The thesis contains four essays covering topics in the field of macroeconomic forecasting. The first two chapters consider factor models in the context of real-time forecasting with many indicators. Using a large number of predictors offers an opportunity to exploit a rich information set and is also considered to be a more robust approach in the presence of instabilities. On the other hand, it poses a challenge of how to extract the relevant information in a parsimonious way. Recent research shows that factor models provide an answer to this problem. The fundamental assumption underlying those models is that most of the co-movement of the variables in a given dataset can be summarized by only few latent variables, the factors. This assumption seems to be warranted in the case of macroeconomic and financial data. Important theoretical foundations for large factor models were laid by Forni, Hallin, Lippi and Reichlin (2000) and Stock and Watson (2002). Since then, different versions of factor models have been applied for forecasting, structural analysis or construction of economic activity indicators. Recently, Giannone, Reichlin and Small (2008) have used a factor model to produce projections of the U.S GDP in the presence of a real-time data flow. They propose a framework that can cope with large datasets characterised by staggered and nonsynchronous data releases (sometimes referred to as “ragged edge”). This is relevant as, in practice, important indicators like GDP are released with a substantial delay and, in the meantime, more timely variables can be used to assess the current state of the economy. The first chapter of the thesis entitled “A look into the factor model black box: publication lags and the role of hard and soft data in forecasting GDP” is based on joint work with Gerhard Rünstler and applies the framework of Giannone, Reichlin and Small (2008) to the case of euro area. In particular, we are interested in the role of “soft” and “hard” data in the GDP forecast and how it is related to their timeliness. The soft data include surveys and financial indicators and reflect market expectations. They are usually promptly available. In contrast, the hard indicators on real activity measure directly certain components of GDP (e.g. industrial production) and are published with a significant delay. We propose several measures in order to assess the role of individual or groups of series in the forecast while taking into account their respective publication lags. We find that surveys and financial data contain important information beyond the monthly real activity measures for the GDP forecasts, once their timeliness is properly accounted for. The second chapter entitled “Maximum likelihood estimation of large factor model on datasets with arbitrary pattern of missing data” is based on joint work with Michele Modugno. It proposes a methodology for the estimation of factor models on large cross-sections with a general pattern of missing data. In contrast to Giannone, Reichlin and Small (2008), we can handle datasets that are not only characterised by a “ragged edge”, but can include e.g. mixed frequency or short history indicators. The latter is particularly relevant for the euro area or other young economies, for which many series have been compiled only since recently. We adopt the maximum likelihood approach which, apart from the flexibility with regard to the pattern of missing data, is also more efficient and allows imposing restrictions on the parameters. Applied for small factor models by e.g. Geweke (1977), Sargent and Sims (1977) or Watson and Engle (1983), it has been shown by Doz, Giannone and Reichlin (2006) to be consistent, robust and computationally feasible also in the case of large cross-sections. To circumvent the computational complexity of a direct likelihood maximisation in the case of large cross-section, Doz, Giannone and Reichlin (2006) propose to use the iterative Expectation-Maximisation (EM) algorithm (used for the small model by Watson and Engle, 1983). Our contribution is to modify the EM steps to the case of missing data and to show how to augment the model, in order to account for the serial correlation of the idiosyncratic component. In addition, we derive the link between the unexpected part of a data release and the forecast revision and illustrate how this can be used to understand the sources of the latter in the case of simultaneous releases. We use this methodology for short-term forecasting and backdating of the euro area GDP on the basis of a large panel of monthly and quarterly data. In particular, we are able to examine the effect of quarterly variables and short history monthly series like the Purchasing Managers' surveys on the forecast. The third chapter is entitled “Large Bayesian VARs” and is based on joint work with Domenico Giannone and Lucrezia Reichlin. It proposes an alternative approach to factor models for dealing with the curse of dimensionality, namely Bayesian shrinkage. We study Vector Autoregressions (VARs) which have the advantage over factor models in that they allow structural analysis in a natural way. We consider systems including more than 100 variables. This is the first application in the literature to estimate a VAR of this size. Apart from the forecast considerations, as argued above, the size of the information set can be also relevant for the structural analysis, see