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on Econometric Time Series |
| By: | Stanislav Anatolyev (New Economic School) |
| Abstract: | We enhance the theory of asymptotic inference about predictive ability by considering the case when a set of variables used to construct predictions is sizable. To this end, we consider an alternative asymptotic framework where the number of predictors tends to innity with the sample size, although more slowly. Depending on the situation the asymptotic normal distribution of an average prediction criterion either gains additional variance as in the few predictors case, or gains non-zero bias which has no analogs in the few predictors case. By properly modifying conventional test statistics it is possible to remove most size distortions when there are many predictors, and improve test sizes even when there are few of them. |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:cfr:cefirw:w0096&r=ets |
| By: | Doz, Catherine; Giannone, Domenico; Reichlin, Lucrezia |
| Abstract: | This paper shows consistency of a two step estimator of the parameters of a dynamic approximate factor model when the panel of time series is large (n large). In the first step, the parameters are first estimated from an OLS on principal components. In the second step, the factors are estimated via the Kalman smoother. This projection allows to consider dynamics in the factors and heteroskedasticity in the idiosyncratic variance. The analysis provides theoretical backing for the estimator considered in Giannone, Reichlin, and Sala (2004) and Giannone, Reichlin, and Small (2005). |
| Keywords: | Factor Models; Kalman filter; large cross-sections; principal components |
| JEL: | C32 C33 C51 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6043&r=ets |
| By: | Ovidiu Precup (King’s College London); Giulia Iori (Department of Economics, City University, London) |
| Abstract: | On a high-frequency scale, financial time series are not homogeneous, therefore standard correlation measures can not be directly applied to the raw data. To deal with this problem the time series have to be either homogenized through interpolation or methods that can handle raw non-synchronous time series need to be employed. This paper compares two traditional methods that use interpolation with an alternative method applied directly to the actual time series. The three methods are tested on simulated data and actual trades time series. The temporal evolution of the correlation matrix is revealed through the analysis of the full correlation matrix and of the Minimum Spanning Tree representation. To perform the analysis we implement several measures from the theory of random weighted networks. |
| Keywords: | High-Frequency Correlation, Fourier method, Epps Effect, Minimum Spanning Tree, random networks |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:cty:dpaper:0504&r=ets |
| By: | Giulia Iori (Department of Economics, City University, London); Ovidiu V. Precup |
| Abstract: | In this paper we implement a Fourier method to estimate high frequency correlation matrices from small data sets. The Fourier estimates are shown to be considerably less noisy than the standard Pearson correlation measure and thus capable of detecting subtle changes in correlation matrices with just a month of data. The evolution of correlation at different time scales is analysed from the full correlation matrix and its Minimum Spanning Tree representation. The analysis is performed by implementing measures from the theory of random weighted networks. |
| Keywords: | High Frequency Correlation, Fourier Method, Random weighted Networks |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:cty:dpaper:0610&r=ets |
| By: | Angelica Gonzalez |
| Abstract: | This paper proposes and analyses an hybrid of Owen's (1988, 1990, 1991) Empirical Likelihood (EL) and bootstrap, EL-bootstrap, as an alternative to the General Method of Moments (GMM) within dynamic panel data models. We concentrate on the finite-sample size properties of their overidentification tests. Our results show that EL-bootstrap may be a good alternative to GMM estimation within this setting. The practical usefulness of our findings is illustrated via application on an AR(1) univariate panel data model with individual effects using the cash-flow series of 174 firms in the United States. |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:154&r=ets |
| By: | Christian Kascha; Karel Mertens |
| Abstract: | An important question in empirical macroeconomics is whether structural vector autoregressions (SVARs) can reliably discriminate between competing DSGE models. Several recent papers have suggested that one reason SVARs may fail to do so is because they are finite-order approximations to infinite-order processes. In this context, we investigate the performance of models that do not suffer from this type of misspecification. We estimate VARMA and state space models using simulated data from a standard economic model and compare true with estimated impulse responses. For our examples, we find that one cannot gain much by using algorithms based on a VARMA representation. However, algorithms that are based on the state space representation do outperform VARs. Unfortunately, these alternative estimates remain heavily biased and very imprecise. The findings of this paper suggest that the reason SVARs perform weakly in these types of simulation studies is not because they are simple finite-order approximations. Given the properties of the generated data, their failure seems almost entirely due to the use of small samples. |
