1,580 research outputs found
A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics
This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties. Le prĂ©sent document propose une nouvelle catĂ©gorie de distributions asymĂ©triques suivant la loi t de Student (Asymmetric Student-t Distribution - AST). Il en examine les propriĂ©tĂ©s, suggĂšre des procĂ©dures dâestimation et propose des applications dans le domaine de lâĂ©conomĂ©trie financiĂšre. Nous Ă©tablissons des expressions analytiques pour la fonction de distribution cumulative, la fonction quantile, les moments et les quantitĂ©s, ces aspects Ă©tant utiles dans certaines applications liĂ©es Ă lâĂ©conomĂ©trie financiĂšre, par exemple lâestimation du manque Ă gagner prĂ©vu. Nous mettons aussi de lâavant une reprĂ©sentation stochastique de la distribution. MĂȘme si la densitĂ© suivant la loi t de Student ne rĂ©pond pas aux conditions habituelles de rĂ©gularitĂ© pour lâestimation du maximum de vraisemblance, nous Ă©tablissons nĂ©anmoins la consistance, la normalitĂ© asymptotique et lâefficacitĂ© des estimateurs du maximum de vraisemblance et arrivons Ă une expression analytique explicite en ce qui concerne la matrice de covariance asymptotique. Une Ă©tude selon la mĂ©thode Monte Carlo indique gĂ©nĂ©ralement une bonne conformitĂ© des Ă©chantillons finis avec ces propriĂ©tĂ©s asymptotiques.asymmetric distribution, expected shortfall, maximum likelihood estimation, distribution asymĂ©trique, manque Ă gagner prĂ©vu, estimation du maximum de vraisemblance
Circuit Breakers and the Tail Index of Equity Returns
Using the tail index of returns on US equities as a summary measure of extreme behaviour, we examine changes in the equity markets surrounding the development of program trading for portfolio insurance, the crash of 1987, and the subsequent introduction of circuit breakers and other changes in market architecture. Recently-developed tests for the null of constancy of the tail index, versus the alternative of a change at an unknown date, permit inference on changes in extreme behaviour over a long time period while allowing for second-moment dependence in the return data. We find strong evidence of a decrease in the tail index (increase in the probability of extreme events) around the beginning of large scale program trading, and weaker, but still substantial, evidence of further significant change in the tail index following the introduction of circuit breakers. Point estimates of the tail index suggest that the tail index has nonetheless not regained pre-program-trading levels. Utilisant l'indice de queue de distribution (index tail) des rendements financiers sur actions dans les marchĂ©s amĂ©ricains comme mesure sommaire des comportements extrĂȘmes, nous examinons les changements dans le marchĂ© des actions entourant le dĂ©veloppement de programmes automatiques de transaction (Trading Program) pour l'assurance de portefeuille, le krach de 1987, l'introduction des coupe-circuits et autres changements dans les systĂšmes financiers. De nouveaux tests, rĂ©cemment dĂ©veloppĂ©s, permettent l'infĂ©rence statistique sur le changement des comportements extrĂȘmes sur une longue pĂ©riode ; tests qui sont valides dans le cas d'hĂ©tĂ©roscĂ©dasticitĂ© conditionnelle. L'hypothĂšse nulle est que l'indice de queue de distribution est constant alors que l'hypothĂšse alternative est le changement de cet indice Ă une date inconnue. Nous avons trouvĂ© de maniĂšre trĂšs significative que d'une part, l'indice de queue de distribution a diminuĂ© (la probabilitĂ© d'Ă©vĂšnements extrĂȘmes a augmentĂ©) au dĂ©but de la pĂ©riode des programmes de transactions. D'autre part, l'introduction de coupe-circuits a augmentĂ© cet indice mais est restĂ© plus faible que sa valeur avant l'introduction des programmes de transactions. Les estimateurs de l'indice de queue de distribution suggĂšrent qu'il n'a pas retrouvĂ© sa valeur initiale.Circuit breaker, structural change tests, tail index, Coupe-circuits, tests sur le changement structurel, indice de queue de distribution
Information Content of Volatility Forecasts at Medium-term Horizons
Using realized volatility to estimate daily conditional volatility of financial returns, we compare forecasts of daily volatility from standard QML-estimated GARCH models, and from projections on past realized volatilities obtained from high-frequency data. We consider horizons extending to thirty trading days. The forecasts are compared with the unconditional sample variance of daily returns treated as a daily volatility forecast, allowing us to estimate the maximum horizon at which the model-based forecasts provide forecasting power, measured by MSE reduction. Using data from a Toronto Stock Exchange equity index and foreign exchange returns (DM/US), we find evidence of forecasting power at horizons of up to thirty trading days, on