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on Econometric Time Series |
| By: | Daisuke Nagakura (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp)); Toshiaki Watanabe (Professor, Institute of Economic Research, Hitotsubashi University, and Institute for Monetary and Economic Studies, Bank of Japan (E-mail: watanabe@hit-u.ac.jp, toshiaki.watanabe@boj.or.jp)) |
| Abstract: | We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency. |
| Keywords: | Realized Variance, Integrated Variance, Microstructure Noise |
| JEL: | C0 G0 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:09-e-11&r=ets |
| By: | Areosa, W.D.; McAleer, M.; Medeiros, M.C. (Erasmus Econometric Institute) |
| Abstract: | Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, Smooth Transition Regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature. |
| Keywords: | smooth transition;nonlinear models;nonlinear instrumental variables;generalized method of moments;endogeneity;inflation targeting |
| Date: | 2008–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765014154&r=ets |
| By: | Franses, Ph.H.B.F. (Erasmus Econometric Institute) |
| Abstract: | In this paper it is advocated to select a model only if it significantly contributes to the accuracy of a combined forecast. Using hold-out-data forecasts of individual models and of the combined forecast, a useful test for equal forecast accuracy can be designed. An illustration for real-time forecasts for GDP in the Netherlands shows its ease of use. |
| Keywords: | forecast combination;model selection |
| Date: | 2008–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765012552&r=ets |
| By: | Pooter, M.D. de; Ravazzolo, F.; Segers, R.; Dijk, H.K. van (Erasmus Econometric Institute) |
| Abstract: | Several lessons learnt from a Bayesian analysis of basic macroeconomic time series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time series models like unit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented. |
| Keywords: | Gibbs sampler;MCMC;autocorrelation;nonstationarity;reduced rank models;state space models;error correction models;random effects panel data models;Bayesian model averaging |
| Date: | 2008–08–25 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765013055&r=ets |
| By: | Franses, Ph.H.B.F.; Segers, R. (Erasmus Econometric Institute) |
| Abstract: | We analyze five vintages of eighteen quarterly macroeconomic variables for the Netherlands and we focus on the degree of deterministic seasonality in these series. We document that the data show most such deterministic seasonality for their first release vintage and for the last available vintage. In between vintages show a variety of seasonal patterns. We show that seasonal patterns in later vintages can hardly be predicted by those in earlier vintages. The consequences of these findings for the interpretation and modeling of macroeconomic data are discussed. |
| Keywords: | seasonality;real-time data |
| Date: | 2008–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765012211&r=ets |
| By: | Franses, Ph.H.B.F. (Erasmus Econometric Institute) |
| Abstract: | This paper links judgemental adjustment of model-based forecasts with the potential presence of exceptional observations in time series. Specific attention is given to current and future additive outliers, as these require most consideration. A brief illustration to a quarterly real GDP series demonstrates various issues. The main focus of the paper is on various testable propositions, which should facilitate the creation and the evaluation of judgemental adjustment of time series forecasts. |
| Date: | 2008–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765011705&r=ets |
| By: | Kunst, R.M.; Franses, Ph.H.B.F. (Erasmus Econometric Institute) |
| Abstract: | We consider the problem of testing for seasonal unit roots in monthly panel data. To this aim, we generalize the quarterly CHEGY test to the monthly case. This parametric test is contrasted with a new nonparametric test, which is the panel counterpart to the univariate RURS test that relies on counting extrema in time series. All methods are applied to an empirical data set on tourism in Austrian provinces. The power properties of the tests are evaluated in simulation experiments that are tuned to the tourism data. |
| Keywords: | seasonality;nonparametric test;unit roots;panel;tourism |
| Date: | 2009–02–19 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765014861&r=ets |
| By: | M. Hashem Pesaran; Andreas Pick |
| Abstract: | This paper considers forecast averaging when the same model is used but estimation is carried out over different estimation windows. It develops theoretical results for random walks when their drift and/or volatility are subject to one or more structural breaks. It is shown that compared to using forecasts based on a single estimation window, averaging over estimation windows leads to a lower bias and to a lower root mean square forecast error for all but the smallest of breaks. Similar results are also obtained when observations are exponentially down-weighted, although in this case the performance of forecasts based on exponential down-weighting critically depends on the choice of the weighting coefficient. The forecasting techniques are applied to 20 weekly series of stock market futures and it is found that average forecasting methods in general perform better than using forecasts based on a single estimation window. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:dnb:dnbwpp:207&r=ets |
| By: | Kirstin Hubrich (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.); Kenneth D. West (University of Wisconsin, Madison, Department of Economics, 1180 Observatory Drive, Madison, WI 53706, USA.) |
| Abstract: | We propose two new procedures for comparing the mean squared prediction error (MSPE) of a benchmark model to the MSPEs of a small set of alternative models that nest the benchmark. Our procedures compare the benchmark to all the alternative models simultaneously rather than sequentially, and do not require reestimation of models as part of a bootstrap procedure. Both procedures adjust MSPE differences in accordance with Clark and West (2007); one procedure then examines the maximum t-statistic, the other computes a chi-squared statistic. Our simulations examine the proposed procedures and two existing procedures that do not adjust the MSPE differences: a chi-squared statistic, and White’s (2000) reality check. In these simulations, the two statistics that adjust MSPE differences have most accurate size, and the procedure that looks at the maximum t-statistic has best power. We illustrate, our procedures by comparing forecasts of different models for U.S. inflation. JEL Classification: C32, C53, E37. |
| Keywords: | Out-of-sample, prediction, testing, multiple model comparisons, inflation forecasting. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:200901030&r=ets |