Abstracts
Articles
2006
The Effect of Seasonal Adjustment on the Properties of Business Cycle Regimes
Antonio Matas-Mir, Denise. R. Osborn, Marco J. Lombardi
forthcomingJournal of Applied Econometrics
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.
A Multiple Indicators Model for Volatility Using Intra-Daily Data
Robert F. Engle, Giampiero M. Gallo
Journal of Econometrics131, 3-27 (doi:10.1016/j.econom.2005.01.018)
Many ways exist to measure and model nancial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a true or best measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of speci cations for the error density function. The estimation results show signi cant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by the VIX i ndex as recently rede ned by the CBOE.
Volatility Estimation via Hidden Markov Models
Alessandro Rossi, Giampiero M. Gallo
Journal of Empirical Finance13, 203-230 (doi:10.1016/j.empfin.2005.09.003)
We propose a stochastic volatility model where the conditional variance of asset returns switches
across a potentially large number of discrete levels, and the dynamics of the switches are driven
by a latent Markov chain. A simple parameterization overcomes the commonly encountered problem
in Markov-switching models that the number of parameters becomes unmanageable when the number of
states in the Markov chain increases. This framework presents some interesting features in modelling
the persistence of volatility, and that, far from being constraining in data fitting, it performs
comparably well as other popular approaches in forecasting short-term volatility.
Keywords: Stochastic volatility, Markov chain, GARCH, SWARCH, Forecasting.
JEL: C22, C53, G13
Bayesian inference for alpha-stable distributions: A random walk MCMC approach
Marco J. Lombardi
forthcoming CSDA
The author introduces a novel approach for Bayesian inference in the setting of alpha-stable distributions that resorts to a FFT of the characteristic function in order to approximate the likelihood function; the posterior distributions of the parame- ters are then produced via a random walk MCMC method. Contrary to the other MCMC schemes proposed in the literature, the proposed approach does not require auxiliary variables, and so it is less computationally expensive, especially when large sample sizes are involved. A simulation exercise highlights the empirical properties of the sampler; an application on audio noise data demonstrates how this estimation scheme performs in practical applications.
On-line Bayesian Estimation of Signals in Symmetric alpha-Stable Noise
Marco J. Lombardi and Simon J. Godsill
forthcomingIEEE transactions on signal processing
Abstract In this paper we describe on-line Bayesian filtering methods for time series models with heavy-tailed alpha-stable noise. The filtering methodology is based on a scale mixtures of normals (SMiN) representation of the alpha-stable distribution, which reexpresses the intractable stable distribution in a conditionally Gaussian form. We describe how the method can be used for estimation of TVAR signals buried in symmetric alpha-stable noise, efficiently implemented using an adaptation to an existing Rao- Blackwellised particle filter. The methodology is shown to work well with both simulated and real corrupted audio data, for which the alpha-stable noise distribution is found to fit the noise data better than other more standard heavy-tailed distributions.
2005
A Comparison of Complementary Automatic Modeling Methods: RETINA and PcGets
Teodosio Perez-Amaral, Halbert White, Giampiero M. Gallo
Econometric Theory, 21, 262-277, 2005.
In Perez-Amaral, Gallo, and White (2003), the authors proposed an automatic predictive modelling tool called Relevant Transformation of the Inputs Network Approach (RETINA). It is designed to embody flexibility (using nonlinear transformations of the predictors of interest), selective search within the range of possible models, control of collinearity, out-of-sample forecasting ability, and computational simplicity. In this paper we compare the characteristics of RETINA with PcGets, a well-known automatic modeling method proposed by David Hendry. We point out similarities, differences, and complementarities of the two methods. In an example using US telecommunications demand data we find that RETINA can improve both in- and out-of-sample over the usual linear regression model, and over some models suggested by PcGets. Thus, both methods are useful components of the modern applied econometrician s automated modelling tool chest.
2004
Mixture Processes for Financial Intradaily Durations
Giovanni De Luca, Giampiero M. Gallo
Studies in Nonlinear Dynamics and Econometrics, Volume 8; N. 2; Article 8. 2004
The instantaneous volatility of the price process is analyzed through the intraday financial durations between price changes. Previous research has traditionally dealt with parametric models without reaching a satisfactory level of adequacy. In this study, it is shown that by using a mixture of two exponential distributions a highly satisfactory fit can be obtained. The presence on financial markets of traders with different information sets makes reasonable the mixture assumption.
2003
Teodosio Perez-Amaral, Halbert White, Giampiero M. Gallo
Oxford Bulletin of Economics and Statistics, 65-81, 821-838 , 2003.
