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(DISCLAIMER: Not all mathematical symbols in the abstract will display properly - please see the abstract in the pdf). An important issue in the analysis of cross-sectional dependence which has received renewed interest in the past few years is the need for a better understanding of the extent and nature of such cross dependencies. In this paper we focus on measures of cross-sectional dependence and how such measures are related to the behaviour of the aggregates defined as cross-sectional averages. We endeavour to determine the rate at which the cross-sectional weighted average of a set of variables appropriately demeaned, tends to zero. One parameterisation sets this to be 0(N2α-2), for 1/2

Many statistical applications require the forecast of a random variable of interest over several periods into the future. The sequence of individual forecasts, one period at a time, is called a path forecast, where the term path refers to the sequence of individual future realizations of the random variable. The problem of constructing a corresponding joint prediction region has been rather neglected in the literature so far: such a region is supposed to contain the entire future path with a prespecified probability. We develop bootstrap methods to construct joint prediction regions. The resulting regions are proven to be asymptotically consistent under a mild high-level assumption. We compare the finitesample performance of our joint prediction regions to some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.

This paper investigates the macroeconomic effects of fiscal policy in New Zealand using a structural Vector Autoregression (SVAR) model. The model is the five-variable structural vector autoregression (SVAR) framework proposed by Blanchard and Perotti (2005), further augmented to allow for the possibility that taxes, spending and interest rates might respond to the level of the debt over time. We examine the dynamic responses of output, inflation and the interest rate to changes in government spending and revenues and analyse the contribution of shocks to New Zealand's business cycle for the period 1983:1-2010:2. We find that the effects of government expenditure shocks in New Zealand appear to be positive but small in the short-run at the cost of higher interest rates and lower output in the medium to long-run. The sign of the effects of tax policy changes are less clear cut, but again the effects on GDP appear similarly modest. Past fiscal policy is analysed through a historical decomposition of the shocks in the model. This suggests that discretionary fiscal policy has had a generally pro-cyclical impact on GDP over the last fifteen years, and a material impact on the real long-term interest rate. A fiscal expansion has a positive but limited impact on inflation.

Changing time series properties of US inflation and economic activity are analyzed within a class of extended Phillips Curve (PC) models. First, the misspecification effects of mechanical removal of low frequency movements of these series on posterior inference of a basic PC model are analyzed using a Bayesian simulation based approach. Next, structural time series models that describe changing patterns in low and high frequencies and backward as well as forward inflation expectation mechanisms are incorporated in the class of extended PC models. Empirical results indicate that the proposed models compare favorably with existing Bayesian Vector Autoregressive and Stochastic Volatility models in terms of fit and predictive performance. Weak identification and dynamic persistence appear less important when time varying dynamics of high and low frequencies are carefully modeled. Modeling inflation expectations using survey data and adding level shifts and stochastic volatility improves substantially in sample fit and out of sample predictions. No evidence is found of a long run stable cointegration relation between US inflation and marginal costs. Tails of the complete predictive distributions indicate an increase in the probability of disinflation in recent years.

Changing time series properties of US inflation and economic activity, measured as marginal costs, are modeled within a set of extended Phillips Curve (PC) models. It is shown that mechanical removal or modeling of simple low frequency movements in the data may yield poor predictive results which depend on the model specification used. Basic PC models are extended to include structural time series models that describe typical time varying patterns in levels and volatilities. Forward as well as backward looking expectation mechanisms for inflation are incorporated and their relative importance evaluated. Survey data on expected inflation are introduced to strengthen the information in the likelihood. Use is made of simulation based Bayesian techniques for the empirical analysis. No credible evidence is found on endogeneity and long run stability between inflation and marginal costs. Backward-looking inflation appears stronger than forward-looking one. Levels and volatilities of inflation are estimated more precisely using rich PC models. Estimated inflation expectations track nicely the observed long run inflation from the survey data. The extended PC structures compare favorably with existing basic Bayesian Vector Autoregressive and Stochastic Volatility models in terms of fit and prediction. Tails of the complete predictive distributions indicate an increase in the probability of disinflation in recent years.

