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on Econometric Time Series |
| By: | Javier Gomez-Biscarri; Javier Hualde |
| Abstract: | We propose a residual-based augmented Dickey-Fuller (ADF) test statistic that allows for detection of stationary cointegration within a system that may contain both I (2) and I (1) observables. The test is also consistent under the alternative of multicointegration, where first differences of the I (2) observables enter the cointegrating relationships. We find the null limiting distribution of this statistic and justify why our proposal improves over related approaches. Critical values are computed for a variety of situations. Additionally, building on this ADF test statistic, we propose a procedure to test the null of no stationary cointegration which overcomes the drawback, suffered by any residual-based method, of the lack of power with respect to some relevant alternatives. Finally, a Monte Carlo experiment is carried out and an empirical application is provided as an illustrative example. |
| Keywords: | systems, stationary cointegration, multicointegration, residual-based tests |
| JEL: | C12 C22 C32 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:779&r=ets |
| By: | Myung Hwan Seo; Yongcheol Shin |
| Abstract: | This paper addresses an important and challenging issue as how best to model nonlinear asymmetric dynamics and cross-sectional heterogeneity, simultaneously, in the dynamic threshold panel data framework, in which both threshold variable and regressors are allowed to be endogenous. Depending on whether the threshold variable is strictly exogenous or not, we propose two different estimation methods: first-differenced two-step least squares and first-differenced GMM. The former exploits the fact that the threshold variable is strictly exogenous to achieve the super-consistency of the threshold estimator. We provide asymptotic distributions of both estimators. The bootstrap-based test for the presence of threshold effect as well as the exogeneity test of the threshold variable are also developed. Monte Carlo studies provide a support for our theoretical predictions. Finally, using the UK and the US company panel data, we provide two empirical applications investigating an asymmetric sensitivity of investment to cash flows and an asymmetric dividend smoothing. |
| Keywords: | Dynamic Panel Threshold Models, Endogenous Threshold Effects and Regressors, FD-GMM and FD-2SLS Estimation, Linearity Test, Exogeneity Test, Investment and Dividend Smoothing. |
| JEL: | C13 C33 G31 G35 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:/2014/577&r=ets |
| By: | Omer, Gamal Salih; Masih, Mansur |
| Abstract: | Volatility is a measure of variability in the price of an asset and is associated with unpredictability and uncertainty about the price. Even it is a synonym for risk; higher volatility means higher risk in the respective context. With regard to stock market, the extent of variation in stock prices is referred to stock market volatility. A spiky and rapid movement in the stock prices may throw out risk-averse investors from the market. Hence a desired level of volatility is demanded by the markets and its investors. The traditional methods of volatility and correlation analysis did not consider the effect of conditional (or time-varying) volatility and correlation. Hence a major issue facing the investors in the contemporary financial world is how to minimize risk while investing in a portfolio of assets. An understanding of how volatilities of and correlations between asset returns change over time including their directions (positive or negative) and size (stronger or weaker) is of crucial importance for both the domestic and international investors with a view to diversifying their portfolios for hedging against unforeseen risks as well as for dynamic option pricing. Therefore, appropriate modelling of volatility is of importance due to several reasons such as it becomes a key input to many investment decisions and portfolio creations, the pricing of derivative securities and financial risk management. Thus, in this paper, we aim to estimate and forecast conditional volatility of and correlations between daily returns of the seven selected Dow Jones Islamic and conventional price indexes spanning from 01/1/2003 to 31/3/2013. The sample period from January 30, 2003 to December, 13, 2010 amounting to 2053 daily observations are used for estimation and the remaining sample period is used for evaluation, through the application of the recently-developed Dynamic Multivariate GARCH approach to investigate empirical questions of the time-varying volatility parameters of these selected Dow Jones stock indices and time varying correlation among them. The contribution of this work is an improvement on others‘ works particularly in terms of time-varying volatility and correlation of assets incorporating Islamic assets. We find that all volatility parameters are highly significant, with the estimates very close to unity implying a gradual 2 volatility decay. The t-distribution appears to be more appropriate in capturing the fat-tailed nature of the distribution of stock returns and the conditional correlations of returns of all Dow Jones Islamic Markets, Dow Jones Islamic UK, and Dow Jones Islamic US Indices with other indices are not found constant but changing. The policy implications of this finding are that the shariah investors should monitor these correlations and mange their investment portfolios accordingly. In addition to this, the different financial markets offer different opportunities for portfolio diversification. |
| Keywords: | conditional volatility and correlations of Islamic assets, forecast, MGARCH-DCC |
| JEL: | C22 C58 G11 G15 |
| Date: | 2014–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58862&r=ets |
| By: | Gloria Gonzalez-Rivera (Department of Economics, University of California Riverside); Wei Lin |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:201429&r=ets |