A new method, called Relevant Transformation of the Inputs Network Approach is proposed as a tool for model building. It is designed around exibility (with nonlinear transformations of the predictors of interest), selective search within the range of possible models, out-of-sample forecasting ability and computational simplicity. In tests on simulated data, it shows both a high rate of successful retrieval of the data generating process, which increases with the sample size and a good performance relative to other alternative procedures. A telephone service demand model is built to show how the procedure applies on real data.
2002
A Nonparametric Bayesian Approach to Detect the Number of Regimes in Switching Models
Edoardo Otranto, Giampiero M. Gallo
Econometric Reviews, 21, 477 496, 2002.
The Impact of the Use of Forecasts in Information Sets
Giampiero M. Gallo, C.W.J. Granger, Y. Jeon
IMF Staff Papers, 49, 4-21, 2002.
This paper presents evidence, using data from Consensus Forecasts, that there is an attraction to conform to the mean forecasts; in other words, views expressed by other forecasters in the previous period influence individuals current forecast. The paper then discusses and provides further evidence on two important implications of this finding. The first is that the forecasting performance of these groups may be severely affected by the detected imitation behavior and lead to convergence to a value that is not the right target. Second, since the forecasts are not independent, the common practice of using the standard deviation from the forecasts distribution, as if they were standard errors of the estimated mean, is not warranted.
Analytic Hessian Matrices and the Computation of FIGARCH Estimates
Marco J. Lombardi, Giampiero M. Gallo
Statistical Methods and Applications, 11: 247-264, 2002.
Long memory in conditional variance is one of the empirical features of most financial time series. One class of models that was suggested to capture this behavior refers to the so-called Fractionally Integrated GARCH processes (Baillie, Bollerslev and Mikkelsen 1996) in which the ideas of fractional integration originally introduced by Granger (1980) and Hosking (1981) for processes for the mean are applied to a GARCH framework. In this paper we derive analytic expressions for the second-order derivatives of the log-likelihood function of FIGARCH processes with a view to the advantages that can be gained in computational speed and estimation accuracy. The comparison is computationally intensive given the typical sample size of the time series involved and the way the likelihood function is built. An illustration is provided on exchange rate and stock index data.
2001
Modelling the Impact of Overnight Surprises on Intra-daily Volatility
Giampiero M. Gallo
Australian Economic Papers, 40, 567-580, 2001.
Dati finanziari ad alta frequenza: trattamento e applicazioni
Massimiliano Cecconi e Marco J. Lombardi
Scienza e Business 9: 17-24, 2001
Una delle tendenze più moderne della finanza consiste nello studio dei cosiddetti dati ad alta frequenza, ovvero osservazioni registrate in tempo reale sui mercati. A differenza degli studi tradizionali, nei quali si tende a considerare dati misurati ad intervalli equispaziati, nel caso dell’alta frequenza si registra ogni singola transazione (e anche richiesta di transazione) che avviene sul mercato. La possibilità di sfruttare questa enorme mole di informazione costituisce un indubbio vantaggio; le applicazioni di stime econometriche ricavate da dati ad altissima frequenza (ultra-high frequency, Engle [4]) si riflettono su gran parte della moderna teoria finanziaria: dal prezzaggio di opzioni alla previsione della volatilità intragiornaliera, dal calcolo del Value at Risk alla gestione della liquidità. Tuttavia, l’impiego di tali dati pone delle difficoltà sia per quanto concerne la loro raccolta che il loro trattamento. Difatti, oltre al problema di gestire ed organizzare enormi quantità di osservazioni (si può anche arrivare ad alcune migliaia di registrazioni nell’arco di una sola giornata borsistica), si pone quello del trattamento di osservazioni a frequenza irregolare. Una delle possibilità che sta riscuotendo maggior successo in letteratura consiste nel modellare i tempi che intercorrono tra una transazione e l’altra (le cosiddette durations) tramite un nuovo processo, introdotto da Engle e Russell [5] e noto con l’acronimo di modello ACD (Autoregressive Conditional Duration). Tra le motivazioni che hanno ispirato i due autori vi è la constatazione che la presenza sul mercato di operatori maggiormente informati di altri si riflette in un tempo medio di attesa tra una transazione e l’altra relativamente breve. Viceversa, tempi di attesa più lunghi sono indice di una maggiore calma dei mercati, poiché si ritiene che il prezzo corrente sia prossimo al suo valore di equilibrio. Scopo di questo articolo è quello di presentare sinteticamente i dati ad alta frequenza, le problematiche connesse al loro stoccaggio ed al loro trattamento, e di fornire alcuni spunti sulle possibilità di utilizzo dei dati in svariati ambiti della moderna teoria finanziaria.
