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on Econometric Time Series |
| By: | Gustavo A. Sánchez (StataCorp LP) |
| Abstract: | On a daily basis, we at Stata receive a broad variety of technical questions from users working in different areas with a large number of Stata commands. I selected a few common, interesting questions to help provide a brief view of the tools that are available in Stata for time-series analysis. I will start with a quick, simple introduction to time series in Stata, and I will then illustrate the use of a few commands to perform common tasks that are normally involved in the kind of empirical analysis developed by some of the Stata users who regularly contact us for technical assistance. |
| Date: | 2011–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:boc:msug11:03&r=ets |
| By: | Edoardo Otranto |
| Abstract: | The classification of volatility of financial time series has recently received a lot of contributions - in particular using model based clustering algorithms. Recent works have evidenced how volatility structure can vary along time, with gradual or abrupt changes in the coefficients of the model. We wonder if these changes can affect the classification of series in terms of similar volatility structure. We propose to classify the level of the unconditional volatility obtained from Multiplicative Er- ror Models with the possibility of changes in the parameters of the model in terms of regime switching or time varying smoothed coefficients. They provide different unconditional volatility structures with a proper interpretation, useful to represent different situations of interest. The different methodologies are coherent with each other and provide a common synthetic pattern. The procedure is experimented on fifteen stock indices volatilities. |
| Keywords: | clustering; AMEM; Markov switching; smooth transition; unconditional volatility |
| JEL: | C22 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:201113&r=ets |
| By: | Milan Rippel (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic); Ivo Jánský (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic) |
| Abstract: | The paper evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the ARMA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting accuracy is evaluated on the out-of-sample data, which are more volatile. The main aim of the paper is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index separately. The primary result of the paper is that the volatility is best modelled using a GARCH process and that an ARMA process pattern cannot be found in analyzed time series. |
| Keywords: | VaR, risk analysis, conditional volatility, conditional coverage, garch, egarch, tarch, moving average process, autoregressive process |
| JEL: | C51 C52 C53 G24 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2011_27&r=ets |
| By: | Vogelsang, Timothy J. (Department of Economics, Michigan State University, East Lansing, USA); Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria, and Frisch Centre for Economic Research, Oslo, Norway) |
| Abstract: | We extend fixed-b asymptotic theory to the nonparametric Phillips-Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These non-pivotal limits provide an alternative theoretical explanation for the well known finite sample problems of PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step approaches, contrasting the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long run variance estimator. Based on these results we introduce modified PP tests that allow for fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes which allows to study the asymptotic behavior both under the unit root null hypothesis as well as for local alternatives. The performance of the original and modified tests is compared by means of local asymptotic power and a small simulation study. |
| Keywords: | Nonparametric kernel estimator, long run variance, detrending, one-step, two-step |
| JEL: | C12 C13 C32 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:272&r=ets |
| By: | Dominique Guegan (Centre d'Economie de la Sorbonne); Philippe de Peretti (Centre d'Economie de la Sorbonne) |
| Abstract: | This paper focuses on a procedure to test for structural changes in the first two moments of a time series, when no information about the process driving the breaks is available. To approximate the process, an orthogonal Bernstein polynomial is used and testing for the null is achieved either by using an AICu information criterion, or a restriction test. The procedure covers both the pure discrete structural change and the continuous changes models. Running Monte-Carlo simulations, we show that the test has power against various alternatives. |
| Keywords: | Structural changes, Bernstein polynomial, AICu. |
| JEL: | C01 C12 C15 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11042&r=ets |
| By: | Andrés González (Banco de la República, Bogotá, Colombia.); Kirstin Hubrich (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.); Timo Teräsvirta (CREATES, Aarhus University, Denmark.) |
| Abstract: | We propose a new method for medium-term forecasting using exogenous information. We first show how a shifting-mean autoregressive model can be used to describe characteristic features in inflation series. This implies that we decompose the inflation process into a slowly moving nonstationary component and dynamic short-run fluctuations around it. An important feature of our model is that it provides a way of combining the information in the sample and exogenous information about the quantity to be forecast. This makes it possible to form a single model-based inflation forecast that also incorporates the exogenous information. We demonstrate, both theoretically and by simulations, how this is done by using the penalised likelihood for estimating the model parameters. In forecasting inflation, the central bank inflation target, if it exists, is a natural example of such exogenous information. We illustrate the application of our method by an out-of-sample forecasting experiment for euro area and UK inflation. We find that for euro area inflation taking the exogenous information into account improves the forecasting accuracy compared to that of a number of relevant benchmark models but this is not so for the UK. Explanations to these outcomes are discussed. JEL Classification: C22, C52, C53, E31, E47. |
| Keywords: | Nonlinear forecast, nonlinear model, nonlinear trend, penalised likelihood, structural shift, time-varying parameter. |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20111363&r=ets |
| By: | Athanasopoulos, George; Guillén, Osmani Teixeira de Carvalho; Issler, João Victor; Vahid, Farshid |
| Abstract: | We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditionalcriteria and criteria with data-dependant penalties and we prove its consistency. A MonteCarlo study explores the finite sample performance of this procedure and evaluates the forecastingaccuracy of models selected by this procedure. Two empirical applications confirm the usefulnessof the model selection procedure proposed here for forecasting. |
| Date: | 2011–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:713&r=ets |
| By: | Gabriele La Spada; Fabrizio Lillo |
| Abstract: | We study how quantization, occurring when a continuously varying process is approximated by or observed on a grid of discrete values, changes the properties of a Gaussian long-memory process. By computing the asymptotic behavior of the autocovariance and of the spectral density, we find that the quantized process has the same Hurst exponent of the original process. We show that the log-periodogram regression and the Detrended Fluctuation Analysis (DFA) are severely negatively biased estimators of the Hurst exponent for quantized processes. We compute the asymptotics of the DFA for a generic long-memory process and we study them for quantized processes. |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1107.4476&r=ets |