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on Econometric Time Series |
| By: | Roger Hammersland (Norges Bank) |
| Abstract: | This paper addresses cointegration in small cross-sectional panel data models. In addition to dealing with cointegrating relationships within the cross-sectional dimension, the paper explicitly addresses the issue of cointegration between cross-sections. The approach is based upon a well-known distributional result for the trace test when some of the cointegrating vectors are a priori known, and advocates a three-step procedure for the identification of the cointegrating space when dealing with two-dimensional data. The first step of this procedure utilizes traditional techniques to identify the long-run relationships within each cross-sectional unit separately. In the second step these first step relationships are then treated as known when searching for potential long run relationships between units in a joint analysis comprising the whole cross-sectional dimension. The third step of the procedure then finally reestimate all free parameters of the identified long-run structure to get rid of a potential simultaneity bias as a result of a non-diagonal covariance matrix. Identification of the long-run structures of Norwegian exports and international interest rate relationships are used as examples. Norwegian mainland exports have here been divided into two cross-sectional units; the traditional goods sector and the service sector. While in the study of international interest rate relationships the two sectors investigated are Germany and the US. The examples are used to address the more general issues of the degree of independence in capital markets and in goods markets of small open economies. |
| Keywords: | Cointegration, Panel data, transmission mechanism, monopolistic competition, exports |
| JEL: | C32 C33 E43 F12 F41 |
| Date: | 2004–11–12 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2004_15&r=ets |
| By: | M. Hashem Pesaran; Takashi Yamagata |
| Abstract: | This paper proposes a modified version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). We exploit the cross section dispersion of individual slopes weighted by their relative precision. Using Monte Carlo experiments, we show that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. For autoregressive (AR) models the test performs well for moderate values of the root of the autoregressive process, but with roots near unity a bias-corrected bootstrapped version performs well even if N is large relative to T. The cross section dispersion tests are used to test the homogeneity of slopes in autoregressive models of individual earnings using the PSID data and show statistically significant evidence of slope heterogeneity in the earnings dynamics. |
| Keywords: | Testing Slope Homogeneity, Hausman Type Tests, Cross Section Dispersion Tests, Monte Carlo Results, PSID Earnings Dynamics |
| JEL: | C12 C33 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0513&r=ets |
| By: | Jean-Marie Dufour; Tarek Jouini |
| Abstract: | In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed. <P>Dans cet article, nous étudions la distribution asymptotique d’un estimateur linéaire simple en deux étapes (de type Hannan-Rissanen) pour un processus vectoriel autorégressif-moyenne-mobile (VARMA) stationnaire et inversible, formulé sous la forme échelon. Nous donnons des conditions générales qui assurent la convergence et la normalité asymptotique de l’estimateur. Nous fournissons aussi un estimateur convergent de la matrice de covariance asymptotique de l’estimateur, ce qui permet de construire facilement des tests et des intervalles de confiance. |
| Keywords: | time series, VARMA, stationary; invertible; echelon form, estimation, asymptotic normality, bootstrap, Hannan-Rissanen, séries chronologiques; VARMA, stationnaire, inversible, forme échelon, estimation, normalité asymptotique, bootstrap, Hannan-Rissanen |
| JEL: | C3 C32 C53 |
| Date: | 2005–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2005s-06&r=ets |
| By: | A Garratt; K Lee; M H Pesaran; Yongcheol Shin |
| Abstract: | In this paper we discuss the 'structural cointegrating VAR' approach to macroeconometric modelling and compare it to other approaches currently followed in the literature, namely the large-scale simultaneous equation macroeconometric models, the structural VARs, and the dynamic stochastic general equilibrium models. The structural cointegrating VAR approach has the attractive features that the estimated long-run relationships embedded in the model are theory consistent, and have a clear economic interpretation, and yet the short-run dynamics are flexibly estimated within a VAR framework. The approach is illustrated using a small quarterly macroeconometric model of the UK. The uses of the model in impulse response analysis and probability forecasting is also discussed. |
| Keywords: | Structural Cointegrating VAR, Macroeconomic Modelling, Generalised Impulse Responses, Persistence Profiles, Probability Forecasts. |