2000
Risk-related Asymmetries in Foreign Exchange Markets
Giampiero M. Gallo, Barbara Pacini
Nonlinear Econometric Modelling in Time Series, edited by W. Barnett, D.Hendry, S. Hylleberg, T. Teräsvirta, D. Tiostheim e A.H. Wurtz, Cambridge University Press,
We consider a new nonparametric evaluation of the time-varying risk-related term in the relationship between spot and forward rates, suggesting it as an instrument for an estimator which is compared to others present in the literature. The nature of the time{varying term is discussed, focussing on possible asymmetries in the perception of risk for di erent currencies in a number of market situations approximated by standard trading strategies. The results con rm the existence of asymmetries in the size and magnitude of risk-related e ects in exchange rate determination.
The Effects of Trading Activity on Stochastic Volatility
Giampiero M. Gallo, Barbara Pacini
European Journal of Finance, 6, 163-75, 2000.
The paper re-examines the ques tion of exces s ive implied pers is tence of volatility estimates when GARCH-type models are used. Ten actively t raded US s tocks are cons id ered and as already established in the lit erature, when volume traded is inser ted in the GARCH(1,1) or EGARCH(1,1) models for returns , the es timated per s is tence is decreased. Since volume is affected also by within-the-day price movements and hence is not weakly exogenous relative to returns , alternative proxie s for t rading activit ies are sugges ted. It is concluded that the difference between the opening pr ice and the closing price of the previous day accounts also for mos t of the pers is tence in the autoregressive conditional heteroskedasticity.
Working Papers
2006
Financial Econometric Analysis at Ultra High Frequency: Data Handling Concerns
Christian T. Brownlees, Giampiero M. Gallo
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.
Multi Model Inference for Conditionally Heteroschedastic Dynamic Models
Christian T. Brownlees
Conditionally heteroskedastic dynamic models are ubiquitous in Financial Econometrics literature, starting from the ARCH models (Engle (1982), Bollerslev (1986)) for the modelling of stock returns, through the ACD models for the modelling of the durations between events in the fi- nancial market (Engle & Russell (1998)) to models which directly model estimates/proxies of volatility (Engle & Gallo (2006)). Furthermore Engle (2002) has introduced a generalisation of these models, the class of Multiplicative Error Models (MEM), which is suitable for the modelling of non–negative time series processes. The choice of the most appropriate model specification and the assessment of the consequences of model uncertainty on inference for this class of models, as in many other classes, are still problematic. The developments of Hjort & Claeskens (2003) and Claeskens & Hjort (2003) on Frequentist Model Averaging (FMA) introduce a very interesting machinery which provides methods capable of evaluating the impact of model uncertainty on inference and developing specific model selection/model averaging schemes which are tailored for the purposes of the statistical application of the model. This paper discusses the development of FMA machinery for the class of MEMs. A Monte Carlo experiment highlights the finite sample performance of the FMA asymptotic results. Finally, the paper also addresses the issues of how FMA machinery can be used in practise in time series analysis.
2005
Volatility Transmission in Financial Markets: A New Approach
Edoardo Otranto, Giampiero M. Gallo
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.
Time-varying Mixing Weights in Mixture Autoregressive Conditional Duration Models
Giovanni De Luca, Giampiero M. Gallo
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.
Theoretical and Empirical Issues in Assessing Exchange Market Pressure for Developing Countries
Simone Bertoli, Giorgio Ricchiuti
This paper attempts to highlight the shortcomings in the application of
the Exchange Market Pressure index, developed by Eichengreen et al.
[1994], to the study of currency crises in developing countries. The
main innovation of this index relies on its ability to signal those
pressures on a currency that are softened or warded off through
monetary authorities' interventions, thus avoiding a bias in the selection of
crisis episodes due to the missing observation of unsuccessful
speculative attacks, as it would happen if the selection rested merely
on nominal exchange rate movements. Different kinds of problems in
adopting this index have been detected. First, we discuss the
statistical issues that arise with the use of an index with a
multi-dimensional informational basis. We point out how arbitrary, and
often hidden, choices are required to aggregate the information
conveyed by the three components of the index. Then, we highlight the ad hoc
assumptions introduced to build a binary crisis variable that is based
on the EMP. In an attempt to tackle the problems to which the indirect
use of the EMP gives rise to, we propose a different rule for the
identification of crisis episodes. The proposed crisis identification
rule retains the spatial relativity introduced by Eichengreen et al.
