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on Econometric Time Series |
| By: | Chang, C-L.; McAleer, M.J. |
| Abstract: | An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns, was the portmanteau statistic for non-causality in variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test of non-causality in the conditional variance by Hafner and Herwartz (2006), who provided simulations results to show that their LM test was more powerful than the portmanteau statistic. While the LM test for causality proposed by Hafner and Herwartz (2006) is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so that the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and for which the (quasi-) maximum likelihood estimates have valid asymptotic properties. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger’s (1969, 1988) notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test. |
| Keywords: | Random coefficient stochastic process, Simple test, Granger non-causality, Regularity conditions, Asymptotic properties, Conditional volatility |
| JEL: | C22 C32 C52 C58 |
| Date: | 2016–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:98603&r=ets |
| By: | Sujay Mukhoti; Pritam Ranjan |
| Abstract: | In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs. |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.06603&r=ets |
| By: | Guglielmo Maria Caporale; Luis A. Gil-Alana; Alex Plastun |
| Abstract: | This paper investigates persistence in financial time series at three different frequencies (daily, weekly and monthly). The analysis is carried out for various financial markets (stock markets, FOREX, commodity markets) over the period from 2000 to 2016 using two different long memory approaches (R/S analysis and fractional integration) for robustness purposes. The results indicate that persistence is higher at lower frequencies, for both returns and their volatility. This is true of the stock markets (both developed and emerging) and partially of the FOREX and commodity markets examined. Such evidence against the random walk behavior implies predictability and is inconsistent with the Efficient Market Hypothesis (EMH), since abnormal profits can be made using specific option trading strategies (butterfly, straddle, strangle, iron condor, etc.). |
| Keywords: | Persistence, Long Memory, R/S Analysis, Fractional Integration |
| JEL: | C22 G12 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1647&r=ets |
| By: | Matthew T. Holt (University of Alabama, Department of Economics, Finance & Legal Studies); Timo Teräsvirta (Aarhus University and CREATES, C.A.S.E., Humboldt-Universität zu Berlin) |
| Abstract: | This paper examines local changes in annual temperature data for the northern and southern hemispheres (1850-2014) by using a multivariate generalisation of the shifting-mean autoregressive model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the QuickShift methodology. Full information maximum likelihood estimates of a bivariate system of temperature equations are then obtained and asymptotic properties of the corresponding estimators considered. The system is then used to perform formal tests of co-movements, called co-shifting, in the series. The results show evidence of co-shifting in the two series. Forecasting this pair of series is considered as well. |
| Keywords: | Co-breaking, Hemispheric temperatures, Vector nonlinear model, Testing linearity, Structural change |
| JEL: | C22 C32 C52 C53 Q54 |
| Date: | 2401 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-05&r=ets |
| By: | Peter Exterkate (University of Sydney and CREATES); Oskar Knapik (Aarhus University and CREATES) |
| Abstract: | In a recent review paper, Weron (2014) pinpoints several crucial challenges outstanding in the area of electricity price forecasting. This research attempts to address all of them by i) showing the importance of considering fundamental price drivers in modeling, ii) developing new techniques for probabilistic (i.e. interval or density) forecasting of electricity prices, iii) introducing an universal technique for model comparison. We propose new regime-switching stochastic volatility model with three regimes (negative jump, normal price, positive jump (spike)) where the transition matrix depends on explanatory variables. Bayesian inference is explored in order to obtain predictive densities. The main focus of the paper is on shorttime density forecasting in Nord Pool intraday market. We show that the proposed model outperforms several benchmark models at this task. |
| Keywords: | Electricity prices, density forecasting, Markov switching, stochastic volatility, fundamental price drivers, ordered probit model, Bayesian inference, seasonality, Nord Pool power market, electricity prices forecasting, probabilistic forecasting |
| JEL: | C22 C24 Q41 Q47 |
| Date: | 2601 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-03&r=ets |
| By: | Giuseppe Cavaliere (University of Bologna); Morten Ørregaard Nielsen (Queen?s University and CREATES); Robert Taylor (University of Essex) |
| Abstract: | We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of squares estimators in the context of parametric fractional time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short memory parameters of the model. The limiting null distributions of these test statistics are shown to be non-pivotal under heteroskedasticity, while that of a robustWald statistic (based around a sandwich estimator of the variance) is pivotal. We show that wild bootstrap implementations of the tests deliver asymptotically pivotal inference under the null. We demonstrate the consistency and asymptotic normality of the bootstrap estimators, and further establish the global consistency of the asymptotic and bootstrap tests under fixed alternatives. Monte Carlo simulations highlight significant improvements in finite sample behaviour using the bootstrap in both heteroskedastic and homoskedastic environments. Our theoretical developments and Monte Carlo simulations include two bootstrap algorithms which are based on model estimates obtained either under the null hypothesis or unrestrictedly. Our simulation results suggest that the former is preferable to the latter, displaying superior size control yet largely comparable power. |
| Keywords: | conditional/unconditional heteroskedasticity, conditional sum-of-squares, fractional integration, quasi-maximum likelihood estimation, wild bootstrap |
| JEL: | C12 C13 C22 |
| Date: | 2501 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-02&r=ets |
| By: | Timo Teräsvirta (Aarhus University and CREATES, C.A.S.E., Humboldt-Universität zu Berlin) |
| Abstract: | Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger's contributions to a few other aspects of nonlinearity are reviewed as well. JEL Classification: C22, C51, C52, C53 |
| Keywords: | cointegration, nonlinearity, nonstationarity, testing linearity |
| Date: | 2701 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-04&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen); Morten Nyboe Tabor (Department of Economics, University of Copenhagen) |
| Abstract: | In a linear state space model Y(t)=BT(t)+e(t), we investigate if the unobserved trend, T(t), cointegrates with the predicted trend, E(t), and with the estimated predicted trend, in the sense that the spreads are stationary. We find that this result holds for the spread B(T(t)-E(t)) and the estimated spread. For the spread between the trend and the estimated trend, T(t)-E(t), however, cointegration depends on the identification of B. The same results are found, if the observations Y(t), from the state space model are analysed using a cointegrated vector autoregressive model, where the trend is defined as the common trend. Finally, we investigate cointegration between the spread beteween trends and their estimators based on the two models, and find the same results. We illustrate with two examples and confirm the results by a small simulation study. |
| Keywords: | Cointegration of trends, State space models, CVAR models |
| JEL: | C32 |
| Date: | 2017–03–13 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1702&r=ets |
| By: | Jinyuan Chang; Bin Guo; Qiwei Yao |
| Abstract: | We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the the endogeneity that there exist correlations between the observed regressors and the unobserved factors. We also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors. The convergence rates for the estimators of regression coefficients, the number of factors, factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size. The proposed method is illustrated with both simulated and real data examples. |
| Keywords: | α-mixing; dimension reduction; instrument variables; nonstationarity; time series |
| JEL: | C13 C32 C39 |
| Date: | 2015–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:61886&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Professor T.W. Anderson passed away on September 17, 2016 at the age of 98 years after an astonishing career that spanned more than seven decades. Standing at the nexus of the statistics and economics professions, Ted Anderson made enormous contributions to both disciplines, playing a significant role in the birth of modern econometrics with his work on structural estimation and testing in the Cowles Commission during the 1940s, and educating successive generations through his brilliant textbook expositions of time series and multivariate analysis. This article is a tribute to his many accomplishments. |
| Keywords: | T. W. Anderson, Cowles Commission, Limited information maximum likelihood, Multivariate analysis, Time series |
| JEL: | A14 B23 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2081&r=ets |