aarhus, Denmark); Kirstin Hubrich (European Central Bank, Frankfurt am Main and CREATES, University of Aarhus, Denmark); Timo Teräsvirta (CREATES, University of Aarhus, Denmark) |
| Abstract: | In this work, we make use of the shifting-mean autoregressive model which is a flexible univariate nonstationary model. It is suitable for describing characteristic features in inflation series as well as for medium-term forecasting. With this model we decompose the inflation process into a slowly moving nonstationary component and dynamic short-run fluctuations around it. We fit the model to the monthly euro area, UK and US inflation series. An important feature of our model is that it provides a way of combining the information in the sample and the a priori information about the quantity to be forecast to form a single inflation forecast. We show, both theoretically and by simulations, how this is done by using the penalised likelihood in the estimation of model parameters. In forecasting inflation, the central bank inflation target, if it exists, is a natural example of such prior information. We further illustrate the application of our method by an ex post forecasting experiment for euro area and UK inflation. We find that that taking the exogenous information into account does im- prove the forecast accuracy compared to that of a linear autoregressive benchmark model. |
| Keywords: | Nonlinear forecast, nonlinear model, nonlinear trend, penalised likelihood, structural shift, time-varying parameter |
| JEL: | C22 C52 C53 E31 E47 |
| Date: | 2009–01–28 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-03&r=ets |
| By: | Eichler Michael; Motta Giovanni; Sachs Rainer von (METEOR) |
| Abstract: | Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a "double-asymptotic" framework of both cross-section and time dimension tending to infinity. A simulation study illustrates the performance of our estimators. |
| Keywords: | econometrics; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009002&r=ets |
| By: | Eichler Michael; Didelez Vanessa (METEOR) |
| Abstract: | We combine two approaches to causal reasoning. Granger-causality, on the one hand, is popular in fields like econometrics, where randomised experiments are not very common. Instead information about the dynamic development of a system is explicitly modelled and used to define potentially causal relations. On the other hand, the notion of causality as effect of interventions is predominant in fields like medical statistics or computer science. In this paper, we consider the effect of external, possibly multiple and sequential, interventions in a system of multivariate time series, the Granger-causal structure of which is taken to be known. We address the following questions: under what assumptions about the system and the interventions does Granger-causality inform us about the effectiveness of interventions, and when does the possibly smaller system of observable times series allow us to estimate this effect? For the latter we derive criteria that can be checked graphica lly and are in the same spirit as Pearl''s back-door and front-door criteria (Pearl 1995). |
| Keywords: | econometrics; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009003&r=ets |
| By: | María José Rodríguez; Esther Ruiz |
| Abstract: | In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage effect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH specication is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models differ among them and with respect to the other three specications. |
| Keywords: | EGARCH, GJR, QGARCH, TGARCH, APARCH |
| JEL: | C22 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws090302&r=ets |
| By: | Aurea Grané; Helena Veiga |
| Abstract: | Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes a general detection and correction method based on wavelets that can be applied to a large class of volatility models. The effectiveness of our proposal is tested by an intensive Monte Carlo study for six well known volatility models and compared to alternative proposals in the literature, before applying it to three daily stock market indexes. The Monte Carlo experiments show that our method is both very effective in detecting isolated outliers and outlier patches and much more reliable than other wavelet-based procedures since it detects a significant smaller number of false outliers. |
| Keywords: | Outliers, Outlier patches, Volatility models, Wavelets |
| JEL: | C22 C5 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws090403&r=ets |
| By: | Athanasopoulos, George; Issler, João Victor; Guillén, Osmani Teixeira de Carvalho; Farshid, Vahid |
| Abstract: | We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank, relative to the commonly used procedure of selecting the lag-length only and then testing for cointegration. |
| Date: | 2009–02–05 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:689&r=ets |