e.g. Bernanke, Boivin and Eliasz (2005), Giannone and Reichlin (2006) or Christiano, Eichenbaum and Evans (1999) for a discussion. In addition, many problems may require the study of the dynamics of many variables: many countries, sectors or regions. While we use standard priors as proposed by Litterman (1986), an important novelty of the work is that we set the overall tightness of the prior in relation to the model size. In this we follow the recommendation by De Mol, Giannone and Reichlin (2008) who study the case of Bayesian regressions. They show that with increasing size of the model one should shrink more to avoid overfitting, but when data are collinear one is still able to extract the relevant sample information. We apply this principle in the case of VARs. We compare the large model with smaller systems in terms of forecasting performance and structural analysis of the effect of monetary policy shock. The results show that a standard Bayesian VAR model is an appropriate tool for large panels of data once the degree of shrinkage is set in relation to the model size. The fourth chapter entitled “Forecasting euro area inflation with wavelets: extracting information from real activity and money at different scales” proposes a framework for exploiting relationships between variables at different frequency bands in the context of forecasting. This work is motivated by the on-going debate whether money provides a reliable signal for the future price developments. The empirical evidence on the leading role of money for inflation in an out-of-sample forecast framework is not very strong, see e.g. Lenza (2006) or Fisher, Lenza, Pill and Reichlin (2008). At the same time, e.g. Gerlach (2003) or Assenmacher-Wesche and Gerlach (2007, 2008) argue that money and output could affect prices at different frequencies, however their analysis is performed in-sample. In this Chapter, it is investigated empirically which frequency bands and for which variables are the most relevant for the out-of-sample forecast of inflation when the information from prices, money and real activity is considered. To extract different frequency components from a series a wavelet transform is applied. It provides a simple and intuitive framework for band-pass filtering and allows a decomposition of series into different frequency bands. Its application in the multivariate out-of-sample forecast is novel in the literature. The results indicate that, indeed, different scales of money, prices and GDP can be relevant for the inflation forecast.

This thesis suggests a Bayesian vector autoregressive (VAR) model which allows for explicit parametrization of the unconditional mean for data measured at different frequencies, without the need to aggregate data to the lowest common frequency. Using a normal prior for the steady-state and a normal-inverse Wishart prior for the dynamics and error covariance, a Gibbs sampler is proposed to sample the posterior distribution. A forecast study is performed using monthly and quarterly data for the US macroeconomy between 1964 and 2008. The proposed model is compared to a steady-state Bayesian VAR model estimated on data aggregated to quarterly frequency and a quarterly least squares VAR with standard parametrization. Forecasts are evaluated using root mean squared errors and the log-determinant of the forecast error covariance matrix. The results indicate that the inclusion of monthly data improves the accuracy of quarterly forecasts of monthly variables for horizons up to a year. For quarterly variables the one and two quarter forecasts are improved when using monthly data.

Au cours de la dernière décennie, les prix des logements ont augmenté de façon spectaculaire dans plusieurs pays à travers le monde. Par exemple, les prix des logements aux États-Unis, en Espagne et en Irlande ont été marqués par des cycles d'expansion et de récession les plus marquants de leur histoire. L'augmentation concomitante des prix des logements (et dans certains cas l’occurrence des épisodes d'expansion - récession) dans de nombreuses économies avancées soulève quelques questions importantes. Y a t-il eu une bulle immobilière dans les pays avancés? Quels sont les principaux déterminants de l'évolution des prix des logements dans ces pays? Est-ce que les marchés immobiliers des pays avancés sont-ils interdépendants? Le premier chapitre propose une modélisation structurelle des modèles VAR Bayésiens pour les États-Unis, la France, l'Espagne et la Grèce qui examinent les effets relatifs de l'évolution du secteur réel de production, du secteur financier et des flux internationaux de capitaux sur les marchés du logement. Un deuxième exercice tente d'identifier la présence de régimes de bulles immobilières à partir d’une modélisation Markovienne à deux états. Les principaux résultats liés au marche américain montrent que les entrées de capitaux étrangers, mesurées par le solde de la balance courante en pourcentage du PIB, comptent pour plus de 30 % de la variance des chocs qui frappent les prix des logements, tandis que les taux d’intérêt contribuent pour environ 38 %. En France, la politique monétaire a le plus grand pouvoir explicatif des évolutions du marché du logement, tandis qu'en Espagne et en Grèce, les taux hypothécaires variables et les investissements dans le logement exercent la plus grande influence sur le marché du logement. Tous les pays ont connu un