We describe stationarity and ergodicity (SE) regions for a recently proposed class of score driven dynamic correlation models. These models have important applications in empirical work. The regions are derived from sufficiency conditions in Bougerol (1993) and take a non-standard form. We show that the non-standard shape of the sufficiency regions cannot be avoided by reparameterizing the model or by rescaling the score steps in the transition equation for the correlation parameter. This makes the result markedly different from the volatility case. Observationally equivalent decompositions of the stochastic recurrence equation yield regions with different sizes and shapes. We illustrate our results with an analysis of time-varying correlations between UK and Greek equity indices. We find that also in empirical applications different decompositions can give rise to different conclusions regarding the stability of the estimated model.

Multiplicative error models (MEM) became a standard tool for modeling conditional durations of intraday transactions, realized volatilities and trading volumes. The parametric estimation of the corresponding multivariate model, the so-called vector MEM (VMEM), requires a specification of the joint error term distribution, which is due to the lack of multivariate distribution functions on Rd + defined via a copula. Maximum likelihood estimation is based on the assumption of constant copula parameters and therefore, leads to invalid inference, if the dependence exhibits time variations or structural breaks. Hence, we suggest to test for time-varying dependence by calibrating a time-varying copula model and to reestimate the VMEM based on identified intervals of homogenous dependence. This paper summarizes the important aspects of (V)MEM, its estimation and a sequential test for changes in the dependence structure. The techniques are applied in an empirical example.

Several economic data series of Liechtenstein are backwardly estimated in order to achieve consistent historic time series. The generated series consist for instance of the national income for the years 1954 to 1992 (by regressive inter- and retropolation with indicators) and 1993 to 1997 (by approximative computation after national accounting scheme). Also, the sectoral and total employment of some missing years in the 70s, 80s and 90s is complemented and the gross domestic product from 1972 until 1997 is provided by an approximative computation/estimation relying on the identity of the generation of income account as part of the national accounts. These methods and the presented series are being evaluated with respect to their accuracy, which turns out to be satisfying, and can be linked with the released results from the official national accounts, which were introduced for the year 1998 and have been published until 2009 so far. Along with the provision of these figures, Liechtenstein's economic growth pattern is being identified, the business cycles are detected and first analytical insights are obtained.

This study examines the long-memory properties of German energy price indices (specifically, import and export prices, as well as producer and consumer prices) for hard coal, lignite, mineral oil and natural gas adopting a fractional integration modelling framework. The analysis is undertaken using monthly data from January 2000 to August 2011. The results suggest nonstationary long memory in the series (with orders of integration equal to or higher than 1) when breaks are not allowed for. However, endogenous break tests indicate a single break in all series except for producer prices for lignite for which two breaks are detected. When such breaks are taken into account, and with autocorrelated disturbances, evidence of mean reversion is found in practically all cases.

Spectral analysis is one of the most important areas of time series econometrics. The use of spectral measures is widespread in different science fields such as economics, physics, engineering, geology. The SPECTRAN toolbox has been developed to facilitate the application of spectral concepts to univariate as well as to multivariate series. It offers a variety of frequency-domain techniques and supports the statistical inference. It also provides convenient tools for the examination of the results, e.g.functions for writing the output to a file or functions specially designed for plotting the estimated spectral measures. The key feature of SPECTRAN is the user-friendliness embodied in, e.g., the central function spectran which performs the whole analysis with default settings, but also gives the user the possibility to adjust them. This document sets out the most relevant spectral concepts and their implementation in SPECTRAN. Finally, three examples shall illustrate the application of different toolbox function to macroeconomic data.

This article provides new insights into the cyclical behavior of consumer and producer real wages in the USA and Germany. We apply two methods for the estimation of the cyclical components from the data: the approach based on the structural time series models and the ARIMA-model-based approach combined with the canonical decomposition and a band-pass filter. We examine the extracted cycles drawing on two wavelet concepts: wavelet coherence and wavelet phase angle. In contrast to the analysis in the time or frequency domains, wavelet analysis allows for the identification of possible changes in cyclical patterns over time. From the findings of our study, we can infer that the USA and Germany differ with respect to the lead-lag relationship of real wages and the business cycle. In the USA, both real wages are leading the business cycle in the entire time interval. The German consumer real wage is, on the other hand, lagging the business cycle. For the German producer real wage, the lead-lag pattern changes over time. We also find that real wages in the USA as well in Germany are procyclical or acyclical until 1980 and countercyclical thereafter.

