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on Econometric Time Series |
| By: | Andrew Binning; Junior Maih |
| Abstract: | In this paper we take three well known Sigma Point Filters, namely the Unscented Kalman Filter, the Divided Difference Filter, and the Cubature Kalman Filter, and extend them to allow for a very general class of dynamic nonlinear regime switching models. Using both a Monte Carlo study and real data, we investigate the properties of our proposed filters by using a regime switching DSGE model solved using nonlinear methods. We find that the proposed filters perform well. They are both fast and reasonably accurate, and as a result they will provide practitioners with a convenient alternative to Sequential Monte Carlo methods. We also investigate the concept of observability and its implications in the context of the nonlinear filters developed and propose some heuristics. Finally, we provide in the RISE toolbox, the codes implementing these three novel filters. |
| Keywords: | Regime Switching, Higher-order Perturbation, Sigma Point Filters, Nonlinear DSGE estimation, Observability |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:bny:wpaper:0032&r=ets |
| By: | Jean-Marie Dufour; Tarek Jouini |
| Abstract: | Usual inference methods for stable distributions are typically based on limit distributions. But asymptotic approximations can easily be unreliable in such cases, for standard regularity conditions may not apply or may hold only weakly. This paper proposes finite-sample tests and confidence sets for tail thickness and asymmetry parameters (a and b ) of stable distributions. The confidence sets are built by inverting exact goodness-of-fit tests for hypotheses which assign specific values to these parameters. We propose extensions of the Kolmogorov-Smirnov, Shapiro-Wilk and Filliben criteria, as well as the quantile-based statistics proposed by McCulloch (1986) in order to better capture tail behavior. The suggested criteria compare empirical goodness-of-fit or quantile-based measures with their hypothesized values. Since the distributions involved are quite complex and non-standard, the relevant hypothetical measures are approximated by simulation, and p-values are obtained using Monte Carlo (MC) test techniques. The properties of the proposed procedures are investigated by simulation. In contrast with conventional wisdom, we find reliable results with sample sizes as small as 25. The proposed methodology is applied to daily electricity price data in the U.S. over the period 2001-2006. The results show clearly that heavy kurtosis and asymmetry are prevalent in these series. |
| Keywords: | stable distribution; skewness; asymmetry; exact test; Monte Carlo test; specification test; goodness-of-fit; tail parameter; electricity price, |
| Date: | 2015–06–12 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2015s-26&r=ets |
| By: | Morten Ørregaard Nielsen (Queen's University and CREATES); Sergei S. Shibaev (Queen's University) |
| Abstract: | We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. The model is applied to daily polling data of political support in the United Kingdom for 2010-2015. We compare with popular competing models and at various forecast horizons. Our findings show that the precision of forecasts generated by the FCVAR model is better than all multivariate and univariate models in the portfolio, and the four variants of the FCVAR model considered are generally ranked as the top four models in terms of forecast accuracy. Furthermore, the FCVAR model significantly outperforms the standard cointegrated VAR (CVAR) model at all forecast horizons and the relative forecast improvement is highest at longer forecast horizons, where the root mean squared forecast error of the FCVAR model is up to 20% lower than that of the CVAR benchmark model. In an empirical application to the prediction of vote shares in the 2015 UK general election, forecasts generated by the FCVAR model leading into the election appear to provide a more informative assessment of the current state of public opinion on electoral support than that suggested by the hung government prediction of the opinion poll. Specifically, the FCVAR model projects the correct direction for the realized vote shares in the election for both the Conservative and Labour parties. |
| Keywords: | forecasting, fractional cointegration, opinion poll data, vector autoregressive model |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1340&r=ets |
| By: | Helmut Luetkepohl; George Milunovich; ; |
| Abstract: | Changes in residual volatility in vector autoregressive (VAR) models can be used for identifying structural shocks in a structural VAR analysis. Testable conditions are given for full identification for the case where the volatility changes can be modelled by a multivariate GARCH process. Formal statistical tests are presented for identification and their small sample properties are investigated via a Monte Carlo study. The tests are applied to investigate the validity of the identification conditions in a study of the effects of U.S. monetary policy on exchange rates. It is found that the data do not support full identification in most of the models considered, and the implied problems for the interpretation of the results are discussed. |
| Keywords: | Structural vector autoregression, conditional heteroskedasticity, GARCH, identification via heteroskedasticity |
| JEL: | C32 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2015-030&r=ets |
| By: | Alexander Dokumentov; Rob J. Hyndman |