régime de bulle immobilière sur la majeure partie des années 2000.Le deuxième chapitre utilise une approche de type Global VAR (ou GVAR) qui porte sur la modélisation des interdépendances internationales des prix immobiliers. Le modèle GVAR a été estimé empiriquement en utilisant des données trimestrielles de sept pays, pour la période 1987-2011. Les résultats montrent que les chocs des prix immobiliers originaires des États-Unis ont de fortes répercussions sur tous les pays, avec les plus fortes magnitudes observées pour l'Irlande. Ce résultat suggère que les marchés immobiliers pourraient être soumis à des effets de contagion du comportement des marchés financiers et que le secteur immobilier peut être analysé comme un actif spéculatif. Les liens entre les taux d'intérêt réels à long terme sont positifs et statistiquement significatifs dans tous les pays, même si ils ont un rôle limité sur l'évolution des prix immobiliers. Les chocs négatifs sur les prix immobiliers aux États-Unis ont des effets négatifs et statistiquement significatifs sur le PIB réel aux États-Unis, le Canada et l'Irlande.Le troisième chapitre est consacré au financement de la première guerre mondiale par les Etats-Unis et le rôle de la War Finance Corporation (WFC). Plus spécifiquement, on s’intéresse aux fluctuations des rendements des bons du Trésor américain émis entre novembre 1917 et décembre 1920. L’analyse économétrique est basée sur des techniques de séries temporelles Bayésiennes. Les principaux résultats montrent que les chocs positifs sur les achats de la WFC engendrent une réponse négative et statistiquement significative sur tous les types de rendements des bons de guerre. En outre, les achats de la WFC des bons Liberty et Victory, à l'exception du premier prêt des bons Liberty, ont eu un effet statistiquement significatif sur l'évolution des taux à court terme. Les achats de la WFC de la deuxième et de la quatrième émission des bons Liberty ont eu des effets significatifs et positifs sur les taux à court terme, ce qui suggère une déformation de la courbe des taux. / During the last decade, housing prices have increased dramatically in several countries around the world. For instance, housing prices in the United States, Spain, and Ireland have been marked by one of the most striking boom-bust cycles in their history. The concomitant increase in housing prices (and in some cases boom-bust episodes) across many advanced economies raises the following important questions. Was there a housing bubble across advanced countries? What are the main determinants of the housing price movements in these countries? Are the advanced countries' housing markets interrelated? The first chapter of the dissertation estimates a set of structural Bayesian VAR models for the U.S., France, Spain, and Greece that examine the relative effects of developments in the real production sector, the financial sector, and international capital flows on the housing market. A second exercise attempts to identify the presence of housing price bubble regimes by estimating a set of two state Markov-switching Bayesian VAR models. The main results for the U.S. show that foreign capital inflows, measured by the current account balance as a percentage of GDP, account for more than 30\% of the variance of the shocks hitting housing prices, while adjustable mortgage rates contribute about 38\%. In France, monetary policy has the largest explanatory power for the housing market evolutions, while in Spain and Greece, the variable mortgage rates and housing investments exert the largest influence on the housing market. All the countries experienced a bubble regime over most of the 2000s. The second chapter uses a Global VAR model estimated using quarterly data from seven countries, for the period 1987-2011, to analyze the interdependencies that exist between domestic and international factors in housing markets. We find that housing price shocks originating in the U.S. have large spillover effects on all the countries, with the largest magnitudes on Ireland. This result suggests that housing markets may be subject to contagion effects and that housing can be analyzed as a speculative asset, based on international data spanning the past two decades. Linkages in long-run real interest rates are positive and statistically significant across all the countries, although they have a limited role on the evolution of housing prices. Negative shocks to the U.S. housing prices have negative and statistically significant effects on real GDP in the U.S., Canada, and Ireland. The third chapter studies the price fluctuations of war bonds issued by the U.S Treasury in order to finance the World War I between November 1917 and December 1920. Bayesian time series techniques are used to carry out the analyses. We are focusing on the effects that the bond-purchasing program of the War Finance Corporation (WFC) had on the evolution of war bond yields. Our main results show that positive shocks to WFC purchases display a negative and statistically significant effect on all types of war bond yields. Furthermore, WFC purchases of Liberty and Victory Bonds, except the First Liberty Loan, had a statistically significant effect on the evolution of commercial paper rates. WFC purchases of the Second and Fourth Liberty Bonds had significant and positive effects on commercial paper rates, suggesting a twist in the bond yield curve.