This paper develops an improved test of economic convergence or divergence using time series methods. The usefulness of the method is illustrated in an analysis of the growth pattern between Chinese regions in 1952–2007. Comparing all combinations of regional pairs, the analysis yields support for economic divergence in roughly half of the cases. In the other half, we instead find that regions have grown while maintaining stable income differences. As such, the results show the co-existence of divergence and conditional convergence among China's regions.

Divergent priors are improper when defined on unbounded supports. Bartlett's paradox has been taken to imply that using improper priors results in ill-defined Bayes factors, preventing model comparison by posterior probabilities. However many improper priors have attractive properties that econometricians may wish to access and at the same time conduct model comparison. We present a method of computing well defined Bayes factors with divergent priors by setting rules on the rate of diffusion of prior certainty. The method is exact; no approximations are used. As a further result, we demonstrate that exceptions to Bartlett's paradox exist. That is, we show it is possible to construct improper priors that result in well defined Bayes factors. One important improper prior, the Shrinkage prior due to Stein (1956), is one such example. This example highlights pathologies with the resulting Bayes factors in such cases, and a simple solution is presented to this problem. A simple Monte Carlo experiment demonstrates the applicability of the approach developed in this paper.

In this paper, we empirically assess the extent to which early release inefficiency and definitional change affect prediction precision. In particular, we carry out a series of ex-ante prediction experiments in order to examine: the marginal predictive content of the revision process, the trade-offs associated with predicting different releases of a variable, the importance of particular forms of definitional change which we call 'definitional breaks', and the rationality of early releases of economic variables. An important feature of our rationality tests is that they are based solely on the examination of ex-ante predictions, rather than being based on in-sample regression analysis, as are many tests in the extant literature. Our findings point to the importance of making real-time datasets available to forecasters, as the revision process has marginal predictive content, and because predictive accuracy increases when multiple releases of data are used when specifying and estimating prediction models. We also present new evidence that early releases of money are rational, whereas prices and output are irrational. Moreover, we find that regardless of which release of our price variable one specifies as the 'target' variable to be predicted, using only 'first release' data in model estimation and prediction construction yields mean square forecast error (MSFE) 'best' predictions. On the other hand, models estimated and implemented using 'latest available release' data are MSFE-best for predicting all releases of money. We argue that these contradictory finding are due to the relevance of definitional breaks in the data generating processes of the variables that we examine. In an empirical analysis, we examine the real-time predictive content of money for income, and we find that vector autoregressions with money do not perform significantly worse than autoregressions, when predicting output during the last 20 years.

It is generally accepted that regional labor markets are characterized by strong interdependencies. However, only few studies include spatial elements to their estimations. Using the model framework proposed by Cli and Ord (1973, 1981) and the estimation technique proposed by Kelejian and Prucha (1998), we estimate a spatial time series model for the Swiss cantonal unemployment rates on a quarterly level. Our model contains a spatial lag in the level and in the error term, as well as further exogenous explanatory variables. While both spatial lags turn out to be significant in our estimations, the dependency in the error term seems to be even stronger than the one in the level., KOF Working Papers, 274

This paper develops a Markov-Switching vector autoregressive model that allows for imperfect synchronization of cyclical regimes in multiple variables, due to phase shifts of a single common cycle. The model has three key features: (i) the amount of phase shift can be different across regimes (as well as across variables), (ii) it allows the cycle to consist of any number of regimes J is larger than or equal to 2, and (iii) it allows for regime-dependent volatilities and correlations. In an empirical application to monthly returns on size-based stock portfolios, a three-regime model with asymmetric phase shifts and regime-dependent heteroscedasticity is found to characterize the joint distribution of returns most adequately. While large- and small-cap portfolios switch contemporaneously into boom and crash regimes, the large-cap portfolio leads the small-cap portfolio for switches to a moderate regime by a month.

