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on Econometric Time Series |
| By: | Chih-Hao Lin; Chia-Seng Chang; Sai-Ping Li |
| Abstract: | An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.1292&r=ets |
| By: | Anna Zaremba; Tomaso Aste |
| Abstract: | This article investigates causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and Hilbert-Schmidt norm of the cross-covariance operator) and transfer entropy, examining each method and comparing their theoretical properties, with special attention given to the ability to capture nonlinear causality. We also analyse the theoretical benefits of applying non symmetrical measures rather than symmetrical measures of dependence. We applied the measures to a range of simulated and real data. The simulated data sets have been generated with linear and several types of nonlinear dependence, using bivariate as well as multivariate setting. Application to real-world financial data highlights the practical difficulties as well as the potential of the methods. We use two sets of real data: (1) US inflation and 1 month Libor, (2) S$\&$P data and exchange rates for the following currencies: AUDJPY, CADJPY, NZDJPY, AUDCHF, CADCHF, NZDCHF. Overall, we reached the conclusion that no single method can be recognised as the best in all circumstances and each of the methods has its domain of best applicability. We also describe the areas for improvement and future research. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.1457&r=ets |
| By: | Tao Xiong; Yukun Bao; Zhongyi Hu |
| Abstract: | Highly accurate interval forecasting of a stock price index is fundamental to successfully making a profit when making investment decisions, by providing a range of values rather than a point estimate. In this study, we investigate the possibility of forecasting an interval-valued stock price index series over short and long horizons using multi-output support vector regression (MSVR). Furthermore, this study proposes a firefly algorithm (FA)-based approach, built on the established MSVR, for determining the parameters of MSVR (abbreviated as FA-MSVR). Three globally traded broad market indices are used to compare the performance of the proposed FA-MSVR method with selected counterparts. The quantitative and comprehensive assessments are performed on the basis of statistical criteria, economic criteria, and computational cost. In terms of statistical criteria, we compare the out-of-sample forecasting using goodness-of-forecast measures and testing approaches. In terms of economic criteria, we assess the relative forecast performance with a simple trading strategy. The results obtained in this study indicate that the proposed FA-MSVR method is a promising alternative for forecasting interval-valued financial time series. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.1916&r=ets |
| By: | Claudia Foroni (Norges Bank (Central Bank of Norway)); Massimiliano Marcellino (Bocconi University and CEPR) |
| Abstract: | A mismatch between the time scale of a structural VAR (SVAR) model and that of the time series data used for its estimation can have serious consequences for identification, estimation and interpretation of the impulse response functions. However, the use of mixed frequency data, combined with a proper estimation approach, can alleviate the temporal aggregation bias, mitigate the identification issues, and yield more reliable responses to shocks. The problems and possible remedy are illustrated analytically and with both simulated and actual data. |
| Keywords: | Phillips curve, neoclassical, indexation, trend inflation, regime switch |
| JEL: | C32 C43 E32 |
| Date: | 2014–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2014_01&r=ets |
| By: | A. POISSONNIER (Insee) |
| Abstract: | Since the seminal paper by Chow and Lin the literature on temporal disaggregation has focused on temporal disaggregation of flow variables. Moreover, this literature on optimal methods has traditionally emphasized static models and forced all dynamic dimension of the link between time series to be embedded in the unexplained component. Nevertheless, these techniques have proved particularly useful to compute quarterly national accounts in numbers of countries in Europe (France, Italy, Spain, Portugal, Switzerland). Following this literature, this paper builds an optimal method to derive higher frequency estimates of stocks variables using their annual value and related flow indicators at high frequency. An example of this method is given for quarterly non-financial corporations' capital in computers and communication equipment. Although presented in the case of stock variables, all the results from this paper hold in the case of flow variables disaggregated either with static or dynamic models. |
| Keywords: | temporal disaggregation, Chow-Lin, Denton, quarterly national accounts |
| JEL: | C22 C51 C82 E01 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpdeee:g2013-03&r=ets |
| By: | Dimitra Chatzi (University of Crete); Dikaios Tserkezos (Department of Economics, University of Crete, Greece) |
| Abstract: | This letter proposes a simple test for the linearity of a time series. We compare the small and large samples properties of the suggested test via Monte Carlo techniques with well known time domain linearity tests. Our results suggest that the suggested test over performs the power of the other competitive tests in small samples. |
| Keywords: | Testing nonlinearity, Hinich portmanteau bicorrelation test, Keenan, Mcleodi-Li tests, ARCH & Luukkonen LST Test |
| Date: | 2014–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:crt:wpaper:1401&r=ets |
| By: | Helmut Lütkepohl |
| Abstract: | Large panels of variables are used by policy makers in deciding on policy actions. Therefore it is desirable to include large information sets in models for economic analysis. In this survey methods are reviewed for accounting for the information in large sets of variables in vector autoregressive (VAR) models. This can be done by aggregating the variables or by reducing the parameter space to a manageable dimension. Factor models reduce the space of variables whereas large Bayesian VAR models and panel VARs reduce the parameter space. Global VARs use a mixed approach. They aggregate the variables and use a parsimonious parametrisation. All these methods are discussed in this survey although the main emphasize is on factor models. |
| Keywords: | factor models, structural vector autoregressive model, global vector autoregression, panel data, Bayesian vector autoregression |
| JEL: | C32 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1351&r=ets |
| By: | Chevillon, Guillaume (ESSEC Business School) |
| Abstract: | Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality. |
| Keywords: | Cointegration; Deterministic trend; Likelihood ratio; Local trends; Global Warming |
