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on Econometric Time Series |
| By: | Kristoffer Nimark |
| Abstract: | This note describes how the Kalman filter can be modified to allow for the vector of observables to be a function of lagged variables without increasing the dimension of the state vector in the filter. This is useful in applications where it is desirable to keep the dimension of the state vector low. The modified filter and accompanying code (which nests the standard filter) can be used to compute (i) the steady state Kalman filter (ii) the log likelihood of a parameterized state space model conditional on a history of observables (iii) a smoothed estimate of latent state variables and (iv) a draw from the distribution of latent states conditional on a history of observables. |
| Keywords: | Kalman filter, lagged observables, Kalman smoother, simulation smoother |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1182&r=ets |
| By: | Jouchi Nakajima (Institute for Monetary and Economic Studies, Bank of Japan. Currently in the Personnel and Corporate Affairs Department ( studying at Duke University, E-mail: jouchi.nakajimaa@sstat.duke.edu)); Tsuyoshi Kunihama (Graduate student, Graduate School of Economics, University of Tokyo. (E-mail: ee097005@mail.ecc.u-tokyo.ac.jp)); Yasuhiro Omori (Professor, Faculty of Economics, University of Tokyo. (E-mail: omori@e.u-tokyo.ac.jp)); Sylvia Fruwirth-Scnatter (Professor, Department of Applied Statistics, Johannes Kepler University in Lintz. (E-mail: Sylvia.Fruehwirth-Schnatter@jku.at)) |
| Abstract: | A new state space approach is proposed to model the time- dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit a very accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence for time-dependence among the observed minimum returns. |
| Keywords: | Extreme values, Generalized extreme value distribution, Markov chain Monte Carlo, Mixture sampler, State space model, Stock returns |
| JEL: | C11 C51 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:09-e-32&r=ets |
| By: | Richard Anton Braun (Faculty of Economics, University of Tokyo); Huiyu Li (Graduate School of Economics, University of Tokyo); John Stachurski (Institute of Economic Research, Kyoto University) |
| Abstract: | We propose a generalized conditional Monte Carlo technique for computing densities in economic models. Global consistency and functional asymptotic normality are established under ergodicity assumptions on the simulated process. The asymptotic normality result allows us to characterize the asymptotic distribution of the error in density space, and implies faster convergence than nonparametric kernel density estimators. We show that our results nest several other well-known density estimators, and illustrate potential applications. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2009cf678&r=ets |
| By: | Michael McAleer (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo); Marcelo C. Medeiros (Department of Economics, Pontifical Catholic University of Rio de Janeiro) |
| Abstract: | In this paper we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 indexes. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high frequency intra-day returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analyzed in the paper. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2009cf686&r=ets |
| By: | D Agostino, Antonello; Gambetti, Luca; Giannone, Domenico |
| Abstract: | The aim of this paper is to assess whether explicitly modeling structural change increases the accuracy of macroeconomic forecasts. We produce real time out-of-sample forecasts for inflation, the unemployment rate and the interest rate using a Time-Varying Coefficients VAR with Stochastic Volatility (TV-VAR) for the US. The model generates accurate predictions for the three variables. In particular for inflation the TV-VAR outperforms, in terms of mean square forecast error, all the competing models: fixed coefficients VARs, Time-Varying ARs and the naïve random walk model. These results are also shown to hold over the most recent period in which it has been hard to forecast inflation. |
| Keywords: | Forecasting; Inflation; Stochastic Volatility; Time Varying Vector Autoregression |
| JEL: | C32 E37 E47 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:7542&r=ets |
| By: | Guerron-Quintana, Pablo A.; Inoue, Atsushi; Kilian, Lutz |
| Abstract: | We show that in weakly identified models (1) the posterior mode will not be a consistent estimator of the true parameter vector, (2) the posterior distribution will not be Gaussian even asymptotically, and (3) Bayesian credible sets and frequentist confidence sets will not coincide asymptotically. This means that Bayesian DSGE estimation should not be interpreted merely as a convenient device for obtaining asymptotically valid point estimates and confidence sets from the posterior distribution. As an alternative, we develop new frequentist confidence sets for structural DSGE model parameters that remain asymptotically valid regardless of the strength of the identification. |
| Keywords: | Bayes factor; Bayesian estimation; Confidence set; DSGE models; Identification; Inference; Likelihood ratio |
| JEL: | C32 C52 E30 E50 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:7447&r=ets |
| By: | Kuzin, Vladimir; Marcellino, Massimiliano; Schumacher, Christian |
| Abstract: | This paper compares the mixed-data sampling (MIDAS) and mixed-frequency VAR (MF-VAR) approaches to model specification in the presence of mixed-frequency data, e.g., monthly and quarterly series. MIDAS leads to parsimonious models based on exponential lag polynomials for the coefficients, whereas MF-VAR does not restrict the dynamics and therefore can suffer from the curse of dimensionality. But if the restrictions imposed by MIDAS are too stringent, the MF-VAR can perform better. Hence, it is difficult to rank MIDAS and MF-VAR a priori, and their relative ranking is better evaluated empirically. In this paper, we compare their performance in a relevant case for policy making, i.e., nowcasting and forecasting quarterly GDP growth in the euro area, on a monthly basis and using a set of 20 monthly indicators. It turns out that the two approaches are more complementary than substitutes, since MF-VAR tends to perform better for longer horizons, whereas MIDAS for shorter horizons. |
| Keywords: | euro area growth; MIDAS; mixed-frequency data; mixed-frequency VAR; nowcasting |
| JEL: | C53 E37 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:7445&r=ets |
| By: | Bacchetta, Philippe; Beutler, Toni; van Wincoop, Eric |
| Abstract: | The empirical literature on nominal exchange rates shows that the current exchange rate is often a better predictor of future exchange rates than a linear combination of macroeconomic fundamentals. This result is behind the famous Meese-Rogoff puzzle. In this paper we evaluate whether parameter instability can account for this puzzle. We consider a theoretical reduced-form relationship between the exchange rate and fundamentals in which parameters are either constant or time varying. We calibrate the model to data for exchange rates and fundamentals and conduct the exact same Meese-Rogoff exercise with data generated by the model. Our main finding is that the impact of time-varying parameters on the prediction performance is either very small or goes in the wrong direction. To help interpret the findings, we derive theoretical results on the impact of time-varying parameters on the out-of-sample forecasting performance of the model. We conclude that it is not time-varying parameters, but rather small sample estimation bias, that explains the Meese-Rogoff puzzle. |
| Keywords: | Exchange rate forecasting; exchange rate models |
| JEL: | F31 F37 F41 |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:7383&r=ets |
| By: | Torben G. Andersen; Dobrislav Dobrev; Ernst Schaumburg |
| Abstract: | We propose two new jump-robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tripower variation measure and displays better finite-sample robustness to both jumps and the occurrence of "zero'' returns in the sample. Unlike the bipower variation measure, the new estimators allow for the development of an asymptotic limit theory in the presence of jumps. Finally, they retain the local nature associated with the low order multipower variation measures. This proves essential for alleviating finite sample biases arising from the pronounced intraday volatility pattern which afflict alternative jump-robust estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks and an extensive simulation study corroborate the robustness and efficiency properties of the new estimators. |
| JEL: | C14 C15 C22 C80 G10 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:15533&r=ets |