Studies of aid effectiveness abound in the literature, often with opposing conclusions. Since most time-series studies use data from the exact same publicly available data bases, our claim here is that such differences in results must be due to the use of different econometric models and methods. To investigate this we perform a comprehensive study of the long-run effect of foreign aid (ODA) on a set of key macroeconomic variables in 36 sub-Saharan African countries from mid-1960s to 2007. We use a well-specified (Cointegrated) VAR (CVAR) model as our statistical benchmark. It represents a much-needed general-to-specific approach which can provide broad confidence intervals within which empirically relevant claims should fall. Based on stringent statistical testing, our results provide broad support for a positive long-run impact of ODA flows on the macroeconomy. For example, we find a positive effect of ODA on investment in 33 of the 36 included countries, but hardly any evidence supporting the view that aid has been harmful. From a methodological point of view our study documents the importance of transparency in results reporting in particular when the statistical null does not correspond to a natural economic null hypothesis. Our study identifies three reasons for econometrically unsatisfactory results in the literature: failure to adequately account for unit roots and breaks; imposing seemingly innocuous but invalid data transformations; and imposing aid endogeneity/exogeneity without testing.

We introduce a long memory autoregressive conditional Poisson (LMACP) model to model highly persistent time series of counts. The model is applied to forecast quoted bid-ask spreads, a key parameter in stock trading operations. It is shown that the LMACP nicely captures salient features of bid-ask spreads like the strong autocorrelation and discreteness of observations. We discuss theoretical properties of LMACP models and evaluate rolling window forecasts of quoted bid-ask spreads for stocks traded at NYSE and NASDAQ. We show that Poisson time series models significantly outperform forecasts from ARMA, ARFIMA, ACD and FIACD models. The economic significance of our results is supported by the evaluation of a trade schedule. Scheduling trades according to spread forecasts we realize cost savings of up to 13 % of spread transaction costs.

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the continuous-time and the discrete-time experiments are proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier nonparametric approaches in the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between the various proposed methods.

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an integrated solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an oracle under such scenarios. The tuning parameters are chosen via a data driven 'rolling scheme' method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators.

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that the variable may follow over time is summarized by the simultaneous con…dence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one cannot derive analytic expressions for this con…dence region, and its non-parametric estimation is impractical given commonly available predictive sample sizes. Instead, this paper derives the approximate rectangular con…dence regions that control false discovery rate error, which are a function of the predictive sample covariance matrix and the empirical distribution of the Mahalanobis distance of the path-forecast errors. These rectangular regions are simple to construct and appear to work well in a variety of cases explored empirically and by simulation. The proposed techniques are applied to provide con…dence bands around the Fed and Bank of England real-time path-forecasts of growth and in‡ation. JEL Classi…cation Codes: C32, C52, C53

Despite the fact that many aggregates are nonlinear functions and the aggregation weights of many macroeconomic aggregates are time-varying, much of the literature on forecasting aggregates considers the case of linear aggregates with fixed, time-invariant aggregation weights. In this study a framework for nonlinear contemporaneous aggregation with possibly stochastic or time-varying weights is developed and different predictors for an aggregate are compared theoretically as well as with simulations. Two examples based on European unemployment and inflation series are used to illustrate the virtue of the theoretical setup and the forecasting results.