[1994], but it differentiates from their definition as it is also
characterized by temporal relativity and by the independence of the
identification of past observations from future values of the index. In
a preliminary attempt to show how methodological choices do matter and
are able to affect the econometric analysis on currency crises
determinants, we finally employ data from a sample of 26 countries -
that comprises both developed and emerging economies - to test the
sensitivity of the EMP index and of the crisis indicator with respect
issues that we are raised in this paper.
Keywords: Currency Crises, Exchange Market Pressure
JEL Classification: F 30
Indirect estimation of alpha-stable stochastic volatility models
Marco J. Lombardi, Giorgio Calzolari
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 between 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. A detailed simulation study and an application to currency crises illustrate the approach.
2003
A Multiple Indicators Model For Volatility Using Intra-Daily Data
Robert F. Engle, Giampiero M. Gallo
Many ways exist to measure and model financial assets volatility. In principle, as the frequency of the data grows larger, the quality of forecasts should improve. Yet, there is no consensus about a true measure of volatility. In this paper we propose to jointly consider absolute returns, daily high-low range and realized volatility and to analyze their conditional dynamics with a multiplicative error model. The estimation results show significant effects of interaction between the indicators. We show that one-month- ahead forecasts have explanatory power (both in and out of sample) for the VIX index (an average of implied volatilities of index options).
Christian T. Brownlees, Giampiero M. Gallo, Paul Kofman
The literature on the characteristics and dynamics of volatility in financial markets has received a boost
from the relatively easy access to ultra-high frequency data. In this paper we make use of data extracted
from the TAQ database which records the transaction data for stocks traded on the NYSE. In doing so, we
pay special attention to the properties of overnight returns which reflect the accumulation of news during
market closing. This paper is concerned with the question about how the price change during market closing
transmits to the volatility during the day once trading resumes.
In this paper we look at the issue more
specifically, by taking advantage of the detail that ultra-high frequency data provide us with: we are
able to extract time series of sub-intra-daily returns at various frequencies. By so doing, we can
construct tests that shows how the impact of the innovation occurred between the closing and the
next business day opening varies accordingly to the di erent sub-intra-daily return considered.
The conditional intra-daily variance of returns is then modeled as a standard GARCH model and tests
are performed as to the significance of the introduction of overnight returns. The performance of
the specifications is evaluated in an out-of-sample forecasting exercise.
2002
GARCH-based Volatility Forecasts for Market Volatility Indices
Massimiliano Cecconi, Giampiero M. Gallo, Marco J. Lombardi
Working Paper Dipartimento di Statistica G. Parenti 2002/06
Volatility forecasting is one of the main issues in the financial econometrics literature. Volatility measures may be derived from statistical models for conditionalvariance, or from option prices. In recent times, indices have been suggested whichsummarize the implied volatility of widely traded market index options. One suchindex is the so-called VXN, an average of 30-day ahead implied volatilities of theoptions written on the NASDAQ-100 Index. In this paper we show how forecastsobtained with traditional GARCH-type models can be used to forecast the volatility index VXN.
2001
Modelling the Impact of Overnight Surprises on Intra-daily Stock Returns
Giampiero M. Gallo, Yongmiao Hong, Tae-Hwy Lee
In this paper we examine under what circumstances the information accumulated during market closing time and conveyed to the price formation at market opening may be exploited to predict where the stock price will be at the end of the trading day. In our sample of three financial time series, we find that, in spite of linear uncorrelatedness, there exists a strong nonlinear dependence structure in the conditional mean of the intra-daily returns. To model this structure we use the functional-coefficient (FC) model of Cai, Fan, and Yao (2000) where the coefficients are time-varying and dependent on the state of stock return volatility. Out-of-sample forecast performances of the FC models and linear models where the coefficients are constant are also compared using the criteria of mean square forecast errors, trading returns, and directional forecasts.
A Nonparametric Bayesian Approach to Detect the Number of Regimes in Markov Switching Models
Edoardo Otranto, Giampiero M. Gallo
The literature on Markov switching models is increasing and producing interesting results both at theoretical and applied levels. Most often the number of regimes, i.e., of data generating processes, is considered known; this strong hypothesis is adopted to somewhat bypass the nuisance parameter problem which affects hypothesis testing for the number of regimes. In this paper we take the view that some results derived from a nonparametric Bayesian approach provide a convenient way to deal with the issue of detecting the number of components in the mixture density, based on the assumption that the parameter distributions are generated by a Dirichlet process. The advantage is that we need no testing (in a classical sense) for the number of regimes, and the approach is not affected by a change point at the beginning or at the end of the sample. A Monte Carlo experiment provides some insights into the performance of the procedure. The potentiality of the approach is illustrated in reference with some well known results on exchange rate modelling.