each of the three financial returns series. We also find some evidence that the result of (e.g.) Bollerslev and Wright (2001), that projections on past realized volatility provide better 1-step forecasts than the QML-GARCH forecasts, appears to extend to longer horizons up to around ten to fifteen trading days. At longer horizons, there appears to be little to distinguish the forecast methods. En utilisant la volatilité réalisée pour estimer la volatilité conditionnelle quotidienne des rendements financiers, nous comparons les prévisions de volatilité quotidienne effectuées à partir de modÚles GARCH-QVM standard et à partir de projections directes sur les volatilités réalisées. Nous considérons un horizon maximal de trente jours de transaction. Les prévisions sont comparées à la variance non conditionnelle des rendements quotidiens, ce qui nous permet d'estimer l'horizon maximal pour lequel les modÚles détiennent un pouvoir de prévision. Nous utilisons des données de l'indice TSE 35 et des taux de change DM/US, et nos résultats montrent qu'il y a un pouvoir de prédiction jusqu'à un horizon de trente jours, et ce, pour chacune des trois séries. Nous montrons aussi que le résultat de Bollerslev et Wright (2001), résultat indiquant que les projections sont supérieures sur l'horizon d'un jour, reste valide dans un horizon s'étendant jusqu'à dix ou quinze jours. Pour des horizons plus longs, les deux types de méthodes de prévision ne se différencient guÚre.GARCH, high-frequency data, integrated volatility, realized volatility, GARCH, données à haute fréquence, volatilité intégrée, volatilité réalisée
A Note on Monitoring Daily Economic Activity Via Electronic Transaction Data
Economists have traditionally relied on monthly or quarterly data supplied by central statistical agencies for macroeconomic monitoring. However, technological advances of the past several years have resulted in new high-frequency data sources that could potentially provide more accurate and timely information on the current level of economic activity. In this paper we explore the usefulness of electronic transactions as real-time indicators of economic activity, using Canadian debit card data, and using two potentially important economic events as examples. In particular we are able to analyze expenditure patterns around the September 11 terrorist attacks and the August 2003 electrical blackout, and are able to note qualitative differences in the effects of these events which could not be observed through aggregate measures. Les Ă©conomistes se sont traditionnellement appuyĂ©s sur les donnĂ©es mensuelles ou trimestrielles publiĂ©es par les agences centrales de statistiques pour suivre la situation macroĂ©conomique. Cependant, les avancĂ©es technologiques qui ont Ă©tĂ© rĂ©alisĂ©es au cours des derniĂšres annĂ©es ont entraĂźnĂ© de nouvelles sources de donnĂ©es Ă haute frĂ©quence, et ces derniĂšres pourraient potentiellement donner lieu Ă une information plus exacte et plus opportune sur lâĂ©tat actuel de lâactivitĂ© Ă©conomique. Dans le document actuel, nous explorons lâutilitĂ© des transactions Ă©lectroniques comme indicateurs en temps rĂ©el de lâactivitĂ© Ă©conomique. Pour ce faire, nous recourons aux donnĂ©es canadiennes sur les cartes de dĂ©bit et utilisons, Ă titre dâexemples, deux Ă©vĂ©nements Ă©conomiques susceptibles dâĂȘtre importants. Plus particuliĂšrement, nous sommes en mesure dâanalyser la structure des dĂ©penses lors des attaques terroristes du 11 septembre et de la panne dâĂ©lectricitĂ© dâaoĂ»t 2003 et de noter des diffĂ©rences qualitatives dans les rĂ©percussions de ces Ă©vĂ©nements, lesquelles ne pourraient ĂȘtre observĂ©es en recourant aux mesures globales.debit cards, electronic transactions, monitoring , cartes de dĂ©bit, transactions Ă©lectroniques, suivi
A GENERALIZED ASYMMETRIC STUDENT-T DISTRIBUTION WITH APPLICATION TO FINANCIAL ECONOMETRICS
This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.
Indicators of wireline/wireless competition in the market for telecommunication services
We address evidence that competition from wireless telecommunications may already be having a substantial effect on the market for wireline services, despite historical estimates of price elasticity suggesting substantial market power (weak competition) in wireline services, considering both the elasticity argument per se and the observable recent trends in the wireline market. Among other points, we suggest that:
Arguments based on observed historical elasticities may be weak in cases where there exists a potential competitor offering a service whose price was substantially higher in the past, but where the price difference between the relevant products has lessened. In these cases, the competitor may have had little effect on demand in the past, but can have a much greater effect as the price difference narrows.
