|
on Econometric Time Series |
| By: | Fernando Espinosa, Klender Cortez and Romà J. Adillon (Universitat de Barcelona) |
| Abstract: | Evidence exists that many natural facts are described better as a fractal. Although fractals are very useful for describing nature, it is also appropiate to review the concept of random fractal in finance. Due to the extraordinary importance of Brownian motion in physics, chemistry or biology, we will consider the generalization that supposes fractional Brownian motion introduced by Mandelbrot. The main goal of this work is to analyse the existence of long range dependence in instantaneous forward rates of different financial markets. Concretelly, we perform an empirical analysis on the Spanish, Mexican and U.S. interbanking interest rate. We work with three time series of daily data corresponding to 1 day operations from 28th March 1996 to 21st May 2002. From among all the existing tests on this matter we apply the methodology proposed in Taqqu, Teverovsky and Willinger (1995). |
| Keywords: | Long-memory processes, interest rate analysis, Fractional Brownian Motion. |
| JEL: | C13 C82 E43 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:bar:bedcje:2006149&r=ets |
| By: | Hui Guo; Christopher J. Neely |
| Abstract: | We revisit the risk-return relation using the component GARCH model and international daily MSCI stock market data. In contrast with the previous evidence obtained from weekly and monthly data, daily data show that the relation is positive in almost all markets and often statistically significant. Likelihood ratio tests reject the standard GARCH model in favor of the component GARCH model, which strengthens the evidence for a positive risk-return tradeoff. Consistent with U.S. evidence, the long-run component of volatility is a more important determinant of the conditional equity premium than the short-run component for most international markets. |
| Keywords: | Stock exchanges ; Securities |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2006-006&r=ets |
| By: | Long Chen; Hui Guo; Lu Zhang |
| Abstract: | This paper revisits the time-series relation between the conditional risk premium and variance of the equity market portfolio. The main innovation is that we construct a measure of the ex ante equity market risk premium using corporate bond yield spread data. This measure is forward-looking and does not rely critically on either realized equity returns or instrumental variables. We find strong support for a positive risk-return tradeoff, and this result is not sensitive to a number of robustness checks, including alternative proxies of the conditional stock variance and controls for hedging demands. |
| Keywords: | Stock exchanges ; Securities |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2006-007&r=ets |
| By: | Justin Wolfers; Eric Zitzewitz |
| Abstract: | Interest in prediction markets has increased in the last decade, driven in part by the hope that these markets will prove to be valuable tools in forecasting, decisionmaking and risk management--in both the public and private sectors. This paper outlines five open questions in the literature, and we argue that resolving these questions is crucial to determining whether current optimism about prediction markets will be realized. |
| Keywords: | Forecasting ; Financial markets ; Econometric models |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedfwp:2006-06&r=ets |
| By: | Christophe Van Nieuwenhuyze (National Bank of Belgium, Research Department) |
| Abstract: | This paper aims to extract the common variation in a data set of 509 conjunctural series as an indication of the Belgian business cycle. The data set contains information on business and consumer surveys of Belgium and its neighbouring countries, macroeconomic variables and some worldwide watched indicators such as the ISM and the OECD confidence indicators. The statistical framework used is the One-sided Generalised Dynamic Factor Model developed by Forni, Hallin, Lippi and Reichlin (2005). The model splits the series in a common component, driven by the business cycle, and an idiosyncratic component. Well-known indicators such as the EC economic sentiment indicator for Belgium and the NBB overall synthetic curve contain a high amount of business cycle information. Furthermore, the richness of the model allows to determine the cyclical properties of the series and to forecast GDP growth all within the same unified setting. We classify the common component of the variables into leading, lagging and coincident with respect to the common component of quarter-on-quarter GDP growth. 22% of the variables are found to be leading. Amongst the most leading variables we find asset prices and international confidence indicators such as the ISM and some OECD indicators. In general, national business confidence surveys are found to coincide with Belgian GDP, while they lead euro area GDP and its confidence indicators. Consumer confidence seems to lag. Although the model captures the dynamic common variation contained in the data set, forecasts based on that information are insufficient to deliver a good proxy for GDP growth as a result of a nonnegligible idiosyncratic part in GDP's variance. Lastly, we explore the dependence of the model's results on the data set and show through a data reduction process that the idiosyncratic part of GDP's quarter-on-quarter growth can be dramatically reduced. However, this does not improve the forecasts. |
