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on Econometric Time Series |
| By: | Rasmus Søndergaard Pedersen (Department of Economics, University of Copenhagen); Anders Rahbek (Department of Economics, University of Copenhagen) |
| Abstract: | Consistency and asymptotic normality are established for the maximum likelihood estimators in the nonstationary ARCH and GARCH models with general t-distributed innovations. The results hold for joint estimation of (G)ARCH effects and the degrees of freedom parameter parametrizing the t-distribution. With T denoting sample size, square root T-convergence is shown to hold with closed form expressions for the multivariate covariances. |
| Keywords: | ARCH, GARCH, asymptotic normality, asymptotic theory, consistency, t-distribution, maximum likelihood, nonstationarity. |
| JEL: | C32 |
| Date: | 2015–04–24 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1507&r=ets |
| By: | Dogru, Bülent |
| Abstract: | Aim of this study is to analyze the non-stationarity of real GDP levels using recently developed Carrion-i Silvestre et al. (2005) panel unit root test allowing different number of structural breaks in panel. For this purpose, this test is applied to panel data of per capita GDP of 20 high income OECD countries covering the time period of 1961 through 2012. Individual time series and first generation panel unit root tests are also employed to make a comparison. Results indicate that per capita GDP series is non-stationary for many OECD countries. This implies that any shock given to per capita GDP will have a long lasting impact on the macroeconomic variable |
| Keywords: | Per capita real GDP, panel stationary tests, Carrion-I Silvestre et al. (2005) |
| JEL: | C12 C23 |
| Date: | 2015–04–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:63856&r=ets |
| By: | Ralph D. Snyder; J. Keith Ord; Anne B. Koehler; Keith R. McLaren; Adrian Beaumont |
| Abstract: | A method is proposed for forecasting composite time series such as the market shares for multiple brands. Its novel feature is that it relies on multi-series adaptations of exponential smoothing combined with the log-ratio transformation for the conversion of proportions onto the real line. It is designed to produce forecasts that are both non-negative and sum to one; are invariant to the choice of the base series in the log-ratio transformation; recognized and exploit features such as serial dependence and non-stationary movements in the data; allow for the possibility of non-uniform interactions between the series; and contend with series that start late, finish early, or which have values close to zero. Relying on an appropriate multivariate innovations state space mode, it can be used to generate prediction distributions in addition to point forecasts and to compute the probabilities of market share increases together with prediction intervals. A shared structure between the series in the multivariate model is used to ensure that the usual proliferation of parameter is avoided. The forecasting method is illustrated using data on the annual market shares of the major (groups of) brands in the U.S. automobile market, over the period 1961-2013. |
| Keywords: | Exponential smoothing; Proportions; Prediction intervals; Automobile sales; Market shares. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2015-11&r=ets |
| By: | Christoph Bergmeir; Rob J Hyndman; Bonsoo Koo |
| Abstract: | One of the most widely used standard procedures for model evaluation in classification and regression is K-fold cross-validation (CV). However, when it comes to time series forecasting, because of the inherent serial correlation and potential non-stationarity of the data, its application is not straightforward and often omitted by practitioners in favor of an out-of-sample (OOS) evaluation. In this paper, we show that the particular setup in which time series forecasting is usually performed using Machine Learning methods renders the use of standard K-fold CV possible. We present theoretical insights supporting our arguments. Furthermore, we present a simulation study where we show empirically that K-fold CV performs favourably compared to both OOS evaluation and other time-series-specific techniques such as non-dependent cross-validation. |
| Keywords: | cross-validation, time series, auto regression. |
| JEL: | C52 C53 C22 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2015-10&r=ets |
| By: | Marcelle Chauvet; Elcyon C. R. Lima; Brisne Vasquez |
| Abstract: | This paper compares the forecasting performance of linear and nonlinear models under the presence of structural breaks for the Brazilian real GDP growth. The Markov switching models proposed by Hamilton (1989) and its generalized version by Lam (1990) are applied to quarterly GDP from 1975:1 to 2000:2 allowing for breaks at the Collor Plans. The probabilities of recessions are used to analyze the Brazilian business cycle. The ability of each model in forecasting out-of-sample the growth rates of GDP is examined. The forecasting ability of the two models is also compared with linear specifications. We find that nonlinear models display the best forecasting performance and that specifications including the presence of structural breaks are important in obtaining a representation of the Brazilian business cycle. Neste artigo são comparadas as habilidades preditivas de modelos lineares e nãolineares, com quebras estruturais, para a taxa de crescimento do PIB do Brasil. São estimados os modelos com mudança de regime markoviana propostos por Hamilton (1989) e Lam (1990) - que generaliza o modelo de Hamilton - com dados trimestrais de 1975:1 a 2000:2. Na estimação dos modelos são permitidas quebras estruturais durante os Planos Collor I e II. As probabilidades de recessão dos modelos são utilizadas para se analisar o ciclo de negócios brasileiro. É examinada a capacidade de se prever a taxa de crescimento do PIB fora da amostra e a habilidade preditiva dos dois modelos é comparada com a de modelos lineares. Os nossos resultados revelam que os modelos não-lineares são os que apresentam o melhor desempenho preditivo e que a inclusão de quebras estruturais é importante para se obter a representação do ciclo de negócios no Brasil. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:ipe:ipetds:0118&r=ets |
| By: | Ajax R. B. Moreira; Dani Gamerman |