| By: | Sinha, Pankaj; Agnihotri, Shalini |
| Abstract: | Joint dynamics of market index returns, volume traded and volatility of stock market returns can unveil different dimensions of market microstructure. It can be useful for precise volatility estimation and understanding liquidity of the financial market. In this study, the joint dynamics is investigated with the help of bivariate GJR-GARCH methodology given by Bollerslev (1990), as this method helps in jointly estimating volatility equation of return and volume in one step estimation procedure and it also eliminates the regressor problem (Pagan ,1984).Three indices of different market capitalization have been considered where, S&P BSE Sensex represent large capitalization firms, BSE mid-cap represents mid-capitalization firms and BSE small-cap index represents small capitalization firms. The study finds that there exist negative conditional correlation between volume traded and return of large cap index. There is unidirectional relation between index returns and volume traded since change in volume can be explained by lags of index returns. The relation between volume traded and volatility is found to be positive in case of large-cap index but it is negative in the case of mid-cap and small-cap indices. It is observed that there exist bidirectional causality between volatility and volume traded in all the three indices considered. Volatility is affected by pronounced persistence in volatility, mean-reversion of returns and asymmetry in market. The rate of information arrival measured by IDV(Intra-day volatility) is found to be a significant source of the conditional heteroskedasticity in Indian markets since the presence of volume (proxy for information flow) in volatility equation, as an independent variable, marginally reduces the volatility persistence, whereas presence of IDV, as a proxy for information flow, completely vanishes the GARCH effect. Finally, it is observed that volume traded spills over from large cap to mid-cap index, from large-cap to small-cap index and from mid-cap to small-cap index, in response to new information arrival. |
| Keywords: | Bivariate GJR-GARCH, Trading volume, Volatility, Stock return, Volatility Persistence, Asymmetry in markets |
| JEL: | C12 C32 G12 |
| Date: | 2014–07–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58303&r=ets |
| By: | Furkan Emirmahmutoglu (Faculty of Economic and Administrative Sciences, Department of Econometrics, Gazi University, 06500, Ankara, Turkey); Rangan Gupta (Department of Economics, University of Pretoria); Stephen M. Miller (Department of Economics, University of Nevada, Las Vegas, 89154-6005, United States); Tolga Omay (Department of Banking and Finance, Çankaya University Eskisehir Yolu 29. km, Ankara, Turkey) |
| Abstract: | This paper re-examines the stochastic properties of US State real per capita personal income, using new panel unit-root procedures. The new developments incorporate non-linearity, asymmetry, and cross-sectional correlation within panel data estimation. Including nonlinearity and asymmetry finds that 43 states exhibit stationary real per capita personal income whereas including only nonlinearity produces the 42 states that exhibit stationarity. Stated differently, we find that 2 states exhibit nonstationary real per capita personal income when considering nonlinearity, asymmetry, and cross-sectional dependence. |
| Keywords: | Nonlinear, Panel Unit Root, Asymmetry, Cross-Sectional Dependence, Sieve Bootstrap |
| JEL: | C12 C15 C23 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201462&r=ets |
| By: | Francisco Blasques; Siem Jan Koopman; Max Mallee (VU University Amsterdam, the Netherlands) |
| Abstract: | The multivariate analysis of a panel of economic and financial time series with mixed frequencies is a challenging problem. The standard solution is to analyze the mix of monthly and quarterly time series jointly by means of a multivariate dynamic model with a monthly time index: artificial missing values are inserted for the intermediate months of the quarterly time series. In this paper we explore an alternative solution for a class of dynamic factor models that is specified by means of a low frequency quarterly time index. We show that there is no need to introduce artificial missing values while the high frequency (monthly) information is preserved and can still be analyzed. We also provide evidence that the analysis based on a low frequency specification can be carried out in a computationally more efficient way. A comparison study with existing mixed frequency procedures is presented and discussed. Furthermore, we modify the method of maximum likelihood in the context of a dynamic factor model. We introduce variable-specific weights in the likelihood function to let some variable equations be of more importance during the estimation process. We derive the asymptotic properties of the weighted maximum likelihood estimator and we show that the estimator is consistent and asymptotically normal. We also verify the weighted estimation method in a Monte Carlo study to investigate the effect of differen t choices for the weights in different scenarios. Finally, we empirically illustrate the new developments for the extraction of a coincident economic indicator from a small panel of mixed frequency economic time series. |
| Keywords: | Asymptotic theory, Forecasting, Kalman filter, Nowcasting, State space |
| JEL: | C13 C32 C53 E17 |
| Date: | 2014–08–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140105&r=ets |
| By: | Federico Carlini (CREATES, Aarhus University, Denmark); Katarzyna Lasak (VU University Amsterdam) |
