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on Econometric Time Series |
| By: | Ryo Okui; Takahide Yanagi |
| Abstract: | This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. Our procedure is model-free and easy to implement, and provides useful visual information, which enables us to understand intuitively the properties of heterogeneity. We rst estimate the sample mean, autocovariances, and auto- correlations for each unit and then apply kernel smoothing to compute estimates of their density and cumulative distribution functions. The kernel estimators are consistent and asymptotically normal under double asymptotics, i.e., when both cross-sectional and time series sample sizes tend to in nity. However, as these exhibit biases given the incidental parameter problem and the nonlinearity of the kernel function, we propose jackknife methods to alleviate any bias. We also develop bandwidth selection methods and bootstrap inferences based on the asymptotic properties. Lastly, we illustrate the success of our procedure using an empirical application of the dynamics of US prices and Monte Carlo simulation. |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1802.08825&r=ets |
| By: | Chambers, Marcus J; Taylor, AM Robert |
| Abstract: | We consider models for both deterministic one-time and continuous stochastic parameter change in a continuous time autoregressive model around a deterministic trend function. For the latter we focus on the case where the autoregressive parameter itself follows a first-order autoregression. Exact discrete time analogue models are detailed in each case and compared to corresponding parameter change models adopted in the discrete time literature. The relationships between the parameters in the continuous time models and their discrete time analogues are also explored. For the one- time parameter change model the discrete time models used in the literature can be justified by the corresponding continuous time model, with a only a minor modification needed for the (most likely) case where the changepoint does not coincide with one of the discrete time observation points. For the stochastic parameter change model considered we show that the resulting discrete time model is characterised by an autoregressive parameter the logarithm of which follows an ARMA(1,1) process. We discuss how this relates to models which have been proposed in the discrete time stochastic unit root literature. The implications of our results for a number of extant discrete time models and testing procedures are discussed. |
| Keywords: | Time-varying parameters, continuous and discrete time, autoregression, trendbreak, unit root, persistence change, explosive bubbles, random coeffcient models |
| Date: | 2018–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:21684&r=ets |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies, Tokyo, Japan) |
| Abstract: | This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma Stochastic Volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse Gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse Gamma and Generalized inverse Gamma processes can greatly outperform the commonly used log normal volatility processes with student-t errors or jumps in the mean equation. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:ngi:dpaper:17-16&r=ets |
| By: | L. Bauwens; E. Otrando |
| Abstract: | New parameterizations of the dynamic conditional correlation (DCC) model and of the regime-switching dynamic correlation (RSDC) model are introduced, such that these models provide a specific dynamics for each correlation. They imply a non-linear autoregressive form of dependence on lagged correlations and are based on properties of the Hadamard exponential matrix. The new models are applied to a data set of twenty stock market indices, comparing them to the classical DCC and RSDC models. The empirical results show that the new models improve their classical versions in terms of several criteria. |
| Keywords: | dynamic conditional correlations;regime-switching dynamic correlations;Hadamard exponential matrix |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:201803&r=ets |
| By: | Yang Lu (CEPN - Centre d'Economie de l'Université Paris Nord - UP13 - Université Paris 13 - USPC - Université Sorbonne Paris Cité - CNRS - Centre National de la Recherche Scientifique); Christian Gourieroux (University of Toronto, TSE - Toulouse School of Economics - Toulouse School of Economics) |
| Abstract: | We introduce Negative Binomial Autoregressive (NBAR) processes for (univariate and bivariate) count time series. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial conditional and marginal distributions. The process is then extended to the bivariate case with a Wishart autoregressive matrix intensity process. The NBAR processes are Compound Autoregressive, which allows for simple stationarity condition and quasi-closed form nonlinear forecasting formulas at any horizon, as well as a computationally tractable generalized method of moment estimator. The model is applied to a pairwise analysis of weekly occurrence counts of a contagious disease between the greater Paris region and other French regions. |
| Keywords: | Compound Autoregressive, Poisson-gamma conjugacy |
| Date: | 2018–03–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cepnwp:hal-01730050&r=ets |
| By: | Josep Lluís Carrion-i-Silvestre (AQR-IREA, University of Barcelona); María Dolores Gadea (Department of Applied Economics, University of Zaragoza); Antonio Montañés (Department of Economic Analysis, University of Zaragoza) |
| Abstract: | The paper investigates the estimation bias of autoregressive models for bounded stochastic processes and the performance of the standard procedures in the literature that aim to correcting the estimation bias. It is shown that, in some cases, the bounded nature of the stochastic processes worsen the estimation bias effect, which suggests the design of bound specific bias correction methods. The paper focuses on two popular autoregressive estimation bias correction procedures which are extended to cover bounded stochastic processes. Finite sample performance analysis of the new proposal is carried out using Monte Carlo simulations which reveal that accounting for the bounded nature of the stochastic processes leads to improvements in the estimation of autoregressive models. Finally, an illustration is given using the current account balance of some developed countries, whose shocks persistence measures are computed. |
| Keywords: | Bounded stochastic processes, estimation bias, unit root tests, current account balance JEL classification: C22, C32, E32, Q43 |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:aqr:wpaper:201710&r=ets |
| By: | Nadia Boussaha; Faycal Hamdi; Saïd Souam |
| Abstract: | The contribution of this paper is twofold. In a first step, we propose the so called Periodic Multivariate Autoregressive Stochastic Volatility (PV ARSV) model, that allows the Granger causality in volatility in order to capture periodicity in stochastic conditional variance. After a thorough discussion, we provide some probabilistic properties of this class of models. We thus propose two methods for the estimation problem, one based on the periodic Kalman filter and the other on the particle filter and smoother with Expectation-Maximization (EM) algorithm. In a second step, we propose an empirical application by modeling oil price and three exchange rates time series. It turns out that our modeling gives very accurate results and has a well volatility forecasting performance. |
| Keywords: | Multivariate periodic stochastic volatility; periodic stationarity; periodic Kalman filter; particle filtering; exchange rates; Saharan Blend oil. |
| JEL: | C32 C53 F31 G17 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2018-14&r=ets |
| By: | Tomás del Barrio Castro (Universitat de les Illes Balears); Paulo M.M. Rodrigues (Banc of Portugal); A. M. Robert Taylor (University of Essex) |
| Abstract: | In this paper we investigate the implications that temporally aggregating, either by average sampling or systematic sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local-to-unity (which includes exact unit roots as a special case) such that the original series is near-integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non-seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near-integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored. |
| Keywords: | Aggregation, systematic sampling, average sampling, seasonal (near-) unit roots, demodulation |
| JEL: | C12 C22 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ubi:deawps:86&r=ets |
| By: | Xiao, Weilin (Zhejiang University); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper extends the asymptotic theory for the fractional Vasicek model developed in Xiao and Yu (2018) from the case where H ∈ (1/2, 1) to the case where H ∈ (0, 1/2). It is found that the asymptotic theory of the persistence parameter (k) critically depends on the sign of k. Moreover, if k > 0, the asymptotic distribution for the estimator of k is different when H ∈ (0, 1/2) from that when H ∈ (1/2, 1). |
| Keywords: | Least squares; Roughness; Strong consistency; Asymptotic distribution |
| JEL: | C15 C22 C32 |
| Date: | 2018–03–19 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2018_007&r=ets |