Volatility spillovers in stock markets have become an important phenomenon, especially in times of crises. Mechanisms of shock transmission from one mar- ket to another are important for the international portfolio diversification. Our thesis examines impulse responses and variance decomposition of main stock in- dices in emerging Central European markets (Czech Republic, Poland, Slovakia and Hungary) in the period of January 2007 to August 2009. Two models are used: A vector autoregression (VAR) model with constant variance of resid- uals and a time varying parameter vector autoregression (TVP-VAR) model with a stochastic volatility. Opposingly of other comparable studies, Bayesian methods are used in both models. Our results confirm the presence of volatility spillovers among all markets. Interestingly, we find significant opposite trans- mission of shocks from Czech Republic to Poland and Hungary, suggesting that investors see the Central European exchanges as separate markets. Bibliographic Record Janhuba, R. (2012): Volatility Spillovers in New Member States: A Bayesian Model. Master thesis, Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies. Supervisor: doc. Roman Horváth Ph.D. JEL Classification C11, C32, C58, G01, G11, G14 Keywords Volatility spillovers,...

This dissertation is composed of two parts, an integrative essay and a set of published papers. The essay and the collection of papers are placed in the context of development and application of time series econometric models in a temporal-axis from 1970s through 2005, with particular focus in the Marketing discipline. The main aim of the integrative essay is on modelling the effects of marketing actions on performance variables, such as sales and market share in competitive markets. Such research required the estimation of two kinds of time series econometric models: multivariate and multiple time series models. I use Autoregressive Integrated Moving Average (ARIMA) intervention models and the Pierce and Haugh statistical test to model the impact of a single marketing instrument, mainly price promotions, to measure own and cross-short term sales effects, and to study asymmetric marketing competition. I develop and apply Vector AutoRegressive (VAR) and Bayesian Vector AutoRegressive (BVAR) models to estimate dynamic relationships in the market and to forecast market share. Especially, BVAR models are advantageous because they contain all relevant dynamic and interactive effects. They accommodate not only classical competitive reaction effects, but also own and cross-market share brand feedback effects and internal decision rules and provided substantively useful insights into the dynamics of demand. The integrative essay is structured in four main parts. The introduction sets the basic ideas behind the published papers, with particular focus on the motivation of the essay, the types of competitive reaction effects analysed, an overview of the time series econometric models in marketing, a short discussion of the basic methodology used in the research and a brief description of the inter-relationships across the published papers and structure of the essay. The discussion is centred on how to model the effects of marketing actions at the selective demand or brand level and at the primary demand or product level. At the brand level I discuss the research contribution of my work on (i) modelling promotional short-term effects of price and non-price actions on sales and market share for consumer packaged goods, with no competition, (ii) how to measure own and cross short-term sales effects of advertising and price, in particular, cross-lead and lag effects, asymmetric sales behaviour and competition without retaliatory actions, in an automobile market, (iii) how to model the marketing-mix effectiveness at the short and long-term on market shares in a car market, (iv) what is the best method to forecast market share, and (v) the study of causal linkages at different time horizons between sales and marketing activity for a particular brand. At the product or commodity level, I propose a way to model the flows of tourists that come from different origins (countries) to the same country-destination as market segments defining the primary demand of a commodity - the product

The recent financial and economic turmoil driven by housing market has led the economists to refocus on the issue about monetary policy and asset price, especially housing price. In this dissertation I investigate the various relationships between monetary policy and asset prices in U.S. economy through steady state Bayesian VAR (SS BVAR) and revised Taylor-typed interest rate rule (Forward-looking rule) based on Generalized Method of Moments (GMM) methodology. In chapter II, steady state Bayesian VAR (SS BVAR) methodology is introduced and multi step-ahead forecasts are executed. Upon usual squared error loss methodology the forecasting performances of SS BVAR are evaluated in comparison with standard BVAR and conventional VAR. Equal predictive ability tests following Giacomini and White (2006) verify that the SS BVAR is superior in forecasting power especially in long-horizons. In chapter III, identification issue involving housing sector is explored through two different ways: economic theory-based approach and algorithms of inductive causations. Despite the different approaches the housing sector’s specifications are somewhat similar. Impulse response analyses demonstrate that monetary shock to housing price is relatively smaller, less significant, and less lasting when compared to Choleski identification. Also historical decomposition and conditional forecast analyses indicate that the housing price shock itself is crucial in accounting the sharp increase and sudden drop of housing price since 2003. Upon the estimated evidences I conjecture that there are much uncertainty between monetary policy and housing price, recalling the consideration of institutional factors when trying to accounting housing sectors. In chapter IV, following Dupor and Conley (2004), I explore