| Keywords: | Dynamic factor model, business cycle, leading indicators, forecasting, data reduction. |
| JEL: | C33 C43 E32 E37 |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:200603-2&r=ets |
| By: | Ole E. Barndorff-Nielsen (Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark); Sven Erik Graversen (Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark); Jean Jacod (Laboratoire de Probabilités et Modéles Aléatoires (CNRS UMR 7599), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France); Neil Shephard (Nuffield College, Oxford) |
| Abstract: | In this paper we provide an asymptotic analysis of generalised bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation and bipower variations which have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects. |
| Keywords: | Bipower variation, Power variation, Quadratic variation, Semimartingales, Stochastic volatility |
| Date: | 2006–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:0506&r=ets |
| By: | Ole E. Barndorff-Nielsen (Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark); Neil Shephard (Nuffield College, Oxford); Matthias Winkel (Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, U.K.) |
| Abstract: | In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale. |
| Keywords: | Bipower variation, Infinite activity, Multipower variation, Power variation, Quadratic variation, Semimartingales, Stochastic volatility |
| Date: | 2006–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:0507&r=ets |
| By: | Bent Nielsen (Nuffield College, Oxford) |
| Abstract: | A vector autoregressive model allowing for unit roots as well as explosive characteristic roots is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Co-integrating and co-explosive vectors can be found which eliminate these common factors. Likelihood ratio tests for linear restrictions on the co-explosive vectors are derived. As an empirical illustration the method is applied to data from the extreme Yugoslavian hyper-inflation of the 1990s. |
| Keywords: | Asymptotic normality, Co-explosiveness, Cointegration, Explosive processes, Hyper-inflation, Likelihood ratio tests, Vector autoregression |
| Date: | 2006–03–09 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:0508&r=ets |
| By: | Kazuhiko NISHINA (Graduate School of Economics, Osaka University); Tatsuro Nabil MAGHREBI (Faculty of Economics, Wakayama University); Moo-Sung KIM (College of Business Administration, Pusan National University) |
| Abstract: | This study develops a new model-free benchmark of implied volatility for the Japanese stock market similar in construction to the new VIX based on the S&P 500 index. It also examines the stochastic dynamics of the implied volatility index and its relationship with realized volatility in both markets. There is evidence that implied volatility is governed by a long-memory process. Despite its upward bias, implied volatility is more reflective of changes in realized volatility than alternative GARCH models, which account for volatility persistence and the asymmetric impact of news. The implied volatility index is also found to be inclusive of some but not all information on future volatility contained in historical returns. However, its higher out-of sample performance provides further support to the rationale behind drawing inference about future stock market volatility based on the incremental information contained in options prices. |
| Keywords: | Licensing; Implied volatility index, Out-of-sample forecasting, GARCH modelling |
| JEL: | C52 C53 G14 |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:0609&r=ets |
| By: | Tatsuma Wada (Department of Economics, Boston University); Pierre Perron (Department of Economics, Boston University) |
| Abstract: | This paper first generalizes the trend-cycle decomposition framework of Perron and Wada (2005) based on an unobserved components models with innovations having a mixtures of Normals distribution, which is able to handle sudden level and slope changes to the trend function as well as outliers. We investigate how important are the differences in the implied trend and cycle compared to the popular decomposition based on the Hodrick and Prescott (HP) (1997) filter. Our results show important qualitative and quantitative differences in the implied cycles for both real GDP and consumption series for the G7 countries. Most of the differences can be ascribed to the fact that the HP filter does not handle well slope changes, level shifts and outliers, while our method does so. Third, we assess how such different cycles affect some socalled “stylized facts” about the relative variability of consumption and output across countries. Our results show again important differences. In particular, the crosscountry consumption correlations are generally higher than the output correlations, except for the period from 1975 to 1985, provided Canada is excluded. Our results therefore provide a partial solution to this puzzle. The evidence is particularly strong for the most recent period. |
| Keywords: | Trend-Cycle Decomposition, Unobserved Components Model, International Business Cycle, Non Gaussian Filter. |
| JEL: | C22 E32 |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-0&r=ets |
| By: | Pierre Perron (Department of Economics, Boston University) |