| Abstract: | We propose new generic methods for decomposing seasonal data: STR (a Seasonal-Trend decomposition procedure based on Regression) and Robust STR. In some ways, STR is similar to Ridge Regression and Robust STR can be related to LASSO. Our new methods are much more general than any alternative time series decomposition methods. They allow for multiple seasonal and cyclic components, and multiple linear regressors with constant, flexible, seasonal and cyclic influence. Seasonal patterns (for both seasonal components and seasonal regressors) can be fractional and flexible over time; moreover they can be either strictly periodic or have a more complex topology. We also provide confidence intervals for the estimated components, and discuss how STR can be used for forecasting. |
| Keywords: | time series decomposition, seasonal data, Tikhonov regularisation, ridge regression, LASSO, STL, TBATS, X-12-ARIMA, BSM |
| JEL: | C10 C14 C22 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2015-13&r=ets |
| By: | Souhaib Ben Taieb; Raphael Huser; Rob J. Hyndman; Marc G. Genton |
| Abstract: | A large body of the forecasting literature so far has been focused on forecasting the conditional mean of future observations. However, there is an increasing need for generating the entire conditional distribution of future observations in order to effectively quantify the uncertainty in time series data. We present two different methods for probabilistic time series forecasting that allow the inclusion of a possibly large set of exogenous variables. One method is based on forecasting both the conditional mean and variance of the future distribution using a traditional regression approach. The other directly computes multiple quantiles of the future distribution using quantile regression. We propose an implementation for the two methods based on boosted additive models, which enjoy many useful properties including accuracy, flexibility, interpretability and automatic variable selection. We conduct extensive experiments using electricity smart meter data, on both aggregated and disaggregated scales, to compare the two forecasting methods for the challenging problem of forecasting the distribution of future electricity consumption. The empirical results demonstrate that the mean and variance forecasting provides better forecasts for aggregated demand, while the flexibility of the quantile regression approach is more suitable for disaggregated demand. These results are particularly useful since more energy data will become available at the disaggregated level in the future. |
| Keywords: | Additive models, boosting, density forecasting, energy forecasting, probabilistic forecasting |
| JEL: | Q47 C14 C22 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2015-12&r=ets |
| By: | Jari Hännäkäinen (School of Management, University of Tampere) |
| Abstract: | In this paper, we analyze the forecasting performance of a set of widely used window selection methods in the presence of data revisions and recent structural breaks. Our Monte Carlo and empirical results show that the expanding window estimator often yields the most accurate forecasts after a recent break. It performs well regardless of whether the revisions are news or noise, or whether we forecast first-release or final values. We find that the differences in the forecasting accuracy are large in practice, especially when we forecast GDP deflator growth after the break of the early 1980s. |
| Keywords: | Recent structural break, choice of estimation window, forecasting, real-time data |
| JEL: | C22 C53 C82 |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:tam:wpaper:1392&r=ets |
| By: | Jari Hännäkäinen (School of Management, University of Tampere) |
| Abstract: | This paper analyzes the relative performance of multi-step forecasting methods in the presence of breaks and data revisions. Our Monte Carlo simulations indicate that the type and the timing of the break affect the relative accuracy of the methods. The iterated method typically performs the best in unstable environments, especially if the parameters are subject to small breaks. This result holds regardless of whether data revisions add news or reduce noise. Empirical analysis of real-time U.S. output and inflation series shows that the alternative multi-step methods only episodically improve upon the iterated method. |
| Keywords: | Structural breaks, multi-step forecasting, intercept correction, real-time data |
| JEL: | C22 C53 C82 |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:tam:wpaper:1494&r=ets |
| By: | Andrew Harvey and Rutger-Jan Lange |
| Abstract: | Beta-t-EGARCH models in which the dynamics of the logarithm of scale are driven by the conditional score are known to exhibit attractive theoretical properties for the t-distribution and general error distribution (GED). The generalized-t includes both as special cases. We derive the information matrix for the generalized-t and show that, when parameterized with the inverse of the tail index, it remains positive definite as the tail index goes to infinity and the distribution becomes a GED. Hence it is possible to construct Lagrange multiplier tests of the null hypothesis of light tails against the alternative of fat tails. Analytic expressions may be obtained for the unconditional moments in the EGARCH model and the information matrix for the dynamic parameters obtained. The distribution may be extended by allowing for skewness and asymmetry in the shape parameters and the asymptotic theory for the associated EGARCH models may be correspondingly extended. For positive variables, the GB2 distribution may be parameterized so that it goes to the generalised gamma in the limit as the tail index goes to infinity. Again dynamic volatility may be introduced and properties of the model obtained. Overall the approach offers a unified, flexible, robust and practical treatment of dynamic scale. |