Statistische Prognosen basieren auf der Annahme, dass ein funktionaler Zusammenhang zwischen der zu prognostizierenden Variable y und anderen j-dimensional beobachtbaren Variablen x = (x1,...xl) besteht. Kann der funktionale Zusammenhang geschätzt werden, so kann im Prinzip für jedes x der zugehörige Wert y prognostiziert werden. Bei den meisten Anwendungen wird angenommen, dass der funktionale Zusammenhang einem niedrigdimensionalen parametrischen Modell entspricht oder durch dieses zumindest gut wiedergegeben wird. Ein Beispiel im univariaten Fall ist das lineare Modell y = b0 + b1x. Sind die beiden unbekannten Parameter b0 und b1 mithilfe historischer Daten geschätzt, so lässt sich für jedes gegebene x sofort der zugehörige Wert y prognostizieren. Allerdings besteht hierbei die Gefahr, dass der wirkliche funktionale Zusammenhang nicht dem gewählten Modell entspricht. Dies kann infolge zu schlechten Prognosen führen. Nichtparametrische Verfahren gehen ebenfalls von einem funktionalen Zusammenhang aus, geben aber kein festes parametrisches Modell vor und zwängen die Daten damit in kein Prokrustes Bett. Sie sind deshalb hervorragend geeignet, um 1) Daten explorativ darzustellen, 2) parametrische Modelle zu überprüfen und 3) selbst als Schätzer für den funktionalen Zusammenhang zu dienen (Cleveland [2], Cleveland und Devlin [3]). Nichtparametrische Verfahren können daher problemlos auch zur Prognose eingesetzt werden. Dieses Kapitel ist wie folgt strukturiert. Abschnitt 9.2 stellt nichtparametrische Verfahren vor und erläutert deren grundsätzliche Struktur. Der Schwerpunkt liegt auf dem univariaten Regressionsmodell und auf der Motivation der vorgestellten Verfahren. Abschnitt 9.3 präsentiert eine praktische Anwendung für eine Zeitreihe von Wechselkursvolatilitäten. Es werden Prognosen mit nichtparametrischen Verfahren berechnet und deren Güte mit den Prognosen eines AR(1)-Zeitreihenmodells verglichen, vgl. auch Kapitel 14 dieses Buches. Es zeigt sich für die gewählte Anwendung, dass das parametrische Modell die Daten sehr gut erfasst. Das nichtparametrische Modell liefert in dieser Anwendung keine bessere Prognosegüte. Zugleich veranschaulicht die Anwendung, wie nichtparametrische Verfahren für die Modelvalidierung eingesetzt werden können. Und natürlich zeigt es auch, wie solche Verfahren für Prognosen eingesetzt werden können. Abschnitt 9.4 präsentiert die Literatur, die für weitere Lektüre herangezogen werden kann. Alle praktischen Beispiele im Text, welche mit dem Symbol [Q] versehen sind, lassen sich von der Addresse www.quantlet.de herunterladen.

This paper establishes stylized facts about the cyclicality of real consumer wages and real producer wages in Germany. As detrending methods we apply the deterministic trend model, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter, the Baxter-King filter and the structural time series model. The detrended data are analyzed both in the time domain and in the frequency domain. The great advantage of an analysis in the frequency domain is that it allows to assess the relative importance of particular frequencies for the behavior of real wages. In the time domain we find that both real wages display a procyclical pattern and lag behind the business cycle. In the frequency domain the consumer real wage lags behind the business cycle and shows an anticyclical behavior for shorter time periods, whereas for longer time spans a procyclical behavior can be observed. However, for the producer real wage the results in the frequency domain remain inconclusive.

This paper establishes stylized facts about the cyclicality of real consumer wages and real producer wages in Germany. As detrending methods we apply the deterministic trend model, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter, the Baxter-King filter and the structural time series model. The detrended data are analyzed both in the time domain and in the frequency domain. The great advantage of an analysis in the frequency domain is that it allows to assess the relative importance of particular frequencies for the behavior of real wages. In the time domain we find that both real wages display a procyclical pattern and lag behind the business cycle. In the frequency domain the consumer real wage lags behind the business cycle and shows an anticyclical behavior for shorter time periods, whereas for longer time spans a procyclical behavior can be observed. However, for the producer real wage the results in the frequency domain remain inconclusive.

We develop Bayesian techniques for estimation and model comparison in a novel Generalised Stochastic Unit Root (GSTUR) model. This allows us to investigate the presence of a deterministic time trend in economic series, while allowing the degree of persistence to change over time. In particular the model allows for shifts from stationarity I(0) to nonstationarity I(1) or vice versa. The empirical analysis demonstrates that the GSTUR model provides new insights on the properties of some macroeconomic time series such as stock market indices, inflation and exchange rates.

