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on Econometric Time Series |
| By: | Donggyu Kim |
| Abstract: | This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Ito models, the instantaneous volatility process has a non-linear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Ito (ERGI) model. Given the auto-regressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and an empirical study with 50 assets among the S\&P 500 compositions. The numerical studies show the advantages of the new proposed model. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2111.04267&r= |
| By: | Gianluca Cubadda (DEF & CEIS,University of Rome "Tor Vergata"); Alain Hecq (Maastricht University) |
| Abstract: | This chapter surveys the importance of reduced rank regression techniques (RRR) for modelling economic and ?nancial time series. We mainly focus on models that are capable to reproduce the presence of common dynamics among variables such as the serial correlation common feature and the multivariate autoregressive index models. Cointegration analysis, for which RRR plays a central role, is not discussed in this chapter as it deserves a speci?c treatment on its own. Instead, we show how to detect and model comovements in time series that are stationary or that have been stationarized after proper transformations. The motivations for the use of RRR in time series econometrics include dimension reductions which simplify complex dynamics and thus making interpretations easier, as well as pursuing e¢ ciency gains in both estimation and prediction. Via the ?nal equation representation, RRR also makes the nexus between multivariate time series and parsimonious marginal ARIMA models. The drawback of RRR, which is common to all the dimension reduction techniques, is that the underlying restrictions may be present or not in the data. We provide in this chapter a couple of empirical applications to illustrate concepts and methods. |
| Keywords: | Reduced-rank regression, common features, vector autoregressive models, multivariate volatility models, dimension reduction. |
| Date: | 2021–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:525&r= |
| By: | Jeronymo Marcondes Pinto; Jennifer L. Castle |
| Abstract: | Forecasting economic indicators is an important task for analysts. However, many indicators suffer from structural breaks leading to forecast failure. Methods that are robust following a structural break have been proposed in the literature but they come at a cost: an increase in forecast error variance. We propose a method to select between a set of robust and non-robust forecasting models. Our method uses time-series clustering to identify possible structural breaks in a time series, and then switches between forecasting models depending on the series dynamics. We perform a rigorous empirical evaluation with 400 simulated series with an artificial structural break and with real data economic series: Industrial Production and Consumer Prices for all Western European countries available from the OECD database. Our results show that the proposed method statistically outperforms benchmarks in forecast accuracy for most case scenarios, particularly at short horizons. |
| Keywords: | Machine Learning, Forecasting, Structural Breaks, Model Selection, Cluster Analysis |
| Date: | 2021–10–13 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:950&r= |
| By: | Carlos A. Abanto-Valle (Department of Statistics, Federal University of Rio de Janeiro); Gabriel Rodríguez (Department of Economics, Pontificia Universidad Católica del Perú); Luis M. Castro Cepero (Department of Statistics, Pontificia Universidad Católica de Chile); Hernán B. Garrafa-Aragón (Escuela de Ingeniería Estadística de la Universidad Nacional de Ingeniería) |
| Abstract: | The stochastic volatility in mean (SVM) model proposed by Koopman and Uspensky (2002) is revisited. This paper has two goals. The first is to offer a methodology that requires less computational time in simulations and estimates compared with others proposed in the literature as in Abanto-Valle et al. (2021) and others. To achieve the first goal, we propose to approximate the likelihood function of the SVM model applying Hidden Markov Models (HMM) machinery to make possible Bayesian inference in real-time. We sample from the posterior distribution of parameters with a multivariate Normal distribution with mean and variance given by the posterior mode and the inverse of the Hessian matrix evaluated at this posterior mode using importance sampling (IS). The frequentist properties of estimators is anlyzed conducting a simulation study. The second goal is to provide empirical evidence estimating the SVM model using daily data for five Latin American stock markets. The results indicate that volatility negatively impacts returns, suggesting that the volatility feedback effect is stronger than the effect related to the expected volatility. This result is exact and opposite to the finding of Koopman and Uspensky (2002). We compare our methodology with the Hamiltonian Monte Carlo (HMC) and Riemannian HMC methods based on Abanto-Valle et al. (2021). JEL Classification-JE: C11, C15, C22, C51, C52, C58, G12. |