| Keywords: | Asymmetric price transmission, cost pass-through, electricity markets, price theory, rockets and feathers |
| Date: | 2015–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1517&r=ets |
| By: | Alessandra Luati (University of Bologna); Tommaso Proietti (DEF and CEIS, Università di Roma "Tor Vergata") |
| Abstract: | The paper introduces the generalised partial autocorrelation (GPAC) coefficients of a stationary stochastic process. The latter are related to the generalised autocovariances, the inverse Fourier transform coefficients of a power transformation of the spectral density function. By interpreting the generalised partial autocorrelations as the partial autocorrelation coefficients of an auxiliary process, we derive their properties and relate them to essential features of the original process. Based on a parameterisation suggested by Barndorff-Nielsen and Schou (1973) and on Whittle likelihood, we develop an estimation strategy for the GPAC coefficients. We further prove that the GPAC coefficients can be used to estimate the mutual information between the past and the future of a time series. |
| Keywords: | Generalised autocovariance, Spectral models, Whittle likelihood, Reparameterisation. |
| JEL: | C22 C52 |
| Date: | 2015–06–05 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:344&r=ets |
| By: | Kascha, Christian; Trenkler, Carsten |
| Abstract: | This paper provides an empirical comparison of various selection and penalized regression approaches for forecasting with vector autoregressive systems. In particular, we investigate the effect of the system size as well as the effect of various prior specification choices on the relative and overall forecasting performance of the methods. The data set is a typical macroeconomic quarterly data set for the US. We find that these specification choices are crucial for most methods. Conditional on certain choices, the variation across different approaches is relatively small. There are only a few methods which are not competitive under any scenario. For single series, we find that increasing the system size can be helpful - depending on the employed shrinkage method. |
| Keywords: | VAR Models , Forecasting , Model Selection , Shrinkage |
| JEL: | C32 C53 E47 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:38872&r=ets |
| By: | Rachida Hennani |
| Abstract: | The existence of nonlinear structures in the mean equation leads some authors [43, 44] to model financial time series by a Mackey-Glass equation, which is a differential equation with delay. We propose, in this paper, to compare the contributions of the [52]’s equation in the modelling of nonlinear structures in the mean equation with that of [48], published the same year but which may lead to different results in finance. Theoretical results point out that these two equations can describe mean dynamics’ of financial time series. These dynamics reflect the interaction between two types of agents, fundamentalists and chartists, that creates chaotic structures. To verify this, we apply these two models to two Europeans stock markets indices [CAC 40 and DAX 30] on the period [2003-2011]. We show the adequacy of these models, associated with a GARCH specification, to financial time series, comparatively to the ARMA-GARCH model. Moreover, it seems that the [48]’s model is more suitable than the [52]’s model for strongly leptokurtic financial time series: these findings are based on the backtesting results’ conducted on VaR forecasts’. |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:15-09&r=ets |
| By: | Antoine Djogbenou; Sílvia Gonçalves; Benoit Perron |
| Abstract: | This paper considers bootstrap inference in a factor-augmented regression context where the errors could potentially be serially correlated. This generalizes results in Gonçalves and Perron (2013) and makes the bootstrap applicable to forecasting contexts where the forecast horizon is greater than one. We propose and justify two residual-based approaches, a block wild bootstrap (BWB) and a dependent wild bootstrap (DWB). Our simulations document improvement in coverage rates of confidence intervals for the coefficients when using BWB or DWB relative to both asymptotic theory and the wild bootstrap when serial correlation is present in the regression errors. |
| Keywords: | Factor model, bootstrap, serial correlation, forecast., |
| Date: | 2015–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2015s-20&r=ets |
| By: | Federico M. Bandi; Benoit Perron; Andrea Tamoni; Claudio Tebaldi |
| Abstract: | Stock return predictive relations found to be elusive when using raw data may hold true for different layers in the cascade of economic shocks. Consistent with this logic, we model stock market returns and their predictors as aggregates of uncorrelated components (details) operating over different scales and introduce a notion of scale-specific predictability, i.e., predictability on the details. We study and formalize the link between scale-specific predictability and aggregation. Using both direct extraction of the details and aggregation, we provide strong evidence of risk compensations in long-run stock market returns - as well as of an unusually clear link between macroeconomic uncertainty and uncertainty in financial markets - at frequencies lower than the business cycle. The reported tent-shaped behavior in long-run predictability is shown to be a theoretical implication of our proposed modelling approach. |
| Keywords: | : long run, predictability, aggregation, risk-return trade-off, Fisher hypothesis, |
| JEL: | C22 E32 E44 G12 G17 |
| Date: | 2015–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2015s-21&r=ets |