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via functional factor analysis. We propose a two-step estimation procedure. At the first step, we detect the deterministic trends of the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under various situations extending current variable selection studies. At the second step, we obtain the detrended low dimensional stochastic process, but it also poses an important question: is it justified, from an inferential point of view, to base further statistical inference on the estimated stochastic time series? We show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible, which finally allows one to study the dynamics of the whole high-dimensional system with a low dimensional representation together with the deterministic trend. We apply the method to our motivating empirical problems: studies of the dynamic behavior of temperatures (further used for pricing weather derivatives), implied volatilities and risk patterns and correlated brain activities (neuro-economics related) using fMRI data, where a panel version model is also presented.

In this paper, I propose an instrumental variable (IV) estimation procedure to estimate global VAR (GVAR) models and show that it leads to consistent and asymptotically normal estimates of the parameters. I also provide computationally simple conditions that guarantee that the GVAR model is stable.

In this paper we present an empirically stable money demand model for Euro area M3. We show that housing wealth is an important explanatory variable of long-run money demand that captures the trending behaviour of M3 velocity, in particular its shift in the first half of this decade. We show that the current financial crisis has no impact on the stability of our money demand model.

A new test is proposed for the null of absence of serial correlation. The test uses a data-driven smoothing parameter. The resulting test statistic has a standard limit distribution under the null. The smoothing parameter is calibrated to achieve rate-optimality against several classes of alternatives. The test can detect alternatives with many small correlation coefficients that can go to zero with an optimal adaptive rate which is faster than the parametric rate. The adaptive rate-optimality against smooth alternatives of the new test is established as well. The test can also detect ARMA and local Pitman alternatives converging to the null with a rate close or equal to the parametric one. A simulation experiment and an application to monthly financial square returns illustrate the usefulness of the proposed approach.

This paper investigates the dynamics of aggregate wages and prices in the United States (US) and the Euro Area (EA) with a special focus on persistence of real wages, wage and price inflation. The analysis is conducted within a structural vector error-correction model, where the structural shocks are identified using the long-run properties of the theoretical model, as well as the cointegrating properties of the estimated system. Overall, in the long run, wage and price inflation emerge as more persistent in the EA than in the US in the face of import price, unemployment, or permanent productivity shocks. This finding is robust to the changes in the sample period and in the models’ specifications entertained in the paper.

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.

This paper proposes a strategy to increase the efficiency of forecast combination. Given the availability of a wide range of forecasts for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, a hierarchical procedure based on an encompassing test is developed. Firstly, forecasting models are ranked according to a measure of predictive accuracy (RMSFE). The models are then selected for combination such that each forecast is not encompassed by any of the competing forecasts. Thus, the procedure aims to unit model selection and model averaging methods. The robustness of the procedure is investigated in terms of the relative RMSFE using ISAE (Institute for Studies and Economic Analyses) short-term forecasting models for monthly industrial production in Italy.

This paper describes the particular impacts of the financial and economic crisis on Central and Eastern European (CEE) countries, studies pro-cyclicality of fiscal policies, discusses the impact of the crisis on fiscal policy, and the policy response of various governments. After drawing some lessons for fiscal policy from previous emerging market crises, the paper concludes with some thoughts on the appropriate policy response from a more normative perspective. The key message of the paper is that the crisis should be used as an opportunity to introduce reforms to avoid future pro-cyclical fiscal policies, to increase the quality of budgeting and to increase credibility. These reforms should include fiscal responsibility laws comprising medium-term fiscal frameworks, fiscal rules, and independent fiscal councils. When fiscal consolidation is accompanied by fiscal reforms that increase credibility, non-Keynesian effects may offset to some extent the contraction caused by the consolidation.

This study presents empirical evidence on the long-run motives for holding euro area money by focusing on the role of equity and labour markets. Equity positively affects money demand through wealth effects, as equities are a significant store of household wealth and thus part of a financial transaction motive. Negative substitution effects through the expected return on equity reflect a speculative motive from the equity market. A precautionary motive from the labour market is captured by the annual change in the unemployment rate. The main conclusion is that equity and labour markets do matter for money. All three new elements, in particular housing and financial wealth, have been found statistically and economically significant in explaining M3 since 1983. These findings are robust across different proxies for the augmented motives and a shorter sample period starting in 1994.