| Abstract: | This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. A central theme of the review is the interplay between structural change and unit root and on methods to distinguish between the two. The topics covered are: methods related to estimation and inference about break dates for single equations with or without restrictions, with extensions to multi-equations systems where allowance is also made for changes in the variability of the shocks; tests for structural changes including tests for a single or multiple changes and tests valid with unit root or trending regressors, and tests for changes in the trend function of a series that can be integrated or trendstationary; testing for a unit root versus trend-stationarity in the presence of structural changes in the trend function; testing for cointegration in the presence of structural changes; and issues related to long memory and level shifts. Our focus is on the conceptual issues about the frameworks adopted and the assumptions imposed as they relate to potential applicability. We also highlight the potential problems that can occur with methods that are commonly used and recent work that has been done to overcome them. |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-017&r=ets |
| By: | Jinyong Hahn (UCLA); Jerry Hausman; Guido Kuersteiner (Department of Economics, Boston University) |
| Abstract: | This paper proposes a new instrumental variables estimator for a dynamic panel model with .xed e¤ects with good bias and mean squared error properties even when identi.cation of the model becomes weak near the unit circle. We adopt a weak instrument asymptotic approximation to study the behavior of various estimators near the unit circle. We show that an estimator based on long di¤erencing the model is much less biased than conventional implementations of the GMM estimator for the dynamic panel model. We also show that under the weak instrument approximation such conventional estimators are dominated in terms of mean squared error by an estimator with far less moment conditions. The long di¤erence estimator mimics the infeasible optimal procedure through its reliance on a small set of moment conditions. |
| Keywords: | dynamic panel, bias correction, second order, unit root, weak instrument |
| JEL: | C13 C23 C51 |
| Date: | 2005–07 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-024&r=ets |
| By: | Pierre Perron (Department of Economics, Boston University); Tomoyoshi Yabu (Department of Economics, Boston University) |
| Keywords: | structural change, unit root, median unbaised estimates, GLS procedure, super efficient estimates |
| JEL: | C22 |
| Date: | 2005–07 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-026&r=ets |
| By: | Ai Deng (Department of Economics, Boston University); Pierre Perron (Columbia Business School) |
| Abstract: | This paper considers various asymptotic approximations to the finite sample distribution of the estimate of the break date in a simple one-break model for a linear trend function that exhibits a change in slope, with or without a concurrent change in intercept. The noise component is either stationary or has an autoregressive unit root. Our main focus is on comparing the so-called “bounded-trend” and “unbounded-trend” asymptotic frameworks. Not surprisingly, the “bounded-trend” asymptotic framework is of little use when the noise component is integrated. When the noise component is stationary, we obtain the following results. If the intercept does not change and is not allowed to change in the estimation, both frameworks yield the same approximation. However, when the intercept is allowed to change, whether or not it actually changes in the data, the “bounded-trend" asymptotic framework completely misses important features of the finite sample distribution of the estimate of the break date, especially the pronounced bimodality that was uncovered by Perron and Zhu (2005) and shown to be well captured using the “unbounded-trend” asymptotic framework. Simulation experiments confirm our theoretical findings, which expose the drawbacks of using the “bounded-trend” asymptotic framework in the context of structural change models. |
| Keywords: | change-point, confidence intervals, shrinking shifts, bounded trend, level shift. |
| Date: | 2005–08 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-029&r=ets |
| By: | Pierre Perron† (Department of Economics, Boston University); Tatsuma Wada (Department of Economics, Boston University) |
| Abstract: | Recent work on trend-cycle decompositions for US real GDP yields the following puzzling features: methods based on Unobserved Components models, the Beveridge- Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bear little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycle, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of a change in the slope of the trend function in real GDP in 1973. Once this is properly accounted for, all methods yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. This cycle is more important in magnitude than previously reported, it accords well with the NBER chronology and implies no correlation between the trend and cycle, since the former is non-stochastic. Our results are corroborated using an alternative trend-cycle decomposition based on a generalized Unobserved Components models with errors having a mixture of Normals distribution for both the slope of the trend function and the cyclical component. It can account endogenously for infrequent changes such as level shifts and change in slope, as well as different variances for expansions and recessions. It yields a decomposition that accords very well with common notions of the business cycle. |
