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on Econometric Time Series |
| By: | Sucarrat, Genaro |
| Abstract: | The log-GARCH model provides a flexible framework for the modelling of economic uncertainty, financial volatility and other positively valued variables. Its exponential specification ensures fitted volatilities are positive, allows for flexible dynamics, simplifies inference when parameters are equal to zero under the null, and the log-transform makes the model robust to jumps or outliers. An additional advantage is that the model admits ARMA-like representations. This means log-GARCH models can readily be estimated by means of widely available software, and enables a vast range of well-known time-series results and methods. This chapter provides an overview of the log-GARCH model and its ARMA representation(s), and of how estimation can be implemented in practice. After the introduction, we delineate the univariate log-GARCH model with volatility asymmetry ("leverage"), and show how its (nonlinear) ARMA representation is obtained. Next, stationary covariates ("X") are added, before a first-order specification with asymmetry is illustrated empirically. Then we turn our attention to multivariate log-GARCH-X models. We start by presenting the multivariate specification in its general form, but quickly turn our focus to specifications that can be estimated equation-by-equation - even in the presence of Dynamic Conditional Correlations (DCCs) of unknown form. Next, a multivariate non-stationary log-GARCH-X model is formulated, in which the X-covariates can be both stationary and/or nonstationary. A common critique directed towards the log-GARCH model is that its ARCH terms may not exist in the presence of inliers. An own Section is devoted to how this can be handled in practice. Next, the generalisation of log-GARCH models to logarithmic Multiplicative Error Models (MEMs) is made explicit. Finally, the chapter concludes. |
| Keywords: | Financial return, volatility, ARCH, exponential GARCH, log-GARCH, Multivariate GARCH |
| JEL: | C22 C32 C51 C58 |
| Date: | 2018–08–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100386&r=all |
| By: | Tong Fang (Shandong University); Tae-Hwy Lee (Department of Economics, University of California Riverside); Zhi Su (Central University of Finance and Economics) |
| Abstract: | We consider a GARCH-MIDAS model with short-term and long-term volatility components, in which the long-term volatility component depends on many macroeconomic and financial variables. We select the variables that exhibit the strongest effects on the long-term stock market volatility via maximizing the penalized log-likelihood function with an Adaptive-Lasso penalty. The GARCH-MIDAS model with variable selection enables us to incorporate many variables in a single model without estimating a large number of parameters. In the empirical analysis, three variables (namely, housing starts, default spread and realized volatility) are selected from a large set of macroeconomic and financial variables. The recursive out-of-sample forecasting evaluation shows that variable selection significantly improves the predictive ability of the GARCH-MIDAS model for the long-term stock market volatility. |
| Keywords: | Stock market volatility, GARCH-MIDAS model, Variable selection, Penalized maximum likelihood, Adaptive-Lasso |
| JEL: | C32 C51 C53 G12 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202009&r=all |
| By: | Husein, Jamal |
| Abstract: | We examine the mean reversion properties in the current account balance as a percentage of GDP under assumptions of smooth breaks and nonlinearity for twenty one African economies. Since there are reasons to indicate that the dynamic adjustment in the current account may follow a nonlinear process, we utilize a range of nonlinear stationarity and unit-root tests and compare across them to obtain a comprehensive picture of the pattern characterizing imbalances in part of the region. In particular, we apply the newly introduced Fourier stationarity test of Tsong, Lee, and Tsai (2019) in conjunction with Enders and Lee (2012a and 2012b) and Rodrigues and Taylor (2012) Fourier unit-root tests. However, rather than assuming a nonlinear current account adjustment, we test for “nonlinearity” using an approach that is robust to whether the current account series are stationary or integrated. We find strong evidence in favor of nonlinearity in eighteen current accounts out of the twenty one examined. Our empirical results show that the traditional linear and the widely used nonlinear unit-root tests of Kapetanios et al. (2003), Sollis (2009), and Kruse (2011) confirm sustainability of the current account balance for a small number of countries. Meanwhile, the Fourier based stationarity and unit-root tests confirm sustainability in a much larger group of countries. |
| Keywords: | Unit-root, Stationarity, Fourier approximation, Current account |
| JEL: | C22 F32 |
