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on Econometric Time Series |
| By: | Tommaso Proietti (DEF & CEIS,Università di Roma "Tor Vergata"); Diego J. Pedregal (Universidad de Castilla-La Mancha) |
| Abstract: | Time series observed at higher frequencies than monthly frequency display complex seasonal patterns that result from the combination of multiple seasonal patterns (with annual, monthly, weekly and daily periodicities) and varying periods, due to the irregularity of the calendar. The paper deals with modelling seasonality in high frequency data from two main perspectives: the stochastic harmonic approach, based on the Fourier representation of a periodic function, and the time-domain random effects approach. An encompassing representation illustrates the conditions under which they are equivalent. Three major challenges are considered: the first deals with modelling the effect of moving festivals, holidays and other breaks due to the calendar. Secondly, robust estimation and filtering methods are needed to tackle the level of outlier contamination, which is typically high, due to the lower level of temporal aggregation and the raw nature of the data. Finally, we focus on model selection strategies, which are important, as the number of harmonic or random components that are needed to account for the complexity of seasonality can be very large. |
| Keywords: | State Space Models. Robust filtering. Seasonal Adjustment. Variable selection |
| JEL: | C22 C52 C58 |
| Date: | 2021–03–11 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:508&r=all |
| By: | Harvey, A.; Palumbo, D. |
| Abstract: | The score-driven approach to time series modeling provides a solution to the problem of modeling circular data and it can also be used to model switching regimes with intra-regime dynamics. Furthermore it enables a dynamic model to be fitted to a linear and a circular variable when the joint distribution is a cylinder. The viability of the new method is illustrated by estimating a model with dynamic switching and dynamic location and/or scale in each regime to hourly data on wind direction and speed in Galicia, north-west Spain. |
| Keywords: | Circular data, conditional score, cylinder, hidden Markov model, von Mises distribution, wind. |
| JEL: | C22 C32 |
| Date: | 2021–03–10 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2123&r=all |
| By: | Christian Conrad (Department of Economics, Heidelberg University, Germany; KOF Swiss Economic Institute, Switzerland; Rimini Centre for Economic Analysis); Robert F. Engle (New York University, Stern School of Business, USA; Rimini Centre for Economic Analysis) |
| Abstract: | We suggest a multiplicative factor multi frequency component GARCH model which exploits the empirical fact that the daily standardized forecast errors of standard GARCH models behave counter-cyclical when averaged at a lower frequency. For the new model, we derive the unconditional variance of the returns, the news impact function and multi-step-ahead volatility forecasts. We apply the model to the S&P 500, the FTSE 100 and the Hang Seng Index. We show that the long-term component of stock market volatility is driven by news about the macroeconomic outlook and monetary policy as well as policy-related news. The new component model significantly outperforms the nested one-component (GJR) GARCH and several HAR-type models in terms of out-of-sample forecasting. |
| Keywords: | Volatility forecasting, long- and short-term volatility, mixed frequency data, volatility cycles |
| JEL: | C53 C58 G12 |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:21-05&r=all |
| By: | Gabriele Fiorentini (Università di Firenze and RCEA); Enrique Sentana (CEMFI, Centro de Estudios Monetarios y Financieros) |
| Abstract: | Likelihood inference in structural vector autoregressions with independent non-Gaussian shocks leads to parametric identification and efficient estimation at the risk of inconsistencies under distributional misspecification. We prove that autoregressive coefficients and (scaled) impact multipliers remain consistent, but the drifts and standard deviations of the shocks are generally inconsistent. Nevertheless, we show consistency when the non-Gaussian log-likelihood is a discrete scale mixture of normals in the symmetric case, or an unrestricted finite mixture more generally. Our simulation exercises compare the efficiency of these estimators to other consistent proposals. Finally, our empirical application looks at dynamic linkages between three popular volatility indices. |
| Keywords: | Consistency, finite normal mixtures, pseudo maximum likelihood estimators, structural models, volatility indices. |
| JEL: | C32 C46 C51 C58 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2020_2023&r=all |
| By: | Yuefeng Han; Rong Chen; Cun-Hui Zhang; Qiwei Yao |
| Abstract: | We propose a contemporaneous bilinear transformation for matrix time series to alleviate the difficulties in modelling and forecasting large number of time series together. More precisely the transformed matrix splits into several small matrices, and those small matrix series are uncorrelated across all times. Hence an effective dimension-reduction is achieved by modelling each of those small matrix series separately without the loss of information on the overall linear dynamics. We adopt the bilinear transformation such that the rows and the columns of the matrix do not mix together, as they typically represent radically different features. As the targeted transformation is not unique, we identify an ideal version through a new normalization, which facilitates the no-cancellation accumulation of the information from different time lags. The non-asymptotic error bounds of the estimated transformation are derived, leading to the uniform convergence rates of the estimation. The proposed method is illustrated numerically via both simulated and real data examples. |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2103.09411&r=all |