how Fed responds to stock price and inflation movements differently across high and low inflation sub-periods. Replicated linear estimation results of Dupor and Conley (2004)’s indicate that Fed raises its target interest rate responding to stock price gap with statistical significance. Linear estimation results, however, are not robust to small change of chosen breakpoint especially in inflation coefficient. So I construct nonlinear model as an alternative way to relax this problem and carry out test of structural change with the nonlinear framework. Consequently both nonlinearity and structural change matter in explanation of Fed’s behavior in this type of reaction function analysis. Given structural change, inflation coefficients movement shows that Fed has responded to expected inflation pressure nonlinearly across sub-period, while stock price gap coefficient shows explicit break around early ’90 in line with Dupor and Conley (2004)’s finding.

M. Comm. / Although there has been several work done on monetary policy and inflation in South Africa, this dissertation is intended to add and expand on the existing literature on the subject with data dating back to 1970. The dissertation was inspired by recent international research that has indentified that a large Bayesian VAR model normally performs better than the normal SVAR model. Given that there has already been differing conclusions in literature on whether interest rates are effective as a tool to control inflation, there is therefore an opportunity to assess monetary policy using a different and more robust modelling framework. The choice of a sample is informed by the fact that prior to inflation targeting and within the period under consideration; interest rates remained a core factor in monetary policy management. Some of the literature will be discussed in detail in chapter 2. This dissertation will introduce the large BVAR model with 14 variables in the South African economy. In comparison, the SVAR model suffers from the curse of dimensionality that is eliminated by using more variables with the Large Bayesian VAR with the response functions of all 14 variables. The objective is therefore to determine whether interest rate changes in South Africa have a meaningful and desired effect on inflation. A substantial amount of recent literature was done within the environment of inflation targeting; however, our study intends to measure more the responsiveness of interest rates and other macro variables to monetary policy. The period of inflation targeting in South Africa provides more useful data and evidence on the responsiveness of the macro variables given the direct policy approach it represents versus the previous regime and hence it is covered in more detail in the dissertation. We also assess, in the process, the main drivers behind inflation in South Africa, in an effort to establish whether the country suffers from cost- push or demandpush. The type of inflation should also assist in providing recommendations on the appropriate response to inflation.

The dissertation contains essays concerning the linkages between macroeconomy and financial market or the conduct of monetary policy via DSGE modelling. The dissertation contributes to the questions of fitting macroeconomic models to the data, and so contributes to our understanding of the driving forces of fluctuations in macroeconomic and financial variables. Chapter one offers an introduction to my thesis and outlines in detail the main results and methodologies. In Chapter two I introduce a statistical measure for model evaluation and selection based on the full information of sample second moments in data. A model is said to outperform its counterpart if it produces closer similarity in simulated data variance-covariance matrix when compared with the actual data. The "distance method" is generally feasible and simple to conduct. A flexible price two-sector open economy model is studied to match the observed puzzles of international finance data. The statistical distance approach favours a model with dominant role played by the expectational errors in foreign exchange market which breaks the international interest rate parity. Chapter three applies the distance approach to a New Keynesian model augmented with habit formation and backward-looking component of pricing behaviour. A macro-finance model of yield curve is developed to showcase the dynamics of implied forward yields. This exercise, with the distance approach, reiterate the inability of macro model in explaining yield curve dynamics. The method also reveals remarkable interconnection between real quantity and bond yield slope. In Chapter four I study a general equilibrium business cycle model with sticky prices and labour market rigidities. With costly matching on labour market, output responds in a hump-shaped and persistent manner to monetary shocks and the resulting Phillips curve seems to radically change the scope for monetary policy because (i) there are speed limit effects for policy and (ii) there is a cost channel for monetary policy. Labour reforms such as in mid-1980s UK can trigger more effective monetary policy. Research on monetary policy shall pay greater attention to output when labour market adjustments are persistent. Chapter five analyzes the link between money and financial spread, which is oft missed in specification of monetary policy making analysis. When liquidity provision by banks dominates the demand for money from the real economy, money may contain information of future output and inflation due to its impact on financial spreads. I use a sign-restriction Bayesian VAR estimation to separate the liquidity provision impact from money market equilibrium. The decomposition exercise shows supply shocks dominate the money-price nexus in the short to medium term. It also uncovers distinctive policy stance of two central banks. Finally Chapter six concludes, providing a brief summary of the research work as well as a discussion of potential limitations and possible directions for future research.