| Keywords: | Structural VARs, VARMA, State Space Models, Identification, Business Cycles |
| JEL: | E32 C15 C52 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2006/37&r=ets |
| By: | Giampiero M. Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti"); Edoardo Otranto (Università di Sassari, Dipartimento di Economia, Impresa e Regolamentazione) |
| Abstract: | In this paper we suggest ways to characterize the transmission mechanisms of volatility between markets by making use of a new Markov Switching bivariate model where the state of one variable feeds into the transition probability of the state of the other. The comparison between this model and other Markov Switching models allows us to derive statistical tests stressing the role of one market relative to another (contagion, interdependence, comovement, independence, Granger causality). We estimate the model on the weekly high–low range of several Asian markets, with a specific interest in the role of Hong Kong. |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2005_10&r=ets |
| By: | Giovanni De Luca (Dipartimento di Statistica e Matematica per la Ricerca Economica Università di Napoli Parthenope.); Giampiero M. Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | Financial market price formation and exchange activity can be investigated by means of ultra-high frequency data. In this paper we investigate an extension of the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998) by adopting a mixture of distribution approach with time varying weights. Empirical estimation of the Mixture ACD model shows that the limitations of the standard base model and its inadequacy of modelling the behavior in the tail of the distribution are suitably solved by our model. When the weights are made dependent on some market activity data, the model lends itself to some structural interpretation related to price formation and information diffusion in the market. |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2005_11&r=ets |
| By: | Antonio Matas-Mir (European central Bank); Denise R. Osborn (University of Manchester, Centre for Growth and Business Cycle Research , Economic Studies, School of Social Sciences); Marco Lombardi (European central Bank) |
| Abstract: | We study the impact of seasonal adjustment on the properties of business cycle expansion and recession regimes using analytical, simulation and empirical methods. Analytically, we show that the X-11 adjustment filter both reduces the magnitude of change at turning points and reduces the depth of recessions, with specific effects depending on the length of the recession. A simulation analysis using Markov switching models confirms these properties, with particularly undesirable effects in delaying the recognition of the end of a recession. However, seasonal adjustment can have desirable properties in clarifying the true regime when this is well underway. The empirical findings, based on four coincident US business cycle indicators, reinforce the analytical and simulation results by showing that seasonal adjustment leads to the identification of longer and shallower recessions than obtained using unadjusted data. |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2005_15&r=ets |
| By: | Christian T. Brownlees (Università di Firenze, Dipartimento di Statistica "G. Parenti"); Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | The financial econometrics literature on Ultra High-Frequency Data (UHFD) has been growing steadily in recent years. However, it is not always straightforward to construct time series of interest from the raw data and the consequences of data handling procedures on the subsequent statistical analysis are not fully understood. Some results could be sample or asset specific and in this paper we address some of these issues focussing on the data produced by the New York Stock Exchange, summarizing the structure of their TAQ ultra high-frequency dataset. We review and present a number of methods for the handling of UHFD, and explain the rationale and implications of using such algorithms. We then propose procedures to construct the time series of interest from the raw data. Finally, we examine the impact of data handling on statistical modeling within the context of financial durations ACD models. |
| Keywords: | Ultra-high Frequency Data, ACD models, Outliers, New York Stock Exchange |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2006_03&r=ets |
| By: | Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti"); Edoardo Otranto (Università di Sassari, Dipartimento di Economia, Impresa e Regolamentazione) |