| By: | Martin Feldkircher; Florian Huber; Gary Koop; Michael Pfarrhofer |
| Abstract: | The Panel Vector Autoregressive (PVAR) model is a popular tool for macroeconomic forecasting and structural analysis in multi-country applications since it allows for spillovers between countries in a very flexible fashion. However, this flexibility means that the number of parameters to be estimated can be enormous leading to over-parameterization concerns. Bayesian global-local shrinkage priors, such as the Horseshoe prior used in this paper, can overcome these concerns, but they require the use of Markov Chain Monte Carlo (MCMC) methods rendering them computationally infeasible in high dimensions. In this paper, we develop computationally efficient Bayesian methods for estimating PVARs using an integrated rotated Gaussian approximation (IRGA). This exploits the fact that whereas own country information is often important in PVARs, information on other countries is often unimportant. Using an IRGA, we split the the posterior into two parts: one involving own country coefficients, the other involving other country coefficients. Fast methods such as approximate message passing or variational Bayes can be used on the latter and, conditional on these, the former are estimated with precision using MCMC methods. In a forecasting exercise involving PVARs with up to $18$ variables for each of $38$ countries, we demonstrate that our methods produce good forecasts quickly. |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2103.04944&r=all |
| By: | Alessia Paccagnini; Fabio Parla |
| Abstract: | We contribute to research on mixed-frequency regressions by introducing an innovative Bayesian approach. Based on a new “high-frequency” identification scheme, we provide novel empirical evidence of identifying uncertainty shock for the US economy. As main findings, we document a “temporal aggregation bias” when we adopt a common low frequency model instead of estimating a mixed-frequency framework. The bias is amplified when we identify a higher frequency shock. |
| Keywords: | Bayesian mixed-frequency VAR, MIDAS, uncertainty shocks, macro-financial linkages |
| JEL: | C32 E44 E52 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2021-26&r=all |
| By: | Gary Koop; Stuart McIntyre; James Mitchell; Aubrey Poon |
| Abstract: | Expenditure side and income side GDP are both measured at the quarterly frequency in the US and contain measurement error. They are noisy proxies of `true’ GDP. Several econometric methods exist for producing estimates of true GDP which reconcile these noisy estimates. Recently, the authors of this paper developed a mixed frequency reconciliation model which produces monthly estimates of true GDP. In the present paper, we investigate whether this model continues to work well in the face of the extreme observations that occurred during the pandemic year of 2020 and consider several extensions of it. These extensions include stochastic volatility and error distributions that are fat tailed or explicitly allow for outliers. We also investigate the performance of conditional forecasting, where we estimate our models using data through 2019 and then use these to nowcast throughout 2020. Nowcasts are updated each month of 2020 conditionally on the new data releases which occur each month, but the parameters are not re-estimated. In total we compare the real-time performance of 12 nowcasting approaches over the pandemic months. We find that our original model with Normal homoskedastic errors produces point nowcasts as good or better than any of the other approaches. A property of Normal homoskedastic models that is often considered bad (i.e. that they are not robust to outliers), actually benefits the KMMP model as it reacts confidently to the rapidly evolving economic data. In terms of nowcast densities, we find many of the extensions lead to larger predictive variances reflecting the great uncertainty of the pandemic months. |
| Keywords: | Pandemic, Nowcasting, Income, Expenditure, Mixed frequency model, Vector Autoregression, Bayesian |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2021-14&r=all |
| By: | Neil R. Ericsson (Division of International Finance, Board of Governors of the Federal Reserve System) |
| Abstract: | David Hendry has made-and continues to make-pivotal contributions to the econometrics of empirical economic modeling, economic forecasting, econometrics software, substantive empirical economic model design, and economic policy. This paper reviews his contributions by topic, emphasizing the overlaps between different strands in his research and the importance of real-world problems in motivating that research. |
| Keywords: | cointegration, consumers' expenditure, dynamic specification, equilibrium correction, forecasting, machine learning, model evaluation, money demand, PcGive, structural breaks |
| JEL: | C52 C53 |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:gwc:wpaper:2021-001&r=all |
| By: | Barend Abeln; Jan P.A.M. Jacobs |
| Abstract: | The COVID19 crisis has a huge impact on economies all over the world. In this note we compare seasonal adjustments of X13 and CAMPLET before and after the COVID19 crisis. We show results of Quasi Real Time analyses for the quarterly series real GDP and the monthly series Consumption of Households in the Netherlands, and STL and CAMPLET seasonal adjustments for the weekly series US Initial Claims. We find that differences in SA values are generally small and that X13 and STL seasonal adjustments are subject to revision. From the analysis of the weekly series initial claims, we learn that STL and CAMPLET SAs follow NSA values closely. In addition, the COVID19 crisis caused a structural increase in initial claims. Before the crisis initial claims fluctuated around a lower level than after the crisis. |
| Keywords: | COVID19 crisis, seasonal adjustment, real GDP, consumption of households, initial claims |
| JEL: | C22 E24 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2021-23&r=all |