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on Econometric Time Series |
| By: | Muhammad Akram (Department of Econometrics and Business Statistics); Rob J Hyndman (Department of Econometrics and Business Statistics,Monash University); J. Keith Ord (McDonough School of Business,Georgetown University) |
| Abstract: | The most common forecasting methods in business are based on exponential smoothing and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process. We first demonstrate that prediction distributions from some commonly used state space models may have an infinite variance beyond a certain forecasting horizon. For multiplicative error models which do not have this flaw, we show that sample paths will converge almost surely to zero even when the error distribution is non-Gaussian. We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model. We then explore the implications of our results for inference, and compare the short-term forecasting performance of the various models using data on the weekly sales of over three hundred items of costume jewelry. The main findings of the research are that the Gaussian approximation is adequate for estimation and one-step-ahead forecasting. However, as the forecasting horizon increases, the approximate prediction intervals become increasingly problematic. When the model is to be used for simulation purposes, a suitably specified scheme must be employed. |
| Keywords: | forecasting; time series; exponential smoothing; positive-valued processes; seasonality; state space models. |
| JEL: | C1 C5 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:gwc:wpaper:2008-003&r=ets |
| By: | Ahlgren, Niklas (Hanken School of Economics); Juselius, Mikael (University of Helsinki) |
| Abstract: | Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence. |
| Keywords: | asymptotic local power; cointegration; companion matrix; convergence; initial condition; likelihood ratio test; unit root |
| Date: | 2009–05–13 |
| URL: | http://d.repec.org/n?u=RePEc:hhb:hanken:0539&r=ets |
| By: | Richard T. Baille; Claudio Morana |
| Abstract: | Previous models of monthly CPI inflation time series have focused on possible regime shifts, non-linearities and the feature of long memory. This paper proposes a new time series model, named Adaptive ARFIMA; which appears well suited to describe inflation and potentially other economic time series data. The Adaptive ARFIMA model includes a time dependent intercept term which follows a Flexible Fourier Form. The model appears to be capable of succesfully dealing with various forms of breaks and discontinities in the conditional mean of a time series. Simulation evidence justifies estimation by approximate MLE and model specfication through robust inference based on QMLE. The Adaptive ARFIMA model when supplemented with conditional variance models is found to provide a good representation of the G7 monthly CPI inflation series. |
| Keywords: | ARFIMA; FIGARCH, long memory, structural change, inflation, G7. |
| JEL: | C15 C22 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:icr:wpmath:06-2009&r=ets |
| By: | Franses, Ph.H.B.F.; Dijk, D.J.C. van (Erasmus Econometric Institute) |
| Abstract: | We analyse the impact of the Engle and Granger (1987) article by its citations over time, and find evidence of a second life starting in the new millennium. Next, we propose a possible explanation of the success of this citation classic. We argue that the conditions for its success were just right at the time of its appearance, because of the growing emphasis on time-series properties in econometric modelling, the empirical importance of stochastic trends, the availability of sufficiently long macro-economic time series, and the availability of personal computers and econometric software to carry out the new techniques. |
| Keywords: | cointegration;citations |
| Date: | 2009–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765015779&r=ets |
| By: | Charalambos G. Tsangarides; Alin Mirestean; Huigang Chen |
| Abstract: | Bayesian Model Averaging (BMA) provides a coherent mechanism to address the problem of model uncertainty. In this paper we extend the BMA framework to panel data models where the lagged dependent variable as well as endogenous variables appear as regressors. We propose a Limited Information Bayesian Model Averaging (LIBMA) methodology and then test it using simulated data. Simulation results suggest that asymptotically our methodology performs well both in Bayesian model selection and averaging. In particular, LIBMA recovers the data generating process very well, with high posterior inclusion probabilities for all the relevant regressors, and parameter estimates very close to the true values. These findings suggest that our methodology is well suited for inference in dynamic panel data models with short time periods in the presence of endogenous regressors under model uncertainty. |
| Date: | 2009–04–17 |
| URL: | http://d.repec.org/n?u=RePEc:imf:imfwpa:09/74&r=ets |
| By: | Michel Beine; Bertrand Candelon; Jan Piplack |
| Abstract: | This paper analyzes common factors in the continuous volatility component, co-extreme and co-jump behavior of a sample of stock market indices. In order to identify those components in stock price processes during a trading day we use high-frequency data and techniques. We show that in most of the cases one common factor is enough to describe the largest part of the international variation in the continuous part of volatility and that this factor's importance has increased over time. Furthermore, we find strong evidence for asymmetries between extremely negative and positive co-extreme close-open returns and of negative and positive co-jumps across countries.. |
| Keywords: | Volatility, realized volatility, high-frequency, comovements, cojumps |
| JEL: | G15 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:0910&r=ets |
| By: | Lanouar Charfeddine (OEP - Université de Marne-la-Vallée); Dominique Guegan (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | Are structural breaks models true switching models or long memory processes ? The answer to this question remain ambiguous. A lot of papers, in recent years, have dealt with this problem. For instance, Diebold and Inoue (2001) and Granger and Hyung (2004) show, under specific conditions, that switching models and long memory processes can be easily confused. In this paper, using several generating models like the mean-plus-noise model, the STOchastic Permanent BREAK model, the Markov switching model, the TAR model, the sign model and the Structural CHange model (SCH) and several estimation techiques like the GPH technique, the Exact Local Whittle (ELW) and the Wavelet methods, we show that, if the answer is quite simple in some cases, it can be mitigate in other cases. Using French and American inflation rates, we show that these series cannot be characterized by the same class of models. The main result of this study suggests that estimating the long memory parameter without taking account existence of breaks in the data sets may lead to misspecification and to overestimate the true parameter. |
| Keywords: | Structural breaks models, Spurious long memory behavior, inflation series. |
| JEL: | C13 C32 E3 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09022&r=ets |
| By: | Dominique Guegan (Centre d'Economie de la Sorbonne - Paris School of Economics); Zhiping Lu (Centre d'Economie de la Sorbonne et East China Normal University) |
| Abstract: | Long memory processes have been extensively studied over the past decades. When dealing with the financial and economic data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity can exist inside financial data sets. To take into account this kind of phenomena, we propose a new class of stochastic process : the locally stationary k-factor Gegenbauer process. We describe a procedure of estimating consistently the time-varying parameters by applying the discrete wavelet packet transform (DWPT). The robustness of the algorithm is investigated through simulation study. An application based on the error correction term of fractional cointegration analysis of the Nikkei Stock Average 225 index is proposed. |
| Keywords: | Discrete wavelet packet transform, Gegenbauer process, Nikkei Stock Average 225 index, non-stationarity, ordinary least square estimation. |
| JEL: | C13 C14 C15 C22 C63 G15 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09015&r=ets |
| By: | Ioannis Kasparis; Peter C. B. Phillips |
| Abstract: | Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed. |
| Keywords: | Dynamic misspecification, Functional regression, Integrable function, Integrated process, Local time, Misspecification, Mixed normality, Nonlinear cointegration, Nonparametric regression |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:2-2009&r=ets |