Forecasting the world economy is a difficult task given the complex interrelationships within and across countries. This paper proposes a number of approaches to forecast short-term changes in selected world economic variables and aims, first, at ranking various forecasting methods in terms of forecast accuracy and, second, at checking whether methods forecasting di- rectly aggregate variables (direct approaches)out-perform methods based on the aggregation of country- specific forecasts (bottom-up approaches). Overall, all methods perform better than a simple benchmark for short horizons (up to three months ahead). Among the forecasting approaches used, factor models appear to perform the best. Moreover, direct approaches out-perform bottom-up ones for real variables, but not for prices. Finally, when country-specific forecasts are adjusted to match direct forecasts at the aggregate levels (top-down approaches), the forecast accuracy is neither improved nor deteriorated (i.e. top-down and bottom-up approaches are broadly equivalent in terms of country-specific forecast accuracy).

The wavelet transform is used to identify a biannual and an annual seasonality in the Phelix Day Peak and to separate the long-term trend from its short-term motion. The short-term/long-term model for commodity prices of Schwartz & Smith (2000) is applied but generalised to account for weekly periodicities and time-varying volatility. Eventually we find a bivariate SARMA-CCC-GARCH model to fit best. Moreover it surpasses the goodness of fit of an univariate GARCH model, which shows that the additional effort of dealing with a two-factor model is worthwile.

In this paper we adopt a principal components analysis (PCA) to reduce the dimensionality of the term structure and employ autoregressive models (AR) to forecast principal components which, in turn, are used to forecast swap rates. Arguing in favor of structural variation, we propose data driven, adaptive model selection strategies based on the PCA/AR model. To evaluate ex-ante forecasting performance for particular rates, different forecast features such as mean squared errors, directional accuracy and big hit ability are considered. It turns out that relative to benchmark models, the adaptive approach offers additional forecast accuracy in terms of directional accuracy and big hit ability.

Likelihood based inference for multi-state latent factor intensity models is hindered by the fact that exact closed-form expressions for the implied data density are not available. This is a common and well-known problem for most parameter driven dynamic econometric models. This paper reviews, adapts and compares three different approaches for solving this problem. For evaluating the likelihood, two of the methods rely on Monte Carlo integration with importance sampling techniques. The third method, in contrast, is based on fully deterministic numerical procedures. A Monte Carlo study is conducted to illustrate the use of each method, and assess its corresponding finite sample performance.

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. The Smolyak operator underlying the sparse grids approach frees global approximation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from rational expectations and in three new nonlinear state space filters. The filters substantially decrease the computational burden compared to the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge for the solution and estimation of a general class of models.

In this paper, we study the dynamic interdependencies between high-frequency volatility, liquidity demand as well as trading costs in an electronic limit order book market. Using data from the Australian Stock Exchange we model 1-min squared mid-quote returns, average trade sizes, number of trades and average (excess) trading costs per time interval in terms of a four-dimensional multiplicative error model. The latter is augmented to account also for zero observations. We find evidence for significant contemporaneous relationships and dynamic interdependencies between the individual variables. Liquidity is causal for future volatility but not vice versa. Furthermore, trade sizes are negatively driven by past trading intensities and trading costs. Finally, excess trading costs mainly depend on their own history.

This paper applies the modelling strategy of Garratt, Lee, Pesaran and Shin (2003) to the estimation of a structural cointegrated VAR model that relates the core macroeconomic variables of the Swiss economy to current and lagged values of a number of key foreign variables. We identify and test a long-run structure between the variables. Moreover, we analyse the dynamic properties of the model using Generalised Impulse Response Functions. In its current form the model can be used to produce forecasts for the endogenous variables either under alternative specifications of the marginal model for the exogenous variables, or conditional on some pre-specified path of those variables (for scenario forecasting). In due course the Swiss VECX model can also be integrated within a Global VAR (GVAR) model where the foreign variables of the model are determined endogenously.

We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or non-nested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student's t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.