| Keywords: | Trend-Cycle Decomposition, Structural Change, Non Gaussian Filtering, Unobserved Components Model, Beveridge-Nelson Decomposition. |
| JEL: | C22 E32 |
| Date: | 2005–01 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-030&r=ets |
| By: | Pierre Perron (Department of Economics, Boston University); Tomoyoshi Yabu (Department of Economics, Boston University) |
| Keywords: | linear trend, unit root, median unbaised estimates, GLS procedure, super efficient estimates |
| JEL: | C22 |
| Date: | 2004–10 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-035&r=ets |
| By: | Ai Deng (Department of Economics, Boston University); Pierre Perron (Department of Economics, Boston University) |
| Abstract: | We consider the CUSUM of squares test in a linear regression model with general mixing assumptions on the regressors and the errors. We derive its limit distribution and show how it depends on the nature of the error process. We suggest a corrected version that has a limit distribution free of nuisance parameters. We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series. Simulation evidence is presented to support this. We illustrate the usefulness of our method by analyzing changes in the variance of stock returns and a variety of macroeconomic time series, as well as by testing for change in the variance of the residuals in a typical four-variable VAR model. Our results show the widespread prevalence of changes in the variance of such series and the fact that the variability of shocks affecting the U.S. economy has decreased. |
| Keywords: | Change-point, Variance shift, Recursive residuals, Dynamic models, Conditional heteroskedasticity. |
| JEL: | D80 D91 G11 E21 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-043&r=ets |
| By: | Ai Deng (Department of Economics, Boston University) |
| Abstract: | This paper provides an asymptotic theory for the spurious regression analyzed by Ferson, Sarkissian and Simin (2003). The asymptotic framework developed by Nabeya and Perron (1994) is used to provide approximations for the various estimates and statistics. Also, using a fixed-bandwidth asymptotic framework, a convergent t test is constructed, following Sun (2005). These are shown to be accurate and to explain the simulation findings in Ferson et al. (2003). Monte Carlo studies show that our asymptotic distribution provides a very good finite sample approximation for sample sizes often encountered in finance. Our analysis also reveals an important potential problem in the theoretical hypothesis testing literature on predictability. A possible reconciling interpretation is provided. |
| Keywords: | spurious regression, observational equivalence, Nabeya-Perron asymptotics, fixed-b asymptotics, data mining, nearly integrated, nearly white noise (NINW) |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2005-044&r=ets |
| By: | Neil Shephard; Ole E. Barndorff-Nielsen |
| Abstract: | We will review the econometrics of non-parametric estimation of the components of the variation of asset prices. This very active literature has been stimulated by the recent advent of complete records of transaction prices, quote data and order books. In our view the interaction of the new data sources with new econometric methodology is leading to a paradigm shift in one of the most important areas in econometrics: volatility measurement, modelling and forecasting. We will describe this new paradigm which draws together econometrics with arbitrage free financial economics theory. Perhaps the two most influential papers in this area have been Andersen, Bollerslev, Diebold and Labys (2001) and Barndorff-Nielsen and Shephard (2002), but many other papers have made important contributions. This work is likely to have deep impacts on the econometrics of asset allocation and risk management. One of our observations will be that inferences based on these methods, computed from observed market prices and so under the physical measure, are also valid as inferences under all equivalent measures. This puts this subject also at the heart of the econometrics of derivative pricing. One of the most challenging problems in this context is dealing with various forms of market frictions, which obscure the efficient price from the econometrician. Here we will characterise four types of statistical models of frictions and discuss how econometricians have been attempting to overcome them. |
| Keywords: | Quadratic Variation, Volatility, Realised Volatility |
| JEL: | C14 C22 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:240&r=ets |
| By: | O.T. Henry; S. Suardi |
| Abstract: | Empirical evidence documents a level effect in the volatility of short term rates of interest. That is, volatility is positively correlated with the level of the short term interest rate. Using Monte-Carlo simulations this paper examines the performance of the commonly used Engle-Ng (1993) tests which differentiate the effect of good and bad news on the predictability of future short rate volatility. Our results show that the tests exhibit serious size distortions and loss of power in the face of a neglected level effect. |
| Keywords: | Level Effects; Asymmetry; Engle-Ng Tests |
| JEL: | C12 G12 E44 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:mlb:wpaper:945&r=ets |