| Keywords: | Stock Latin American Markets, Stochastic Volatility in Mean, Feed-Back Effect, Hamiltonian Monte Carlo, Hidden Markov Models, Riemannian Manifold Hamiltonian Monte Carlo, Non Linear State Space Models. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:pcp:pucwps:wp00502&r= |
| By: | Florian Eckert (ETH Zurich, Switzerland); Nina Mühlebach (ETH Zurich, Switzerland) |
| Abstract: | This paper proposes a multi-level dynamic factor model to identify common components in output gap estimates. We pool multiple output gap estimates for 157 countries and decompose them into one global, eight regional, and 157 country-specific cycles.Our approach easily deals with mixed frequencies, ragged edges, and discontinuities in the underlying output gap estimates. To restrict the parameter space in the Bayesian state space model, we apply a stochastic search variable selection approach and base the prior inclusion probabilities on spatial information. Our results suggest that the global and the regional cycles explain a substantial proportion of the output gaps. On average, 18% of a country’s output gap is attributable to the global cycle, 24% to the regional cycle, and 58% to the local cycle. |
| Keywords: | Multi-Level DFM, Bayesian State Space Model, Output Gap Decomposition, Model Combination, Business Cycles, Variable Selection, Spatial Prior |
| JEL: | C11 C32 C52 F44 R11 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:kof:wpskof:21-497&r= |
| By: | Sattarhoff, Cristina; Lux, Thomas |
| Abstract: | We adapt the multifractal random walk model by Bacry et al. (2001) to realized volatilities (denoted RV-MRW) and take stock of recent theoretical insights on this model in Duchon et al. (2012) to derive forecasts of financial volatility. Moreover, we propose a new extension of the binomial Markov-switching multifractal (BMSM) model by Calvet and Fisher (2001) to the RV framework. We compare the predictive ability of the two against seven classical and multifractal volatility models. Forecasting performance is evaluated out-of-sample based on the empirical MSE and MAE as well as using model confidence sets following the methodology of Hansen et al. (2011). Overall, our empirical study for 14 international stock market indices has a clear message: The RV-MRW is throughout the best model for all forecast horizons under the MAE criterium as well as for large forecast horizons h=50 and 100 days under the MSE criterion. Moreover, the RV-MRW provides most accurate 20-day ahead forecasts in terms of MSE for the great majority of indices, followed by RV-ARFIMA, the latter dominating the competition at the 5-day-horizon. These results are very promising if we consider that this is the first empirical application of the RV-MRW. Moreover, whereas RV-ARFIMA forecasts are often a time consuming task, the RV-MRW stands out due to its fast execution and straightforward implementation. The new RV-BMSM appears to be specialized in short term forecasting, the model providing most accurate one-day ahead forecasts in terms of MSE for the same number of cases as RV-ARFIMA. |
| Keywords: | Realized volatility,multiplicative volatility models,multifractal random walk,longmemory,international volatility forecasting |
| JEL: | C20 G12 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cauewp:202102&r= |
| By: | Sayani Gupta; Rob J Hyndman; Dianne Cook |
| Abstract: | Cyclic temporal granularities are temporal deconstructions of a time period into units such as hour-of-theday and work-day/weekend. They can be useful for measuring repetitive patterns in large univariate time series data, and feed new approaches to exploring time series data. One use is to take pairs of granularities, and make plots of response values across the categories induced by the temporal deconstruction. However, when there are many granularities that can be constructed for a time period, there will also be too many possible displays to decide which might be the more interesting to display. This work proposes a new distance metric to screen and rank the possible granularities, and hence choose the most interesting ones to plot. The distance measure is computed for a single or pairs of cyclic granularities and can be compared across different cyclic granularities or on a collection of time series. The methods are implemented in the open-source R package hakear. |
| Keywords: | data visualization, cyclic granularities, periodicities, permutation tests, distributional difference, Jensen-Shannon distances, smart meter data, R |
| JEL: | C55 C65 C80 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2021-20&r= |