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on Econometric Time Series |
| By: | Aurelio F. Bariviera; Angelo Plastino; George Judge |
| Abstract: | This paper offers a general and comprehensive definition of the day-of-the-week effect. Using symbolic dynamics, we develop a unique test based on ordinal patterns in order to detect it. This test uncovers the fact that the so-called "day-of-the-week" effect is partly an artifact of the hidden correlation structure of the data. We present simulations based on artificial time series as well. Whereas time series generated with long memory are prone to exhibit daily seasonality, pure white noise signals exhibit no pattern preference. Since ours is a non parametric test, it requires no assumptions about the distribution of returns so that it could be a practical alternative to conventional econometric tests. We made also an exhaustive application of the here proposed technique to 83 stock indices around the world. Finally, the paper highlights the relevance of symbolic analysis in economic time series studies. |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1801.07941&r=ets |
| By: | Mazur, Stepan (Örebro University School of Business); Otryakhin, Dmitry (Aarhus University); Podolskij, Mark (Aarhus University) |
| Abstract: | In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $\sigma>0$, the self-similarity parameter $H \in (0,1)$ and the stability index $\alpha \in (0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments L\'evy moving average processes that has been recently studied in \cite{BLP}. More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(\sigma, \alpha, H)$. We present the law of large numbers and some fully feasible weak limit theorems. |
| Keywords: | fractional processes; limit theorems; parametric estimation; stable motion |
| JEL: | C00 C13 |
| Date: | 2018–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2018_003&r=ets |
| By: | Xin Jin (School of Economics, Shanghai University of Finance and Economics, China); John M. Maheu (DeGroote School of Business, McMaster University, Canada; Rimini Centre for Economic Analysis); Qiao Yang (School of Entrepreneurship and Management, ShanghaiTech University, China) |
| Abstract: | This paper introduces a new factor structure suitable for modeling large realized covariance matrices with full likelihood based estimation. Parametric and nonparametric versions are introduced. Due to the computational advantages of our approach we can model the factor nonparametrically as a Dirichlet process mixture or as an infinite hidden Markov mixture which leads to an infinite mixture of inverse-Wishart distributions. Applications to 10 assets and 60 assets show the models perform well. By exploiting parallel computing the models can be estimated in a matter of a few minutes. |
| Keywords: | infinite hidden Markov model, Dirichlet process mixture, inverse-Wishart, predictive density, high-frequency data |
| JEL: | G17 C11 C14 C32 C58 |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:18-02&r=ets |
| By: | Mark Fisher (Federal Reserve Bank of Atlanta, USA); Mark J. Jensen (Federal Reserve Bank of Atlanta, USA; Rimini Centre for Economic Analysis) |
| Abstract: | Change point models using hierarchical priors share in the information of each regime when estimating the parameter values of a regime. Because of this sharing hierarchical priors have been very successful when estimating the parameter values of short-lived regimes and predicting the out-of-sample behavior of the regime parameters. However, the hierarchical priors have been parametric. Their parametric nature leads to global shrinkage that biases the estimates of the parameter coefficient of extraordinary regimes towards the value of the average regime. To overcome this shrinkage we model the hierarchical prior nonparametrically by letting the hyperparameter's prior, in other words, the hyperprior, be unknown and modeling it with a Dirichlet processes prior. To apply a nonparametric hierarchical prior to the probability of a break occurring we extend the change point model to a multiple-change-point panel model. The hierarchical prior then shares in the cross-sectional information of the break processes to estimate the transition probabilities. We apply our multiple-change-point panel model to a longitudinal data set of actively managed, US equity, mutual fund returns to measure fund performance and investigate what the chances are of a skilled fund being skilled in the future. |
| Keywords: | Bayesian nonparametric analysis, change points, Dirichlet process, hierarchical priors, mutual fund performance |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:18-12&r=ets |
| By: | Licht, Adrian; Escribano Sáez, Álvaro; Blazsek, Szabolcs Istvan |
| Abstract: | We introduce the Seasonal-QVAR (quasi-vector autoregressive) model for world crude oil production and global real economic activity that identifies the hidden seasonality not found in linear VAR and VARMA models. World crude oil production has an annual seasonality component, and global real economic activity as measured by ocean freight rates has a six-month seasonality component.Seasonal-QVAR is a dynamic conditional score (DCS) model for the multivariate t distribution.Seasonal-VARMA and Seasonal-VAR are special cases of Seasonal-QVAR, this latter being superior to the two former models and also superior to the basic structural model with local level and stochastic seasonality components |
| Keywords: | Crude oil production; Vector autoregressive moving average (VARMA) model; Vector autoregressive (VAR) model; Basic structural model; Nonlinear multivariate dynamic location models; Score-driven stochastic seasonality; Dynamic conditional score (DCS) models |
| JEL: | C52 C32 |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:26316&r=ets |
| By: | Vandenberghe, Vincent |