| Abstract: | In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following the ideas in Carlini and Santucci de Magistris (2014) for the model of Johansen (2008, 2009). We propose a 4-step estimation procedure that is based on the switching algorithm employed in Carlini and Mosconi (2014) and the GLS procedure in Mosconi and Paruolo (2014). The proposed procedure provides estimates of the long run parameters of the fractionally cointegrated system that are consistent and unbiased, which we demonstrate by a Monte Carlo experiment. |
| Keywords: | Error correction model, Gaussian VAR model, Fractional Cointegration, Estimation algorithm, Maximum likelihood estimation, Switching Algorithm, Reduced Rank Regression |
| JEL: | C13 C32 |
| Date: | 2014–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140052&r=ets |
| By: | Guillaume Gaetan Martinet (ENSAE Paris Tech, France, and Columbia University, United States); Michael McAleer (National Tsing Hua University, Taiwan; Erasmus University Rotterdam, the Netherlands; and Complutense University of Madrid, Spain) |
| Abstract: | Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions. A limitation in the development of asymptotic properties of the QMLE for EGARCH is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH parameters. |
| Keywords: | Leverage, asymmetry, existence, stochastic process, asymptotic properties, invertibility |
| JEL: | C22 C52 C58 G32 |
| Date: | 2014–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140096&r=ets |
| By: | Francisco Blasques; Siem Jan Koopman; Andr� Lucas (VU University Amsterdam, the Netherlands) |
| Abstract: | We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The resulting time-varying autoregressive model is formulated as a nonlinear autoregressive model and is compared with threshold and smooth-transition autoregressive models. We establish the information theoretic optimality of the score driven nonlinear autoregressive process and the asymptotic theory for maximum likelihood parameter estimation. The performance of our model in extracting the time-varying or the nonlinear dependence for finite samples is studied in a Monte Carlo exercise. In our empirical study we present the in-sample and out-of-sample performances of our model for a weekly time series of unemployment insurance claims. |
| Keywords: | Asymptotic theory; Dynamic models, Observation driven time series models; Smooth-transition model; Time-Varying Parameters; Treshold autoregressive model |
| JEL: | C13 C22 C32 |
| Date: | 2014–08–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140103&r=ets |
| By: | Søren Johansen (University of Copenhagen and CREATES); Bent Nielsen (Nuffield College & Department of Economics, University of Oxford & Institute for New Economic Thinking at the Oxford Martin School.) |
| Abstract: | We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator Saturation, iterated 1-step Huber-skip M-estimators and the Forward Search. These methods classify observations as outliers or not. From the asymptotic results we establish a new asymptotic theory for the gauge of these methods, which is the expected frequency of falsely detected outliers. The asymptotic theory involves normal distribution results and Poisson distribution results. The theory is applied to a time series data set. |
| Keywords: | Huber-skip M-estimators, 1-step Huber-skip M-estimators, iteration, Forward Search, Impulse Indicator Saturation, Robusti?ed Least Squares, weighted and marked empirical processes, iterated martingale inequality, gauge |
| JEL: | C22 C52 |
| Date: | 2014–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-39&r=ets |
| By: | Audrone Virbickaite; Hedibert F. Lopes; Concepcion Ausín; Pedro Galeano |
| Abstract: | This paper designs a Particle Learning (PL) algorithm for estimation of Bayesian nonparametric Stochastic Volatility (SV) models for financial data. The performance of this particle method is then compared with the standard Markov Chain Monte Carlo (MCMC) methods for non-parametric SV models. PL performs as well as MCMC, and at the same time allows for on-line type inference. The posterior distributions are updated as new data is observed, which is prohibitively costly using MCMC. Further, a new non-parametric SV model is proposed that incorporates Markov switching jumps.The proposed model is estimated by using PL and tested on simulated data. Finally, the performance of the two non-parametric SV models, with and without Markov switching, is compared by using real financial time series. The results show that including a Markov switching specification provides higher predictive power in the tails of the distribution. |
| Keywords: | Dirichlet Process Mixture, Markov Switching, MCMC, Particle Learning, Stochastic Volatility, Sequential Monte Carlo |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws142819&r=ets |
| By: | Andr� Lucas (VU University Amsterdam); Xin Zhang (Sveriges Riksbank, Sweden) |
| Abstract: | We present a simple new methodology to allow for time variation in volatilities using a recursive updating scheme similar to the familiar RiskMetrics approach. We update parameters using the score of the forecasting distribution rather than squared lagged observations. This allows the parameter dynamics to adapt automatically to any non-normal data features and robustifies the subsequent volatility estimates. Our new approach nests several extensions to the exponentially weighted moving average (EWMA) scheme as proposed earlier. Our approach also easily handles extensions to dynamic higher-order moments or other choices of the preferred forecasting distribution. We apply our method to Value-at-Risk forecasting with Student's t distributions and a time varying degrees of freedom parameter and show that the new method is competitive to or better than earlier methods for volatility forecasting of individual stock returns and exchange rates. |
| Keywords: | dynamic volatilities, time varying higher order moments, integrated generalized autoregressive score models, Exponential Weighted Moving Average (EWMA), Value-at-Risk (VaR) |
| JEL: | C51 C52 C53 G15 |
| Date: | 2014–07–22 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140092&r=ets |