We can use a logistic-type demand relation, with the price difference as a key factor, to model such situations. In the present case, doing so produces results compatible with a substantially higher absolute elasticity of demand than would be observable in historical data.
With respect to observed trends in demand, we note that the total number of wirelines serviced by Bell Canada showed a remarkably stable pattern of seasonal and trend variation which has been interrupted quite abruptly over the last four + years. The change, in the direction of actual demand well below levels compatible with the previous trend, indicates substantial changes in the nature of the wireline market. Since the total market for telecommunications services has continued to expand over this time, this suggests changes in consumersâ choices between different modes of telecommunication.
Relating the wireline displacements to the numbers of wireless customers (for primary wirelines) or wireless and high-speed internet (for secondary and total wirelines) allows us to estimate wireline losses, producing numbers compatible with a reduction of up to 8% in the total size of the market for fixed wirelines as of the end of 2003 (after excluding approximately 3% of the competitive losses), relative to what demand would have been had the previous growth trend continued.
Nous soutenons la thĂšse selon laquelle la concurrence dans les tĂ©lĂ©communications sans fil a dĂ©jĂ un effet important sur les marchĂ©s de services filaires, malgrĂ© les prĂ©visions historiques de la thĂ©orie de lâĂ©lasticitĂ©-prix suggĂ©rant un pouvoir dominant sur le marchĂ© (concurrence dĂ©favorable) des services filaires. Nous traiterons lâargument de lâĂ©lasticitĂ© en soi, ainsi que de rĂ©centes tendances observables dans le marchĂ© des services filaires. Nous suggĂ©rons, entre autres que :
Les arguments fondĂ©s sur les Ă©lasticitĂ©s historiques observĂ©es peuvent ĂȘtre faibles dans les cas oĂč il existe un compĂ©titeur potentiel offrant un service dont les tarifs Ă©taient beaucoup plus Ă©levĂ©s dans le passĂ©, mais dont la diffĂ©rence de prix entre les produits pertinents sâamoindrit. Dans ces cas, le compĂ©titeur peut avoir eu une faible influence sur la demande dans le passĂ©, mais est susceptible dâavoir une influence beaucoup plus grande lorsque la diffĂ©rence de prix se resserre.
Nous pouvons utiliser un modĂšle de type logistique pour lâoffre et la demande ayant comme facteur clĂ© la diffĂ©rence de prix pour dĂ©crire de telles situations. Dans ce cas-ci, une telle mĂ©thode produirait des rĂ©sultats compatibles avec une Ă©lasticitĂ© de la demande plus forte en absolu que celle observĂ©e dans les donnĂ©es historiques.
En ce qui a trait aux tendances observĂ©es de la demande, nous avons notĂ© que le nombre total de services filaires desservis par Bell Canada suit un modĂšle remarquablement stable de variation selon les saisons et les tendances mais qui a Ă©tĂ© soudainement interrompu durant les quatre derniĂšres annĂ©es. Ce changement, orientĂ© vers la demande actuelle bien en dessous des niveaux compatibles avec la tendance prĂ©cĂ©dente, indique des modifications substantielles de la nature mĂȘme du marchĂ© des services filaires. Puisque le marchĂ© global des services de tĂ©lĂ©communications a continuĂ© de prendre de lâexpansion depuis ce temps, cela dĂ©montre des changements dans le processus dĂ©cisionnel des clients entre les diffĂ©rents modes de tĂ©lĂ©communication.
La correspondance entre les dĂ©placements des services filaires et le nombre de clients utilisant les services sans fil (pour le service filaire de base) ou sans fil et Internet haute-vitesse (pour le service filaire secondaire ou total) nous permet dâestimer les pertes de services filaires, produisant des nombres compatibles avec une rĂ©duction approximative de prĂšs de 8 % de la taille totale du marchĂ© des rĂ©seaux filaires pour la fin de 2003 (en excluant environ 3 % de pertes concurrentielles), comparativement Ă ce que la demande aurait Ă©tĂ© si la croissance avait continuĂ©.