| Abstract: | The integration of financial markets across countries has modified the way prices react to news. Innovations originating in one market diffuse to other markets following patterns which usually stress the presence of interdependence. In some cases, though, covariances across markets have an asymmetric component which reflects the dominance of one over the others. The volatility transmission mechanisms in such events may be more complex than what can be modelled as a multivariate GARCH model. In this paper we adopt a new Markov Switching approach and we suppose that periods of high volatility and periods of low volatility represent the states of an ergodic Markov Chain where the transition probability is made dependent on the state of the “dominant” series. We provide some theoretical background and illustrate the model on Asian markets data showing support for the idea of dominant market and the good prediction performance of the model on a multi-period horizon. |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2006_04&r=ets |
| By: | Marco Lombardi (European central Bank); Giorgio Calzolari (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | The alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its many useful properties, including a central limit theorem, are especially appreciated in the financial field. However, estimation difficulties have up to now hindered its diffusion among practitioners. In this paper we propose an indirect estimation approach to stochastic volatility models with alpha-stable innovations that exploits, as auxiliary model, a GARCH(1,1) with t-distributed innovations. We consider both cases of heavytailed noise in the returns or in the volatility. The approach is illustrated by means of a detailed simulation study and an application to currency crises. |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2006_07&r=ets |
| By: | Fabrizio Cipollini (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti"); Robert F. Engle (Department of Finance, Stern School of Business, New York University); Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | The Multiplicative Error Model introduced by Engle (2002) for positive valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support. In this paper we propose a multivariate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated. The estimation procedure is hindered by the lack of probability density functions for multivariate positive valued random variables. We suggest the use of copula functions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure. |
| Date: | 2006–10 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2006_15&r=ets |
| By: | Adrian pagan; Don Harding (National Centre for Econometric Research) |
| Abstract: | Macroeconometric and financial researchers often use secondary or constructed binary random variables that differ in terms of their statistical properties from the primary random variables used in microeconometric studies. One important difference between primary and secondary binary variables is that while the former are, in many instances, independently distributed (i.d.) the later are rarely i.d. We show how popular rules for constructing binary states determine the degree and nature of the dependence in those states. When using constructed binary variables as regressands a common mistake is to ignore the dependence by using a probit model. We present an alternative non-parametric method that allows for dependence and apply that method to the issue of using the yield spread to predict recessions. |
| Keywords: | Business cycle; binary variable, Markov chain, probit model, yield curve |
| Date: | 2006–04 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2006-1&r=ets |
| By: | Adam Clements; Stan Hurn; Scott White (National Centre for Econometric Research) |
| Abstract: | Many approaches have been proposed for estimating stochastic volatility (SV) models, a number of which are filtering methods. While non-linear filtering methods are superior to linear approaches, non-linear filtering methods have not gained a wide acceptance in the econometrics literature due to their computational cost. This paper proposes a discretised non-linear filtering (DNF) algorithm for the estimation of latent variable models. It is shown that the DNF approach leads to significant computational gains relative to other procedures in the context of SV estimation without any associated loss in accuracy. It is also shown how a number of extensions to standard SV models can be accommodated within the DNF algorithm. |
| Keywords: | non-linear filtering, stochastic volatility, state-space models, asymmetries, latent factors, two factor volatility models |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2006-3&r=ets |
| By: | Stan Hurn; Ralf Becker (National Centre for Econometric Research) |
| Abstract: | This paper considers an important practical problem in testing time-series data for nonlinearity in mean. Most popular tests reject the null hypothesis of linearity too frequently if the the data are heteroskedastic. Two approaches to redressing this size distortion are considered, both of which have been proposed previously in the literature although not in relation to this particular problem. These are the heteroskedasticity-robust-auxiliary-regression approach and the wild bootstrap. Simulation results indicate that both approaches are effective in reducing the size distortion and that the wild bootstrap others better performance in smaller samples. Two practical examples are then used to illustrate the procedures and demonstrate the potential pitfalls encountered when using non-robust tests. |