| JEL: | C32 C5 E17 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:8&r=ets |
| By: | Michel Normandin (IEA, HEC Montréal) |
| Abstract: | This paper presents and assesses a procedure to estimate conventional parameters characterizing fluctuations at the business cycle frequency, when the economic agents’ information set is superior to the econometrician’s one. Specifically, we first generalize the conditions under which the econometrician can estimate these ‘cyclical fluctuation’ parameters from augmented laws of motion for forcing variables that fully recover the agents’ superior information. Second, we document the econometric properties of the estimates when the augmented laws of motion are possibly misspecified. Third, we assess the ability of certain information criteria to detect the presence of superior information. |
| Keywords: | Block bootstrap; Hidden variables; Laws of motion for forcing variables; Monte Carlo simulations. |
| JEL: | C14 C15 C32 E32 |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0413&r=ets |
| By: | Jeroen V.K. Rombouts (IEA, HEC Montréal); Marno Verbeek |
| Abstract: | In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed. |
| Keywords: | multivariate GARCH, semi-parametric estimation, Value-at-Risk, asset allocation. |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0414&r=ets |
| By: | Angela Huang (Reserve Bank of New Zealand) |
| Abstract: | Numerous empirical studies investigate whether exchange rates are related to `economic fundamentals' in the long-run and find a range of relationships through cointegration analysis. We report similar cointegrating relationships for the value of the New Zealand dollar relative to the US dollar (NZD/USD) and for the value of the New Zealand dollar relative to the Australian dollar (NZD/AUD). These include determinants such as commodity prices, 90-day interest rate differentials, and inflation and growth differentials. However, Godbout and van Norden (1997) demonstrate that finite-sample problems may have affected the conclusions of such cointegration studies. Through a simple Monte Carlo study, we consider whether the cointegration coefficients can reasonably be interpreted as `long-run' elasticities of the exchange rate to changes in fundamental variables. The simulation results suggest that given a relatively short span of data it is possible for cointegration analysis to indicate that a long-run relationship has been found when in fact there is only a cyclical relationship. Therefore caution is advised when interpreting the empirical results and making policy assessments about the nature of exchange movements relative to its broad trend. |
| JEL: | F31 C15 C22 |
| Date: | 2004–10 |
| URL: | http://d.repec.org/n?u=RePEc:nzb:nzbdps:2004/08&r=ets |
| By: | Nabyl Belgrade (CERMSEM et CDC IXIS-CM,R&D) |
| Abstract: | In this paper, we examine various methods in discrete time to extract and estimate the seasonality component of the CPI curve. One estimated, we show how to include this effect in the construction of the forward CPI curve. We then explain how to link it to a continuous time market model. Last but not least, we study the consistency between the various estimation methods, based on the cycle theory. |
| Keywords: | Historical & forward CPI curve; decomposition scheme; trend; regular & irregular cycle; replication |
| Date: | 2004–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b04051&r=ets |
| By: | John Stachurski (CORE); Cuong Le Van (CERMSEM) |
| Abstract: | The paper gives conditions under which stationary distributions of Markov models depend continuously on the parameters. It extends a well-known parametric continuity theorem for compact state space to the unbounded setting of standard econometrics and time series analysis. Applications to several theoretical and estimation problems are outlined. |
| Keywords: | Stationary distribution; parametric continuity; Markov process; Solow-Phelps golden rule; Foias operator; V norm-like function; Feller property |
| JEL: | O41 |
| Date: | 2004–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b04059&r=ets |
| By: | Cuong Le Van (CERMSEM); John Stachurski (CORE) |
| Abstract: | We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and assigns positive probability to all absorbing sets. |
| Keywords: | Discrete time Markov chains; invariant distribution; nondecomposability; irreducibility; absorbing set |
| JEL: | O41 |
| Date: | 2004–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b04061&r=ets |
| By: | Torben G. Andersen (Kellogg School of Management, Northwestern University); Tim Bollerslev (Department of Economics, Duke University); Peter F. Christoffersen (Faculty of Management, McGill University); Francis X. Diebold (Department of Economics, University of Pennsylvania) |
| Abstract: | Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. |
| JEL: | C10 C53 G1 |
| Date: | 2005–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:05-011&r=ets |