Calibration and Resolution Diagnostics for Bank of England Density Forecasts
This paper applies new diagnostics to the Bank of Englandâs pioneering density forecasts (fan charts). We compute their implicit probability forecast for annual rates of inflation and output growth that exceed a given threshold (in this case, the target inflation rate and 2.5% respectively.) Unlike earlier work on these forecasts, we measure both their calibration and their resolution, providing both formal tests and graphical interpretations of the results. These results both reinforce earlier evidence on some of the limitations of these forecasts and provide new evidence on their information content. Cet Ă©tude dĂ©veloppe et applique des nouvelles techniques pour diagnostiquer les prĂ©visions de densitĂ© de la Banque dâAngleterre (leur âfan chartsâ). Nous calculons leurs probabilitĂ©s implicites pour des taux dâinflation et de croissance du PIB qui dĂ©passent des seuils critiques (soit le taux dâinflation ciblĂ©, soit 2.5%.) En contraste avec des travaux antĂ©rieurs sur ces prĂ©visions, nous gaugeons leur calibration aussi bien que leur rĂ©solution, en donnant des tests formels et des interprĂ©tations graphiques. Les rĂ©sultats renforcent des conclusions dĂ©jĂ existant sur les limites de ces prĂ©visions et ils donnent de nouvelles Ă©vidences sur leurs valeurs ajoutĂ©es.calibration, density forecast, probability forecast, resolu, calibration, prĂ©visions de densitĂ©, probabilitĂ©s implicites, rĂ©solution.
THE CALIBRATION OF PROBABILISTIC ECONOMIC FORECASTS
A probabilistic forecast is the estimated probability with which a future event will satisfy a particular criterion. One interesting feature of such forecasts is their calibration, or the match between predicted probabilities and actual outcome probabilities. Calibration has been evaluated in the past by gropuing probability forecasts into discrete categories. Here we show that we can do so without discrete groupings; the kernel estimators that we use produce efficiency gains and smooth estimated curves relating predicted and actual probabilities. We use such estimates to evaluate the empirical evidence on calibration error in a number of economic applications including recession and inflation prediction, using both forecasts made and stored in real time and pseudo-forecasts made using the data vintage available at the forecast date. We evaluate outcomes using both first-release outcome measures as well as later, thoroughly revised data. We find strong evidence of incorrect calibration in professional forecasts of recessions and inflation. We also present evidence of asymmetries in the performace of inflation forecasts based on real-time output gaps.
The Calibration of Probabilistic Economic Forecasts
A probabilistic forecast is the estimated probability with which a future event will satisfy a specified criterion. One interesting feature of such forecasts is their calibration, or the match between predicted probabilities and actual outcome probabilities. Calibration has been evaluated in the past by grouping probability forecasts into discrete categories. Here we show that we can do so without discrete groupings; the kernel estimators that we use produce efficiency gains and smooth estimated curves relating predicted and actual probabilities. We use such estimates to evaluate the empirical evidence on calibration error in a number of economic applications including recession and inflation prediction, using both forecasts made and stored in real time and pseudoforecasts made using the data vintage available at the forecast date. We evaluate outcomes using both first-release outcome measures as well as later, thoroughly-revised data. We find strong evidence of incorrect calibration in professional forecasts of recessions and inflation. We also present evidence of asymmetries in the performance of inflation forecasts based on real-time output gaps. Une prĂ©vision probabiliste reprĂ©sente la probabilitĂ© quâun Ă©vĂ©nement futur satisfasse une condition donnĂ©e. Un des aspects intĂ©ressants de ces prĂ©visions est leur calibration, câest-Ă -dire lâappariement entre les probabilitĂ©s prĂ©dites et les probabilitĂ©s rĂ©alisĂ©es. Dans le passĂ©, la calibration a Ă©tĂ© Ă©valuĂ©e en regroupant des probabilitĂ©s de prĂ©visions en catĂ©gories distinctes. Nous proposons dâutiliser des estimateurs Ă noyaux, qui sont plus efficaces et qui estiment une relation lisse entre les probabilitĂ©s prĂ©dites et rĂ©alisĂ©es. Nous nous servons de ces estimations pour Ă©valuer lâimportance empirique des erreurs de calibration dans plusieurs pratiques Ă©conomiques, telles que la prĂ©vision de rĂ©cessions et de lâinflation. Pour ce faire, nous utilisons des prĂ©visions historiques, ainsi que des pseudoprĂ©visions effectuĂ©es Ă lâaide de donnĂ©es telles quâelles Ă©taient au moment de la prĂ©vision. Nous analysons les rĂ©sultats en utilisant autant des estimations prĂ©liminaires que des estimations tardives, ces derniĂšres incorporant parfois des rĂ©visions importantes. Nous trouvons une forte Ă©vidence empirique dâune calibration erronĂ©e des prĂ©visions professionnelles de rĂ©cession et dâinflation. Nous prĂ©sentons aussi une Ă©vidence dâasymĂ©tries dans la performance des prĂ©visions dâinflation basĂ©es sur des estimations des Ă©carts de la production en temps rĂ©el.calibration, probability forecast, real-time data, inflation, recession, calibration, probabilitĂ©s de prĂ©visions, donnĂ©es « en temps rĂ©el », inflation, rĂ©cession
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