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on Econometric Time Series |
| By: | Fabian Krüger; Todd E. Clark; Francesco Ravazzolo |
| Abstract: | This paper shows entropic tilting to be a flexible and powerful tool for combining mediumterm forecasts from BVARs with short-term forecasts from other sources (nowcasts from either surveys or other models). Tilting systematically improves the accuracy of both point and density forecasts, and tilting the BVAR forecasts based on nowcast means and variances yields slightly greater gains in density accuracy than does just tilting based on the nowcast means. Hence entropic tilting can offer — more so for persistent variables than not-persistent variables — some benefits for accurately estimating the uncertainty of multi-step forecasts that incorporate nowcast information.Length: 42 pages |
| Keywords: | Forecasting, Prediction, Bayesian Analysis |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:bny:wpaper:0036&r=all |
| By: | Barend Abeln; Jan P. A. M. Jacobs |
| Abstract: | Seasonality in macroeconomic time series can obscure movements of other components in a series that are operationally more important for economic and econometric analyses. Indeed, in practice one often prefers to work with seasonally adjusted data to assess the current state of the economy and its future course. Recently, two most widely used seasonal adjustment methods, Census X-12-ARIMA and TRAMO-SEATS, merged into X-13ARIMA-SEATS to become a new industry standard. In this paper, we compare and contrast X-13ARIMA-SEATS with a seasonal adjustment program called CAMPLET, an acronym of its tuning parameters. CAMPLET consists of a simple adaptive procedure which separates the seasonal component and the non-seasonal component from an observed time series. Once this process has been carried out there will be no need to revise these components at a later stage when more observations become available, in contrast with other seasonal adjustment methods. The paper briefly reviews of X-13ARIMA-SEATS and describes the main features of CAMPLET. We evaluate the outcomes of both methods in a controlled simulation framework using a variety of processes. Finally, we apply the X-13ARIMA-SEATS and CAMPLET methods to three time series: U.S. non-farm payroll employment, operational income of Ahold, and real GDP in the Netherlands. |
| Keywords: | seasonal adjustment, real-time, seasonal pattern, simulations, employment, operational income, real GDP, |
| JEL: | C22 E24 E32 E37 |
| Date: | 2015–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2015s-35&r=all |
| By: | E. Otranto |
| Abstract: | Very often time series are subject to abrupt changes in the level, which are generally represented by Markov Switching (MS) models, hypothesizing that the level is constant within a certain state (regime). This is not a realistic framework because in the same regime the level could change with minor jumps with respect to a change of state; this is a typical situation in many economic time series, such as the Gross Domestic Product or the volatility of financial markets. We propose to make the state flexible, introducing a very general model which provides oscillations of the level of the time series within each state of the MS model; these movements are driven by a forcing variable. The flexibility of the model allows for consideration of extreme jumps in a parsimonious way (also in the simplest 2-state case), without the adoption of a larger number of regimes; moreover this model increases the interpretability and fitting of the data with respect to the analogous MS model. This approach can be applied in several fields, also using unobservable data. We show its advantages in three distinct applications, involving macroeconomic variables, volatilities of financial markets and conditional correlations. |
| Keywords: | abrupt changes, goodness of fit, Hamilton filter, smoothed changes, time–varying parameters |
| JEL: | C22 C32 C5 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:201509&r=all |
| By: | Arnaud Dufays |
| Abstract: | Sequential Monte Carlo (SMC) methods are widely used for non-linear filtering purposes. Nevertheless the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov-Chain Monte-Carlo (MCMC) methods. Not only SMC algorithms draw posterior distributions of static or dynamic parameters but additionally provide an estimate of the marginal likelihood. The tempered and time (TNT) algorithm, developed in the paper, combines (off-line) tempered SMC inference with on-line SMC inference for drawing realizations from many sequential posterior distributions without experiencing a particle degeneracy problem. Furthermore, it introduces a new MCMC rejuvenation step that is generic, automated and well-suited for multi-modal distributions. As this update relies on the wide heuristic optimization literature, numerous extensions are already available. The algorithm is notably appropriate for estimating Change-point models. As an example, we compare Change-point GARCH models through their marginal likelihoods over time. |
| Keywords: | Bayesian inference, Sequential Monte Carlo, Annealed Importance sampling, Change-point models, Differential Evolution, GARCH models |
| JEL: | C11 C15 C22 C58 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:1518&r=all |
| By: | Athanasopoulos, George; Hyndman, Rob J.; Kourentzes, Nikolaos; Petropoulos, Fotios |
| Abstract: | This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments. |
| Keywords: | Hierarchical forecasting, temporal aggregation, reconciliation, forecast combination |
| JEL: | C44 C53 |
| Date: | 2015–08–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:66362&r=all |
| By: | David E. Allen (School of Accounting, Finance and Economics Edith Cowan University, Australia.); Michael McAleer (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute, The Netherlands, Department of Quantitative Economics, Complutense University of Madrid, and Institute of Economic Research, Kyoto University.); Robert J. Powell (School of Accounting, Finance and Economics, Edith Cowan University); Abhay K. Singh (School of Accounting, Finance and Economics, Edith Cowan University, Australia) |
| Abstract: | This paper applies the Hafner and Herwartz (2006) (hereafter HH) approach to the analysis of multivariate GARCH models using volatility impulse response analysis. The data set features ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index from the London Stock Exchange, from 3 January 2005 to 31 January 2015. This period captures both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The attraction of the HH approach is that it involves a novel application of the concept of impulse response functions, tracing the effects of independent shocks on volatility through time, while avoiding typical orthogonalization and ordering problems. Volatility impulse response functions (VIRF) provide information about the impact of independent shocks on volatility. HH’s VIRF extends a framework provided by Koop et al. (1996) for the analysis of impulse responses. This approach is novel because it explores the effects of shocks to the conditional variance, as opposed to the conditional mean. HH use the fact that GARCH models can be viewed as being linear in the squares, and that multivariate GARCH models are known to have a VARMA representation with non-Gaussian errors. They use this particular structure to calculate conditional expectations of volatility analytically in their VIRF analysis. A Jordan decomposition of Σt is used to obtain independent and identically distributed innovations. A general issue in the approach is the choice of baseline volatilities. VIRF is defined as the expectation of volatility conditional on an initial shock and on history, minus the baseline expectation that conditions on history. This makes the process endogenous, but the choice of the baseline shock within the data set makes a difference. We explore the impact of three different shocks, the first marking the onset of the GFC, which we date as 9 August 2007 (GFC1). This began with the seizure in the banking system precipitated by BNP Paribas announcing that it was ceasing activity in three hedge funds that specialised in US mortgage debt. It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, when the US government allowed the investment bank Lehman Brothers to go bankrupt (GFC2). The third shock is 9 May 2010, which marked the point at which the focus of concern switched from the private sector to the public sector. A further contribution of this paper is the inclusion of leverage, or asymmetric effects. Our modelling is undertaken in the context of a multivariate GARCH model featuring pre-whitened return series, which are then analysed using both BEKK and diagonal BEKK models with the t-distribution. A key result is that the impact of negative shocks is larger, in terms of the effects on variances and covariances, but shorter in duration, in this case a difference between three and six months, in the context of the return series. |
| Keywords: | Volatility impulse response functions (VIRF); BEKK; DBEKK; Asymmetry; GFC; ESDC. |
| JEL: | C22 C32 C58 G32 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1510&r=all |