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on Econometric Time Series |
| By: | D'Agostino, Antonello (Central Bank and Financial Services Authority of Ireland); Bermingham, Colin (Central Bank and Financial Services Authority of Ireland) |
| Abstract: | The issue of forecast aggregation is to determine whether it is better to forecast a series directly or instead construct forecasts of its components and then sum these component forecasts. Notwithstanding some underlying theoretical results, it is gener- ally accepted that forecast aggregation is an empirical issue. Empirical results in the literature often go unexplained. This leaves forecasters in the dark when confronted with the option of forecast aggregation. We take our empirical exercise a step further by considering the underlying issues in more detail. We analyse two price datasets, one for the United States and one for the Euro Area, which have distinctive dynamics and provide a guide to model choice. We also consider multiple levels of aggregation for each dataset. The models include an autoregressive model, a factor augmented autoregressive model, a large Bayesian VAR and a time-varying model with stochastic volatility. We find that once the appropriate model has been found, forecast aggrega- tion can significantly improve forecast performance. These results are robust to the choice of data transformation. |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:cbi:wpaper:8/rt/10&r=ets |
| By: | Nikolaus Hautsch (Humboldt-Universität zu Berlin); Mark Podolskij (ETH Zurich and CREATES) |
| Abstract: | This paper provides theory as well as empirical results for pre-averaging estimators of the daily quadratic variation of asset prices. We derive jump robust inference for pre-averaging estimators, corresponding feasible central limit theorems and an explicit test on serial dependence in microstructure noise. Using transaction data of different stocks traded at the NYSE, we analyze the estimators’ sensitivity to the choice of the pre-averaging bandwidth and suggest an optimal interval length. Moreover, we investigate the dependence of pre-averaging based inference on the sampling scheme, the sampling frequency, microstructure noise properties as well as the occurrence of jumps. As a result of a detailed empirical study we provide guidance for optimal implementation of pre-averaging estimators and discuss potential pitfalls in practice. |
| Keywords: | Quadratic Variation, MarketMicrostructure Noise, Pre-averaging, Sampling Schemes, Jumps |
| JEL: | C14 C22 G10 |
| Date: | 2010–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-29&r=ets |
| By: | Martin M. Andreasen (Bank of England and CREATES) |
| Abstract: | This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Cen- tral Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models solved up to third order. A Monte Carlo study shows that this QML estimator is basically unbiased and normally distributed infi?nite samples for DSGE models solved using a second order or a third order approximation. These results hold even when structural shocks are Gaussian, Laplace distributed, or display stochastic volatility. |
| Keywords: | Non-linear filtering, Non-Gaussian shocks, Quasi Maximum Likelihood, Stochastic volatility, Third order perturbation. |
| JEL: | C13 C15 E10 E32 |
| Date: | 2010–07–20 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-30&r=ets |
| By: | David F. Hendry; Grayham E. Mizon |
| Abstract: | Almost no economic time series is either weakly or strictly stationary: distributions of economic variables shift over time. Thus, the present treatment of expectations in economic theories of inter-temporal optimization is inappropriate. It cannot be proved that conditional expectations based on the current distribution are minimum mean-square error 1-step ahead predictors when unanticipated breaks occur, and consequentially, the law of iterated expectations then fails inter-temporally. A second consequence is that dynamic stochastic general equilibrium models are intrinsically non-structural. |
| Keywords: | Inter-temporal optimization, Conditional expectations, Law of interated expectations, Unanticipated breaks |
| JEL: | C02 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:497&r=ets |
| By: | Peers, Y.; Fok, D.; Franses, Ph.H.B.F. |
| Abstract: | Although high frequency diffusion data is nowadays available, common practice is still to only use yearly figures in order to get rid of seasonality. This paper proposes a diffusion model that captures seasonality in a way that naturally matches the overall S-shaped pattern. The model is based on the assumption that additional sales at seasonal peaks are drawn from previous or future periods. This implies that the seasonal pattern does not influence the underlying diffusion pattern. The model is compared with alternative approaches through simulations and empirical examples. As alternatives we consider the standard Generalized Bass Model and ignoring seasonality by using the basic Bass model. One of our main findings is that modeling seasonality in a Generalized Bass Model does generate good predictions, but gives biased estimates. In particular, the market potential parameter will be underestimated. Ignoring seasonality gives the true parameter estimates if the data is available of the entire diffusion period. However, when only part of the diffusion period is available estimates and predictions become biased. Our model gives correct estimates and predictions even if the full diffusion process is not yet available. |
| Keywords: | new product diffusion;seasonality |
| Date: | 2010–07–15 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureri:1765020378&r=ets |
| By: | Mohitosh Kejriwal; Claude Lopez |
| Abstract: | Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi?cation of countries according to the ?growth shift?, ?level shift? and ?linear trend? hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis. |
| Keywords: | growth shift, level shift, structural change, trend breaks, unit root |
| JEL: | C22 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1227&r=ets |
| By: | Liu, Jun M.; Chen, Rong; Yao, Qiwei |
| Abstract: | In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modelling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:ner:lselon:http://eprints.lse.ac.uk/28868/&r=ets |
| By: | Hoffmann, Marc; Munk, Axel; Schmidt-Hieber, Johannes |
| Abstract: | We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility. |
| Keywords: | Adaptive estimation; diffusion processes; high-frequency data; microstructure noise; minimax estimation; semimartingales; wavelets. |
| JEL: | C14 C0 C22 |
| Date: | 2010–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24562&r=ets |