A Bayesian model averaging procedure is presented that makes use of a finite mixture of many model structures within the class of vector autoregressive (VAR) processes. It is applied to two empirical issues. First, stability of the Great Ratios in U.S. macro-economic time series is investigated, together with the effect of permanent shocks on business cycles. Second, the linear VAR model is extended to include a smooth transition function in a (monetary) equation and stochastic volatility in the disturbances. The risk of a liquidity trap in the U.S.A. and Japan is evaluated. Although this risk found to be reasonably high, we find only mild evidence that the monetary policy transmission mechanism is different and that central banks consider the expected cost of a liquidity trap in policy setting. Posterior probabilities of different models are evaluated using Markov chain Monte Carlo techniques.

We use a vector error correction model to study the long-term relationship between aggregate expected default frequency and the macroeconomic development, i.e. CPI, industry production and short-term interest rate. The model is used to forecast the median expected default frequency of the corporate sector by conditioning on external forecasts of macroeconomic developments. Evaluations of the model show that it yields low forecast errors in terms of RMSE. The estimation results indicate that the interest rate has the strongest impact on expected default frequency among the included macroeconomic variables. The forecasts indicate that EDF will rise gradually over the forecast period.

Motivated by economic-theory concepts - the Fisher hypothesis and the theory of the term structure - we consider a small set of simple bivariate closed-loop time-series models for the prediction of price inflation and of long- and short-term interest rates. The set includes vector autoregressions (VAR) in levels and in differences, a cointegrated VAR, and a non-linear VAR with threshold cointegration based on data from Germany, Japan, UK, and the U.S. Following a traditional comparative evaluation of predictive accuracy, we subject all structures to a mutual validation using parametric bootstrapping. Ultimately, we utilize the recently developed technique of Mallows model averaging to explore the potential of improving upon the predictions through combinations. While the simulations confirm the traded wisdom that VARs in differences optimize one-step prediction and that error correction helps at larger horizons, the model-averaging experiments point at problems in allotting an adequate penalty for the complexity of candidate models.

During the last decades a wide literature has focused on the relationship volume-volatility on financial markets. This paper investigates the temporal dynamics of volatility and volumes, supposing, as in Bollerslev and Jubinsky (1999), that the link has to be found in their long-run dependencies, that are supposed to be driven by the same informative process. We analyze the volume-volatility relationship using IBM stocks data. In particular, we rely on the realized volatility based on five minutes stock prices. Tail dependence analysis is carried out with two alternative estimators of the continuous part of the volatility process. The analysis shows that log-realized volatility and log-volumes are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. We also investigate the possibility that volumes and volatility are driven by a common fractionally integrated stochastic trend, i.e. they have the same degree of long memory and are fractionally cointegrated as the Mixture Distribution Hypotesis prescribes. Moreover, we estimate a bivariate ARFIMA specification that explicitly considers the long run relationship between the two series and the tail dependence in the shocks, by parameterizing the joint density by means of different copula functions. The evidence from the model estimates, the simulation results and the forecasts comparison with HAR model highlight the ability of the bivariate ARFIMA with copula density specification to account for the common long memory pattern and tail dependence.

This paper proposes a strategy to increase the efficiency of forecast combining methods. Given the availability of a wide range of forecasting models for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, an algorithm procedure based on a widely used encompassing test (Harvey, Leybourne, Newbold, 1998) is developed. First, forecasting models are ranked according to a measure of predictive accuracy (RMSFE) and, in a consecutive step, each prediction is chosen for combining only if it is not encompassed by the competing models. To assess the robustness of this procedure, an empirical application to Italian monthly industrial production using ISAE short-term forecasting models is provided.

We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over and across difficult regions. More unfavorable properties of standard smoothers become visible when the data is observed on an irregular grid in a non-rectangular domain. In this paper, we adopt smoothing spline methods within a state space framework to smooth data on one- or two-dimensional grids with difficult regions. We make a distinction between two types of missing observations to handle the irregularity of the grid and to ensure that no smoothing takes place over and across the difficult region. For smoothing on two-dimensional grids, we introduce a two-step spline smoothing method. The proposed solution applies to all smoothing methods that can be represented in a state space framework. We illustrate our methods for three different cases of interest.