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on Econometric Time Series |
| By: | G. Kavitha; A. Udhayakumar; D. Nagarajan |
| Abstract: | Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer scientists [17]. This paper gives an idea about the trend analysis of stock market behaviour using Hidden Markov Model (HMM). The trend once followed over a particular period will sure repeat in future. The one day difference in close value of stocks for a certain period is found and its corresponding steady state probability distribution values are determined. The pattern of the stock market behaviour is then decided based on these probability values for a particular time. The goal is to figure out the hidden state sequence given the observation sequence so that the trend can be analyzed using the steady state probability distribution( ) values. Six optimal hidden state sequences are generated and compared. The one day difference in close value when considered is found to give the best optimum state sequence. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.4771&r=ets |
| By: | Geon Ho Choe; Kyungsub Lee |
| Abstract: | In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset return dynamics in which frequencies of the up and down movements of asset price have conditionally independent Poisson distributions with stochastic intensities. The intensities are assumed to be stochastic recurrence equations of the GARCH type in order to capture the volatility clustering and the leverage effect. We provide an important linkage between our model and existing GARCH, explain how to apply maximum likelihood estimation to determine the parameters in the intensity model and show empirical results with the S&P 500 index return series. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.4977&r=ets |
| By: | R\'emy Chicheportiche; Anirban Chakraborti |
| Abstract: | We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study non-linear time dependences and related concepts - like aftershocks, Omori law, recurrences, waiting times. We also critically argue using this global approach that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially mono-scale. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.5101&r=ets |
| By: | Samuel N. Cohen; Robert J. Elliott |
| Abstract: | We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.6257&r=ets |
| By: | Peter M Robinson; Carlos Velasco |
| Abstract: | A dynamic panel data model is considered that contains possibly stochastic individual components and a common fractional stochastic time trend. We propose four different ways of coping with the individual effects so as to estimate the fractional parameter. Like models with autoregressive dynamics, ours nests a unit root, but unlike the nonstandard asymptotics in the autoregressive case, estimates of the fractional parameter can be asymptotically normal. Establishing this property is made difficult due to bias caused by the individual effects, or by the consequences of eliminating them, and requires the number of time series observations T to increase, while the cross-sectional size, N; can either remain fi�xed or increase with T: The biases in the central limit theorem are asymptotically negligible only under stringent conditions on the growth of N relative to T; but these can be relaxed by bias correction. For three of the estimates the biases depend only on the fractional parameter. In hypothesis testing, bias correction of the estimates is readily carried out. We evaluate the biases numerically for a range of T and parameter values, develop and justify feasible bias-corrected estimates, and briefly discuss implied but less effective corrections. A Monte Carlo study of �finite-sample performance is included. |
| Keywords: | Panel data, Fractional time series, Estimation, Testing, Bias correction |
| JEL: | C12 C13 C23 |
| Date: | 2013–03 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:/2013/567&r=ets |
| By: | Anton Skrobotov (Gaidar Institute for Economic Policy) |
| Abstract: | In this paper we propose tests based on GLS-detrending for testing the null hypothesis of deterministic seasonality. Unlike existing tests for deterministic seasonality, our tests do not suer from asymptotic size distortions under near integration. We also investigate the behavior of the proposed tests when the initial condition is not asymptotically negligible. types. |
| Keywords: | Stationarity tests, KPSS test, seasonality, seasonal unit roots, deterministic sea-sonality, size distortion, GLS-detrending. |
| JEL: | C12 C22 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:gai:wpaper:0073&r=ets |
| By: | Anton Skrobotov (Gaidar Institute for Economic Policy) |
| Abstract: | In a recently publicized study, Harvey et al. (2012) investigated procedures for unit root testing employing break detection methods under local break in trend. We apply this methodology to analyze asymptotic and unite sample behavior of procedures under local break to test the stationarity null hypothesis local to unit root, against alternative hypothesis about the pres- ence of a unit root. We extend the GLS-based stationarity test proposed by Harris et al. (2007) to the case of structural break and obtain asymptotic properties under local trend break. Two procedures are considered. The first procedure uses a with-break stationarity test, but with adaptive critical values. The second procedure utilizes the intersection of rejection testing strategy containing tests with and without a break. Application of these approaches help to prevent serious size distortions for small break magnitude that are otherwise undetectable. Additionally, in a similar approach as Harvey et al. (2013) and Busetti and Harvey (2001), we propose a test based on minimizing the sequence of GLS-based stationarity test statistics over all possible break dates. This infimum-test in contrast to Busetti and Harvey (2001) does not require an additional assumption about a faster rate of convergence of break magnitude. Asymptotic and unite sample simulations show that under local to zero behavior of the trend break the asymptotic analysis provides a good approximation of the unite sample behavior of the proposed procedures. Proposed procedures can be used for confirmatory analysis together with tests of Harvey et al. (2012) and Harvey et al. (2013). |
| Keywords: | Stationarity tests, KPSS tests, local break in trend, size distortions, intersection of rejection decision rule.. |
| JEL: | C12 C22 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:gai:wpaper:0074&r=ets |