| Keywords: | nonlinearity in mean, heteroskedasticity, wild bootstrap, empirical size and power |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2007-2&r=ets |
| By: | Monica Billio (Department of Economics, University Of Venice Ca’ Foscari); Massimiliano Caporin (massimiliano.caporin@unipd.it) |
| Abstract: | We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle (2002) and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al. (2006). The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. (2006) and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation. |
| Keywords: | Dynamic correlations, Block-structures, Flexible correlation models |
| JEL: | C51 C32 G18 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:53_06&r=ets |
| By: | Massimiliano Caporin (Department of Economics, Università di Padova); Domenico Sartore (Department of Economics, University Of Venice Ca’ Foscari) |
| Abstract: | This paper provides the theoretical and operational framework for estimating past values of relevant time series starting from a (limited) information set. We consider a general approach that includes as special cases time series aggregation and temporal and/or spatial disaggregation problems. Furthermore, we explore the relevant problems and the possible solutions associated with a retropolation exercise, evidencing that linear models could be the preferred representation for the production of the needed data. The methodology is designed with a focus on economic time series but it could be considered even for other statistical areas. An empirical example is presented: we analyze the back-calculation of Eu15 Industrial Production Index comparing our approach with the Eurostat official one. |
| Keywords: | benchmarking,retropolation, historical reconstruction, back-forecasting, missing past values, aggregation, disaggregation. |
| JEL: | C10 C82 C50 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:56_06&r=ets |
| By: | Eickmeier, Sandra; Ziegler, Christina |
| Abstract: | This paper surveys existing factor forecast applications for real economic activity and inflation by means of a meta-analysis and contributes to the current debate on the determinants of the forecast performance of large-scale dynamic factor models relative to other models. We find that, on average, factor forecasts are slightly better than other models’ forecasts. In particular, factor models tend to outperform small-scale models, whereas they perform slightly worse than alternative methods which are also able to exploit large datasets. Our results further suggest that factor forecasts are better for US than for UK macroeconomic variables, and that they are better for US than for euro-area output; however, there are no significant differences between the relative factor forecast performance for US and euro-area inflation. There is also some evidence that factor models are better suited to predict output at shorter forecast horizons than at longer horizons. These findings all relate to the forecasting environment (which cannot be influenced by the forecasters). Among the variables capturing the forecasting design (which can, by contrast, be influenced by the forecasters), the size of the dataset from which factors are extracted seems to positively affect the relative factor forecast performance. There is some evidence that quarterly data lend themselves better to factor forecasts than monthly data. Rolling forecasts are preferable to recursive forecasts. The factor estimation technique seems to matter as well. Other potential determinants - namely whether forecasters rely on a balanced or an unbalanced panel, whether restrictions implied by the factor structure are imposed in the forecasting equation or not and whether an iterated or a direct multi-step forecast is made - are found to be rather irrelevant. Moreover, we find no evidence that pre-selecting the variables to be included in the panel from which factors are extracted helped to improve factor forecasts in the past. |
| Keywords: | Factor models, forecasting, meta-analysis |
| JEL: | C2 C3 E37 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdp1:5170&r=ets |
| By: | Rao, B. Bhaskara |
| Abstract: | This paper examines the use of specifications based on the endogenous and exogenous growth models for country specific growth policies. It is suggested that time series models based on the Solow (1956) exogenous growth model are useful and they can also be extended to capture the permanent growth effects some variables. Our empirical results, with data from Fiji, show that trade openness and human capital have significant and permanent growth effects. However, these growth effects are small and eventually converge over time. |
| Keywords: | Endogenous and exogenous growth models; human capital; trade openness; permanent growth effects. |
| JEL: | O49 C00 C22 |
| Date: | 2006–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1547&r=ets |