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on Econometric Time Series |
| By: | Anders Bredahl Kock (Aarhus University and CREATES) |
| Abstract: | This paper applies three universal approximators for forecasting. They are the Artificial Neural Networks, the Kolmogorov- Gabor polynomials, as well as the Elliptic Basis Function Networks. Even though forecast combination has a long history in econometrics focus has not been on proving loss bounds for the combination rules applied. We apply the Weighted Average Algorithm (WAA) of Kivinen and Warmuth (1999) for which such loss bounds exist. Specifically, one can bound the worst case performance of the WAA compared to the performance of the best single model in the set of models combined from. The use of universal approximators along with a combination scheme for which explicit loss bounds exist should give a solid theoretical foundation to the way the forecasts are performed. The practical performance will be investigated by considering various monthly postwar macroeconomic data sets for the G7 as well as the Scandinavian countries. |
| Keywords: | Forecasting, Universal Approximators, Elliptic Basis Function Network, Forecast Combination, Weighted Average Algorithm |
| JEL: | C22 C45 C53 |
| Date: | 2009–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-18&r=ets |
| By: | Jorge Caiado (CEMAPRE, School of Economics and Management (ISEG), Technical University of Lisbon); Nuno Crato (CEMAPRE, School of Economics and Management (ISEG), Technical University of Lisbon) |
| Abstract: | This paper proposes volatility and spectral based methods for cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared returns, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the "blue-chip" stocks used to compute the Dow Jones Industrial Average (DJIA) index. |
| Keywords: | Asymmetric effects, Cluster analysis, DJIA stock returns, Periodogram, Threshold GARCH model, Volatility |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:cma:wpaper:0902&r=ets |
| By: | Jorge Caiado (CEMAPRE, School of Economics and Management (ISEG), Technical University of Lisbon) |
| Abstract: | In this article, we examine the daily water demand forecasting performance of double seasonal univariate time series models (Holt-Winters, ARIMA and GARCH) based on multi-step ahead forecast mean squared errors. A within-week seasonal cycle and a within-year seasonal cycle are accommodated in the various model specifications to capture both seasonalities. We investigate whether combining forecasts from different methods for different origins and horizons could improve forecast accuracy. The analysis is made with daily data for water consumption in Granada, Spain. |
| Keywords: | ARIMA, Combined forecasts, Double seasonality, Exponential Smoothing, Forecasting, GARCH, Water demand |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:cma:wpaper:0903&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are allowed. It is shown that the quasi-maximum likelihood estimator is, in general, inconsistent. To solve this problem, we propose a self-weighted least-squares estimator and show that this estimator is asymptotically normal. Furthermore, a score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. The latter have an asymptotic distribution which is far from the standard chi-square. Simulation experiments are carried out to assess the performance of the proposed estimator. |
| Keywords: | Conditional homoscedasticity testing; Inconsistent estimator; Leverage effect; Linear ARCH; Quasi-maximum likelihood; Weighted least-squares. |
| JEL: | C13 C22 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15147&r=ets |
| By: | Kopecky, Karen A.; Suen, Richard M. H. |
| Abstract: | This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. It is shown that, equipped with the Rouwenhorst method, an alternative approach to generating these moments has a higher degree of accuracy than the simulation method. |
| Keywords: | Numerical Methods; Finite State Approximations; Optimal Growth Model |
| JEL: | C63 |
| Date: | 2009–05–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15122&r=ets |
| By: | Amendola, Alessandra; Christian, Francq |
| Abstract: | Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. |
| Keywords: | Consistency and asymptotic normality; MCMC algorithms; Mixing; Nonlinear modelling; Stationarity; Time-series forecasting. |
| JEL: | C22 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15140&r=ets |
| By: | Francq, Christian; Horvath, Lajos; Zakoian, Jean-Michel |
| Abstract: | Variance targeting estimation is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood (QML) estimation of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining parameters are estimated by QML in a second step. This paper establishes the asymptotic distribution of the estimators obtained by this method in univariate GARCH models. Comparisons with the standard QML are provided and the merits of the variance targeting method are discussed. In particular, it is shown that when the model is misspecified, the VTE can be superior to the QMLE for long-term prediction or Value-at-Risk calculation. An empirical application based on stock market indices is proposed. |
| Keywords: | Consistency and Asymptotic Normality; GARCH; Heteroskedastic Time Series; Quasi Maximum Likelihood Estimation; Value-at-Risk; Variance Targeting Estimator. |
| JEL: | C13 C22 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15143&r=ets |
| By: | Boubacar Mainassara, Yacouba; Francq, Christian |
| Abstract: | The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters. |
| Keywords: | Echelon form; Lagrange Multiplier test; Likelihood Ratio test; Nonlinear processes; QMLE; Structural representation; VARMA models; Wald test. |
| JEL: | C32 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15141&r=ets |