| Abstract: | This paper is concerned with the study of Bayesian inference procedures to commonly used time series models. In particular, the dynamic or state-space models, the time-varying vector autoregressive model and the structural vector autoregressive model are considered in detail. Inference procedures are based on a hybrid integration scheme where state parameters are analytically integrated and hyperparameters are integrated by Markov chain Monte Carlo methods. Credibility regions for forecasts and impulse responses are then derived. The procedures are illustrated in real data sets. Este artigo utiliza procedimentos de inferência bayesiana para estimar modelos econométricos freqüentemente usados. Em particular, os modelos dinâmicos ou de espaço de estado são considerados detalhadamente. Procedimentos de inferência baseiam-se em esquemas de integração híbridos, em que as variáveis de estado são integradas analiticamente, e os hiperparâmetros são integrados utilizando o método de cadeias de Markov de Monte Carlo. As regiões de credibilidade da previsão e das funções de resposta a impulso são também avaliadas. Os procedimentos são ilustrados com dados reais da economia brasileira. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:ipe:ipetds:0105&r=ets |
| By: | Didenko, Alexander; Dubovikov, Michael; Poutko, Boris |
| Abstract: | The paper develops an algorithm for making long-term (up to three months ahead) predictions of volatility reversals based on long memory properties of financial time series. The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale is used to decompose volatility into two dynamic components: specific and structural. We introduce two separate models for both, based on different principles and capable of catching long uptrends in volatility. To test statistical significance of its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility. Our results could be used for forecasting points of market transition to an unstable state. |
| Keywords: | stock market; price risk; fractal dimension; market crash; ARCH-GARCH; range-based volatility models; multi-scale volatility; volatility reversals; technical analysis. |
| JEL: | C14 C49 C5 C58 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:63708&r=ets |
| By: | Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Chihwa Kao (Department of Economics, Center for Policy Research, 426 Eggers Hall, Syracuse University, Syracuse, NY 13244); Long Liu (Department of Economics, College of Business, University of Texas at San Antonio) |
| Abstract: | This paper studies the estimation of change point in panel models. We extend Bai (2010) and Feng, Kao and Lazarová (2009) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered. |
| Keywords: | Panel Data, Change Point, Consistency, Nonstationarity |
| JEL: | C12 C13 C22 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:178&r=ets |
| By: | Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Qu Feng (Division of Economics, School of Humanities and Social Sciences, Nanyang Technological University); Chihwa Kao (Center for Policy Research, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244) |
| Abstract: | This paper extends Pesaran's (2006) work on common correlated effects (CCE) estimators for large heterogeneous panels with a general multifactor error structure by allowing for unknown common structural breaks. Structural breaks due to new policy implementation or major technological shocks, are more likely to occur over a longer time span. Consequently, ignoring structural breaks may lead to inconsistent estimation and invalid inference. We propose a general framework that includes heterogeneous panel data models and structural break models as special cases. The least squares method proposed by Bai (1997a, 2010) is applied to estimate the common change points, and the consistency of the estimated change points is established. We find that the CCE estimator has the same asymptotic distribution as if the true change points were known. Additionally, Monte Carlo simulations are used to verify the main results of this paper. |
| Keywords: | Heterogeneous Panels, Cross-sectional Dependence, Structural Breaks, Common Correlated Effects |
| JEL: | C23 C33 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:179&r=ets |
| By: | Elcyon Caidado Rocha Lima |
| Abstract: | Johansen (2002) suggests a counterfactual experiment that can be implemented in the vector autoregressive model to interpret the coefficients of an identified cointegrating relation. This article proposes an alternative counterfactual experiment (“design of experiment”) that, contrary to the one suggested by Johansen, does not imply a dichotomy of short run and long run values. The experiment interprets the coefficients of an identified cointegrating relation. It is based on the idea that the coefficients, and some operations with them, are projections- at different horizons -conditional on paths of the variables of the model and on exogenous shocks in the error terms of the equations of a structural VAR. The model dynamics can be used to test if these values can be generated by exogenous shocks in these error terms. It is also feasible to construct, as was shown by Doan, Litterman and Sims (1984), a plausibility index for these exogenous shocks. The analysis of the proposed conditional projections can be as useful as checking coefficients, of the matrix with the contemporaneous correlations among variables, for the correct sign and significance in a structural VAR. It can be an important complement to the impulse response function analysis. Em Johansen (2002) é sugerido um “desenho de experimento” (design of experiment), que pode ser implementado no modelo de auto-regressão vetorial, com o objetivo de se interpretar os coeficientes numa relação de co-integração identificada. Neste artigo propõe-se um “desenho de experimento” alternativo que, ao contrário do de Johansen, não parte da dicotomia entre o curto e o longo prazos. O experimento permite interpretar os coeficientes em uma relação de co-integração identificada. Partimos da idéia de que os coeficientes, e determinadas operações com eles, são previsões condicionadas - em diversos horizontes - a certos valores das variáveis do modelo e dos choques exógenos nos erros das equações estruturais do VAR. A dinâmica do modelo pode ser utilizada para testar se esses valores podem ser gerados por choques exógenos nesses erros. Pode-se também construir [ver, a esse respeito, Doan, Litterman e Sims (1984)] um índice de plausibilidade desses choques exógenos. A análise das previsões condicionais de curto e longo prazos pode ser tão útil quanto a inspeção dos sinais e significância dos coeficientes da matriz com as relações contemporâneas entre as variáveis em um VAR estrutural. Ela pode ser um complemento importante da análise das funções de resposta a impulsos. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:ipe:ipetds:0142&r=ets |