| Abstract: | A common problem with differences-in-differences (DD) estimates is the failure of the parallel-trend assumption. To cope with this, most authors include polynomial (linear, quadratic…) trends among the regressors, and estimate the treatment effect as a once-in-a-time trend shift. In practice that strategy does not work very well, because inter alia the estimation of the trend uses post-treatment data. An extreme case is when sample covers only one period before treatment and many after. Then the trend's estimate relies almost completely on post-treatment developments, and absorbs most of the treatment effect. What is needed is a method that i) uses pre-treatment observations to capture linear or non-linear trend differences, and ii) extrapolates these to compute the treatment effect. This paper shows how this can be achieved using a fully-flexible version of the canonical DD equation. It also contains an illustration using data on a 1994-2000 EU programme that was implemented in the Belgian province of Hainaut. |
| Keywords: | Treatment-Effect Analysis,Differences-in-Differences Models,Correction for trend differences |
| JEL: | C21 C4 C5 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:172&r=ets |
| By: | Ishanu Chattopadhyay |
| Abstract: | Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite valued processes, providing the latter with the structure of a Hilbert space on the real field. This rigorous construction, based on non-standard generalizations of the notions of sum and scalar multiplication of finite dimensional probability vectors, allows us to meaningfully talk about "angles" between data streams and data sources, and, make precise the notion of orthogonal stochastic processes. In particular, the relative angles appear to be preserved, and identifiable, under severe noise, and will be developed in future as the underlying principle for robust classification, clustering and unsupervised featurization algorithms. |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1801.08256&r=ets |
| By: | Astill, Sam; Taylor, AM Robert |
| Abstract: | We develop tests for the presence of deterministic seasonal behaviour and seasonal mean shifts in a seasonally observed univariate time series. These tests are designed to be asymptotically robust to the order of integration of the series at both the zero and seasonal frequencies. Motivated by the approach of Hylleberg, Engle, Granger and Yoo [1990, Journal of Econometrics vol. 44, pp. 215-238], we base our approach on linear filters of the data which remove any potential unit roots at the frequencies not associated with the deterministic component(s) under test. Test statistics are constructed using the filtered data such that they have well defined limiting null distributions regardless of whether the data are either integrated or stationary at the frequency associated with the deterministic component(s) under test. In the same manner as Vogelsang [1998, Econometrica vol. 66, pp. 123-148], Bunzel and Vogelsang [2005, Journal of Business and Economic Statistics vol. 23, pp. 381-394] and Sayginsoy and Vogelsang [2011, Econometric Theory vol. 27, pp. 992-1025], we scale these statistics by a function of an auxiliary seasonal unit root statistic. This allows us to construct tests which are asymptotically robust to the order of integration of the data at both the zero and seasonal frequencies. Monte Carlo evidence suggests that our proposed tests have good finite sample size and power properties. An empirical application to U.K. GDP indicates the presence of seasonal mean shifts in the data. |
| Keywords: | Seasonality, Seasonal Level Breaks, Seasonal Unit Roots, Robust Tests |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:21470&r=ets |
| By: | Francisco (F.) Blasques (VU Amsterdam, The Netherlands); Paolo Gorgi (VU Amsterdam, The Netherlands); Siem Jan (S.J.) Koopman (VU Amsterdam, The Netherlands) |
| Abstract: | We argue that existing methods for the treatment of missing observations in observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for conditional volatility. To overcome the problem of inconsistent inference, we propose a novel estimation procedure based on indirect inference. This easy-to-implement method delivers consistent inference. The asymptotic properties are formally derived. Our proposed method shows a promising performance in both a Monte Carlo study and an empirical study concerning the measurement of conditional volatility from financial returns data. |
| Keywords: | missing data; observation-driven models; consistency; indirect inference; volatility |
| JEL: | C22 C58 |
| Date: | 2018–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180013&r=ets |
| By: | Lorenzo Camponovo (University of Surrey); Yukitoshi Matsushita (Tokyo Institute of Technology); Taisuke Otsu (London School of Economics) |
| Abstract: | We propose a nonparametric likelihood inference method for the integrated volatility under high frequency financial data. The nonparametric likelihood statistic, which contains the conventional statistics such as empirical likelihood and Pearson’s x^2 as special cases, is not asymptotically pivotal under the so-called infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. We show that multiplying a correction term recovers the x^2 limiting distribution. Furthermore, we establish Bartlett correction for our modified nonparametric likelihood statistic under the constant and general non-constant volatility cases. In contrast to the existing literature, the empirical likelihood statistic is not Bartlett correctable under the infill asymptotics. However, by choosing adequate tuning constants for the power divergence family, we show that the second order refinement to the order O(n^{-2}) can be achieved. |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:sur:surrec:0318&r=ets |