| By: | Saikkonen, Pentti (Department of Mathematics and Statistics, University of Helsinki); Sandberg , Rickard (Department of Economics, Center for Economic Statistics, Stockholm School of Economics) |
| Abstract: | This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons of identification the error term of the model is supposed to be non-Gaussian. In order to derive the tests, asymptotic properties of the maximum likelihood estimators are established under the unit root hypothesis. The limiting distributions of the proposed tests depend on a nuisance parameter determined by the distribution of the error term of the model. A simple procedure to handle this nuisance parameter dependence in applications is proposed. Finite sample properties of the tests are examined by means of Monte Carlo simulations. The results show that the size properties of the tests are satisfactory and the power against stationary NCAR alternatives is significantly higher than the power of conventional Dickey-Fuller tests and the M-tests of Lucas (1995, Econometric Theory 11, 331-346). In an empirical application to a Finnish interest rate series evidence in favour of a stationary NCAR model with leptokurtic errors is found. |
| Keywords: | maximum likelihood estimation; noncausal autoregressive model; non-Gaussian time series; unit root |
| JEL: | C01 C12 C22 |
| Date: | 2013–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:bofrdp:2013_026&r=ets |
| By: | Chang-Jin Kim (Department of Economics, University ofWashington, and Department of Economics, Korea University); Jaeho Kim (Dept. of Economics, Univ. of Washington, Seattle, WA) |
| Abstract: | One goal of this paper is to develop an efficient Markov-Chain Monte Carlo (MCMC) algorithm for estimating an ARMA model with a regime-switching mean, based on a multimove sampler. Unlike the existing algorithm of Billio et al. (1999) based on a single-move sampler, our algorithm can achieve reasonably fast convergence to the posterior distribution even when the latent regime indicator variable is highly persistent or when there exist absorbing states. Another goal is to appropriately investigate the dynamics of the latent ex-ante real interest rate (EARR) in the presence of structural breaks, by employing the econometric tool developed. We argue Garcia and Perron¡¯s (1996) conclusion that the EARR rate is a constant subject to occasional jumps may be sample-specific. For an extended sample that includes recent data, Garcia and Perron¡¯s (1996) AR(2) model of EPRR may be misspecified,and we show that excluding the theory-implied moving-average terms may understate the persistence of the observed ex-post real interest rate (EPRR) dynamics. Our empiricalresults suggest that, even though we rule out the possibility of a unit root in the EARR, it may be more persistent and volatile than has been documented in some of the literature including Garcia and Perron (1996). |
| Keywords: | ARMA model with Regime Switching, Multi-move Sampler, Single-Move Sampler, Metropolis-Hastings Algorithm, Absorbing State, Ex-Ante Real Interest Rate |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:1306&r=ets |
| By: | Andrea Cipollini; Iolanda Lo Cascio; Silvia Muzzioli |
| Abstract: | In this paper we investigate short-run co-movements before and after the Lehman Brothers’ collapse among the volatility series of US and a number of European countries. The series under investigation (implied and realized volatility) exhibit long-memory and, in order to avoid miss-specification errors related to the parameterization of a long memory multivariate model, we rely on wavelet analysis. More specifically, we retrieve the time series of wavelet coefficients for each volatility series for high frequency scales, using the Maximal Overlapping Discrete Wavelet transform and we apply Maximum Likelihood for a factor decomposition of the short-run covariance matrix. The empirical evidence shows an increased interdependence in the post-break period and points at an increasing (decreasing) role of the common shock underlying the dynamics of the implied (realized) volatility series, once we move from the 2-4 days investment time horizon to the 8-16 days. Moreover, there is evidence of contagion from the US to Europe immediately after the Lehman Brothers’ collapse, only for realized volatilities over an investment time horizon between 8 and 16 days. |
| Keywords: | Implied volatility, Realized Volatility, Co-movements, Long Memory, Wavelets |
| JEL: | C32 C38 C58 G13 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:mod:wcefin:13111&r=ets |
| By: | Guo, Shaojun; Ling, Shiqing; Zhu, Ke |
| Abstract: | Testing causality-in-mean and causality-in-variance has been largely studied. However, none of the tests can detect causality-in-mean and causality-in-variance simultaneously. In this article, we introduce a factor double autoregressive (FDAR) model. Based on this model, a score test is proposed to detect causality-in-mean and causality-in-variance simultaneously. Furthermore, strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for the FDAR model are established. A small simulation study shows good performances of the QMLE and the score test in finite samples. A real data example on the causal relationship between Hong Kong stock market and US stock market is given. |
| Keywords: | Asymptotic Normality; Causality-in-mean; Causality-in-variance; Factor DAR model; Instantaneous causality; Score test; Strong consistency. |
| JEL: | C1 C12 C5 |
| Date: | 2013–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51570&r=ets |
| By: | Xiaohu Wang (Chinese University of Hong Kong); Jun Yu (Singapore Management University, School of Economics) |
| Abstract: | Large sample properties are studied for a rst-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coe¢ cient, the least- squares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error distribution, and hence an invariance principle applies. While the invariance principle does not apply to the asymptotic distribution of the LS estimator of the AR coe¢ cient, we show explicitly how it depends on the initial condition and the intercept. Also established are the asymptotic independence between the LS estimators of the intercept and the AR coefficient and the asymptotic independence between their t-statistics. Asymptotic theory for explosive processes is compared to that for unit root AR(1) processes and stationary AR(1) processes. The coefficient based test and the t test have better power for testing the hypothesis of zero intercept in the explosive process than in the stationary process. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:08-2013&r=ets |