| Date: | 2020–05–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100410&r=all |
| By: | NEIFAR, MALIKA |
| Abstract: | The objectif in this paper is to proposes multivariate GARCH volatility models to assess the dynamic interdependence among volatility of returns for 5 tunisian sectorial stock index series (namely : Bank, FINancial service, AUTOmobile, INDustry, and Materials (MATB)) and TUNindex series. The Monthly returns of stock indices have been considered from 2010M02 to 2019M07. Two systems are considered. The first System, with Constant Conditional (C) mean, allows for market interaction. Results from DVECH model reveals that some sectorial stock markets are interdependent, the presence of a significance and positive effect of cross shock of Finance and Bank stock returns on Tunindex return, and volatility is predictable. C Correlation, _ij, have decreasing evolution for full period or for recent years for almost all i and j except CC between Tunindex return and R_FIN (and R_BANK) and CC between R_FIN and R_IND (and R_MATB). The tests for volatility spillovers effects suggests significant volatility spillovers from MATB and AUTO sectors to IND sector and from AUTO sector to MATB sector. The second system, with macroeconomic factor instability effects as Conditional mean, examine the CCC and DCC between different sectors. The main result supports the hypotheses of DCC. The DCC provides evidence of cross border relationship between sectors and macro economic instability factors have significant effect on the mean of returns evolutions (at 5% or 10% level). Volatility of exchange rate has significant positive effect on R, R_FIN, and R_MATB, while volatility of inflation has significant negative effect on R_Fin and volatility of oil price has significant negative effect on R_AUTO. |
| Keywords: | Sectorial stock return, MGARCH model, DVECH and DBEKK models, Conditional Correlations (CC), Dynamic CC (DCC) and Constant CC models (CCC). |
| JEL: | C32 G11 G14 |
| Date: | 2020–04–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99658&r=all |
| By: | Sucarrat, Genaro |
| Abstract: | The R package garchx provides a user-friendly, fast, flexible and robust framework for the estimation and inference of GARCH(p,q,r)-X models, where p is the ARCH order, q is the GARCH order, r is the asymmetry or leverage order, and 'X' indicates that covariates can be included. Quasi Maximum Likelihood (QML) methods ensure estimates are consistent and standard errors valid, even when the standardised innovations are non-normal or dependent, or both. Zero-coefficient restrictions by omission enable parsimonious specifications, and functions to facilitate the non-standard inference associated with zero-restrictions in the null-hypothesis are provided. Finally, in formal comparisons of precision and speed, the garchx package performs well relative to other prominent GARCH-packages on CRAN. |
| Keywords: | Volatility, GARCH, covariates, robust, R |
| JEL: | C1 C58 C87 |
| Date: | 2020–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100301&r=all |
| By: | Camila Figueroa; Michael Pedersen |
| Abstract: | The present paper discusses the extent to which business and consumer survey observations are useful for predicting the Chilean activity. The two surveys examined are called IMCE and IPEC, after their Spanish abbreviations, for the business and consumer survey, respectively. The baseline exercises consist in simple calculations of cross correlations between the surveys and activity variables, test for Granger causality and augmentation of autoregressive activity models with survey data to evaluate if the now- and forecast performances are improved. The evidence suggests that both surveys, in general, contain useful information for making predictions of the Chilean activity, particularly for the longer horizons. An additional exercise indicates that the data in the two surveys are complementary in the sense that the longer horizon forecasts improve further when both of them are included in the econometric model. |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:chb:bcchwp:832&r=all |
| By: | Harvey, David I; Leybourne, Stephen J; Sollis, Robert; Taylor, AM Robert |
| Abstract: | We propose new real-time monitoring procedures for the emergence of end-of-sample predictive regimes using sequential implementations of standard (heteroskedasticity-robust) regression t-statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the U.S. equity premium at the one-month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the one-month ahead equity premium has temporarily been predictable, displaying so-called 'pockets of predictability', and that these episodes of predictability could have been detected in real-time by practitioners using our proposed methodology. |
| Keywords: | Predictive regression; persistence; temporary predictability; subsampling; U.S. equity premium |
| Date: | 2020–06–03 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:27775&r=all |