| JEL: | C12 C32 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-13020&r=ets |
| By: | Franses, Ph.H.B.F. |
| Abstract: | Time series with bubble-like patterns display an unbalance between growth and acceleration, in the sense that growth in the upswing is “too fast” and then there is a collapse. In fact, such time series show periods where both the first differences (1-L) and the second differences (1-L)2 of the data are positive-valued, after which period there is a collapse. For a time series without such bubbles, it can be shown that 1-L2 differenced data should be stable. A simple test based on one-step-ahead forecast errors can now be used to timely monitor whether a series experiences a bubble and also whether a collapse is near. Illustration on simulated data and on two housing prices and the Nikkei index illustrates the practical relevance of the new diagnostic. Monte Carlo simulations indicate that the empirical power of the test is high. |
| Keywords: | acceleration, growth, speculative bubbles, test |
| JEL: | C22 |
| Date: | 2013–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:39598&r=ets |
| By: | Bel, K.; Paap, R. |
| Abstract: | Forecasts of key macroeconomic variables may lead to policy changes of governments, central banks and other economic agents. Policy changes in turn lead to structural changes in macroeconomic time series models. To describe this phenomenon we introduce a logistic smooth transition autoregressive model where the regime switches depend on the forecast of the time series of interest. This forecast can either be an exogenous expert forecast or an endogenous forecast generated by the model. Results of an application of the model to US inflation shows that (i) forecasts lead to regime changes and have an impact on the level of inflation; (ii) a relatively large forecast results in actions which in the end lower the inflation rate; (iii) a counterfactual scenario where forecasts during the oil crises in the 1970s are assumed to be correct leads to lower inflation than observed. |
| Keywords: | forecasting, inflation, nonlinear time series, regime switching |
| Date: | 2013–08–08 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:40884&r=ets |
| By: | Almeida, R.J.; Basturk, N.; Kaymak, U.; Costa Sousa, J.M. |
| Abstract: | In this work we introduce a new flexible fuzzy GARCH model for conditional density estimation. The model combines two different types of uncertainty, namely fuzziness or linguistic vagueness, and probabilistic uncertainty. The probabilistic uncertainty is modeled through a GARCH model while the fuzziness or linguistic vagueness is present in the antecedent and combination of the rule base system. The fuzzy GARCH model under study allows for a linguistic interpretation of the gradual changes in the output density, providing a simple understanding of the process. Such a system can capture different properties of data, such as fat tails, skewness and multimodality in one single model. This type of models can be useful in many fields such as macroeconomic analysis, quantitative finance and risk management. The relation to existing similar models is discussed, while the properties, interpretation and estimation of the proposed model are provided. The model performance is illustrated in simulated time series data exhibiting complex behavior and a real data application of volatility forecasting for the S&P 500 daily returns series. |
| Keywords: | Linguistic descriptions, Volatility forecasting, Conditional density estimation, Fuzzy GARCH models |
| JEL: | C14 C22 G32 |
| Date: | 2013–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureri:40785&r=ets |
| By: | Kole, H.J.W.G.; van Dijk, D.J.C. |
| Abstract: | The state of the equity market, often referred to as a bull or a bear market, is of key importance for financial decisions and economic analyses. Its latent nature has led to several methods to identify past and current states of the market and forecast future states. These methods encompass semi-parametric rule-based methods and parametric regime-switching models. We compare these methods by new statistical and economic measures that take into account the latent nature of the market state. The statistical measure is based directly on the predictions, while the economic mea- sure is based on the utility that results when a risk-averse agent uses the predictions in an investment decision. Our application of this framework to the S&P500 shows that rule-based methods are preferable for (in-sample) identification of the market state, but regime-switching models for (out-of-sample) forecasting. In-sample only the direction of the market matters, but for forecasting both means and volatilities of returns are important. Both the statistical and the economic measures indicate that these differences are significant. |
| Keywords: | economic comparison, forecast evaluation, regime switching, stock market |
| JEL: | C52 C53 G11 G17 G3 M00 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureri:41558&r=ets |
| By: | Brännäs, Kurt (Department of Economics, Umeå School of Business and Economics) |
| Abstract: | This short paper proposes a simultaneous equations model formulation for time series of count data. Some of the basic moment properties of the model are obtained. The inclusion of real valued exogenous variables is suggested to be through the parameters of the model. Some remarks on the application of the model to spatial data are made. Instrumental variable and generalized method of moments estimators of the structural form parameters are also discussed. |
| Keywords: | Integer-valued; Spatial; INAR; Interdependence; Properties; Estimation |
| JEL: | C35 C36 C39 C51 |
| Date: | 2014–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:umnees:0870&r=ets |
| By: | Zhu, Ke; Li, Wai Keung |
| Abstract: | This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH(p; q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE(PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment conditions, the strong consistency and asymptotical normality of the PQMLE are obtained. With no further efforts, the PQMLE can apply to other conditionally heteroskedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to eight major stock indexes and four exchange rates further highlight the importance of our new method. Heavy-tailed and skewed innovations are often observed together in practice, and the PQMLE now gives us a systematical way to capture these two co-existing features. |
| Keywords: | Asymmetric innovation; Conditionally heteroskedastic model; Exchange rates; GARCH model; Leptokurtic innovation; Non-Gaussian QMLE; Pearson’s Type IV distribution; Pearsonian QMLE; Stock indexes. |
| JEL: | C1 C13 C53 C58 |
| Date: | 2014–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:52732&r=ets |