La tesi è organizzata in tre parti. Ognuna delle quali tratta un aspetto cruciale per la trasmissione della politica monetaria. Nella prima parte si impiega un modello Neo Keynesiano per adattarlo all’economia Italiana. A tal fine, Si stimano le risposte dinamiche, sia simulando il modello e sia utilizzando le serie storiche, impiegando la metodologia SMM. Nella seconda parte sono riportate le nuove evidenze sulla persistenza dell’inflazione, attraverso l’utilizzo di una nuova tecnica di identificazione di un modello “Bayesian VAR”; con l’obiettivo di analizzare gli effetti di vari shock di policy sulle variabili macroeconomiche. La terza parte si propone di fornire le evidenze microeconomiche sull’eterogeneità nelle strategie di determinazione dei prezzi tra le imprese italiane sulla base di un nuovo database longitudinale predisposto dalla Banca d’Italia. L’analisi così articolata si propone di identificare le eterogeneità a livello settoriale e/o territoriale tra le imprese, per trarne importanti implicazioni di policy per l’autorità monetaria. / The thesis is structured in three parts. Each part deals with a crucial aspect for monetary policy transmission. In the first one, I set up a New Keynesian model with to Italian economy. To this end, I estimate the dynamic responses both for the theoretical model and for the data using the SMM technique. Chapter 2 presents new evidence about inflation persistence through a novel technique to identify a Bayesian VAR model, and it analyzes the effects of several policy shocks on the macroeconomic variables. Chapter 3 provides the new micro-evidence on price setting and heterogeneity among Italian companies by using a new longitudinal data provided by the Bank of Italy. This allowed an analysis that captures the regional and sectoral disparities among firms’ price setting. This micro-evidence has a very important policy implication for the monetary authority.

Exports are one of the key aggregates in the Argentina’s economy, both because to its links with thedomestic demand and by its influence on the behaviour of the trade balance and current account.Have adequate forecasts for this variable is useful to design policies to keep surpluses in the externalsector and prevent recurring crises seen in the past. In this work, we considered some modelsfor forecasting the performance of this aggregate, which could be an alternative to the estimationof structural econometric models. For this purpose, we used two approaches: the first is based instandard and Bayesian VARs (Minnesota prior, Gibbs sampler, partial BVAR and BVAR-Kalman). Thelatter combines the evidence in the data with any prior information that may also be available. Thesecond approach considers the FAVAR (Factor-augmented VAR) models, which combines the standardVAR with factor analysis. Finally, we evaluated the forecasting ability of different models. / Las exportaciones representan uno de los agregados más importantes de la economía argentina,tanto por su vinculación con la demanda doméstica como por su influencia en el comportamientode la balanza comercial y de la cuenta corriente. Disponer de adecuados pronósticos deesta variable resulta útil a fin de diseñar políticas que permitan mantener superávit en el sectorexterno y evitar las recurrentes crisis observadas en el pasado. En este trabajo, se consideran algunosmodelos destinados a la realización de pronósticos de dicho agregado, los cuales podrían seruna alternativa a la estimación de sistemas econométricos estructurales. A tal efecto, se utilizandos propuestas: la primera se basa en modelos de VAR sin restricciones y Bayesianos (‘Minnesota’prior, ‘Gibbs sampler’, parcial BVAR y BVAR-Kalman). Estos últimos consideran supuestos a priori(‘prior’) e información histórica de las series de tiempo empleadas. La segunda propuesta descansaen modelos FAVAR (Factor-aumentado VAR), que combinan los VAR con el análisis de factores.Finalmente, se evalúa la capacidad de pronóstico de los distintos modelos.