Limit experiments of GARCH

GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model (which was introduced a few years ago by Kl\"{u}ppelberg, Lindner and Maller) and Nelson's diffusion limit are the only functional continuous-time limits of GARCH in distribution. In contrast to Nelson's diffusion limit, COGARCH reproduces most of the stylized facts of financial time series. Since it has been proven that Nelson's diffusion is not asymptotically equivalent to GARCH in deficiency, in the present paper, we investigate the relation between GARCH and COGARCH in Le Cam's framework of statistical equivalence. We show that GARCH converges generically to COGARCH, even in deficiency, provided that the volatility processes are observed. Hence, from a theoretical point of view, COGARCH can indeed be considered as a continuous-time equivalent to GARCH. Otherwise, when the observations are incomplete, GARCH still has a limiting experiment, which we call MCOGARCH, which is not equivalent, but nevertheless quite similar, to COGARCH. In the COGARCH model, the jump times can be more random than for the MCOGARCH, a fact practitioners may see as an advantage of COGARCH.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ328 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Stochastic volatility models for ordinal valued time series with application to finance

In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an e±cient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both models to price changes of the IBM stock in January, 2001 at the NYSE. Dependencies of the price change process on covariates are quantified and compared with theoretical considerations on such processes. We also investigate whether this data set requires modeling with a heavy-tailed Student-t distribution

Modeling migraine severity with autoregressive ordered probit models

This paper considers the problem of modeling migraine severity assessments and their dependence on weather and time characteristics. Since ordinal severity measurements arise from a single patient dependencies among the measurements have to be accounted for. For this the autore- gressive ordinal probit (AOP) model of Müller and Czado (2004) is utilized and fitted by a grouped move multigrid Monte Carlo (GM-MGMC) Gibbs sampler. Initially, covariates are selected using proportional odds models ignoring this dependency. Model fit and model comparison are discussed. The analysis shows that humidity, windchill, sunshine length and pressure differences have an effect in addition to a high dependence on previous measurements. A comparison with proportional odds specifications shows that the AOP models are preferred

Multilateral Economic Cooperation and the International Transmission of Fiscal Policy

During the global financial crisis 2007–2009 fiscal policy was widely used as a stabilization tool. Policymakers allowed a large build-up of public debt resulting from both automatic and discretionary expansionary measures. At the same time, calls for policy coordination stressed that international spillovers of fiscal policy might be sizeable. We reconsider the case for fiscal coordination by providing new evidence on the cross-border effects of discretionary fiscal measures. We rely on a vector autoregression model as well as on a quantitative business cycle model. We find that i) large spillover effects cannot be ruled out and, in contrast to conventional wisdom, ii) financial factors rather than trade flows lie at the heart of the international transmission mechanism. We discuss the implications of these results for policy coordination when markets price sovereign default risk, and put pressure on governments for implementing budget consolidation measures.

Twin Deficits: Squaring Theory, Evidence and Common Sense

In this paper we reconsider the twin deficit hypothesis (that fiscal shocks generating budget deficits also worsen external trade) both from a theoretical point of view and by analyzing data for Australia, Canada, the UK and the US. First, we assess the joint dynamics of budget and trade deficits along the business cycle, uncovering a strikingly recurrent S-shaped relation between the two. The correlation is actually negative, suggesting twin divergence. This observation however cannot rule out the possibility that government spending expansions and/or tax cuts may cause trade deficits, as the overall correlation is likely to be dominated by cyclical factors. Second, we reconsider the transmission of government spending in a standard two-country two-good model: we find that openness and the persistence of fiscal shocks are major determinants of the magnitude (or even sign) of the response of the trade balance to fiscal shocks. For a given persistence of the fiscal shock, the closer an economy, the larger the crowding out effect on investment, the lower the deterioration of the trade balance. Third, we take this insight to the data, investigating the transmission of fiscal shocks in a VAR framework in the four countries in our sample. Our empirical findings tend to support our view. In the US and Australia, which are relatively less open than Canada and the UK, and where government spending shocks are less persistent, we find that the external impact of fiscal policy is rather limited. Instead, private investment responds substantially. The reverse is true for Canada and the UK. These findings confirm and put into perspective earlier results, whereas fiscal expansions in the US are found to have on average a negligible effect on the country's trade balance. However, we emphasize that these results are consistent with a call for a US fiscal retrenchment to address global imbalances: the impact of budget cuts on the US external trade is muted by their positive effect on domestic investment, strengthening the US ability to generate resources against future interest and debt repayment.twin deficits, budget deficit, trade deficits, home-bias, openness, crowding out, international transmission of fiscal policy, current account adjustment, business cycle dynamics.

Fleshing out the monetary transmission mechanism: output composition and the role of financial frictions

Financial frictions affect the way in which different components of GDP respond to a monetary policy shock. We embed the financial accelerator of Bernanke, Gertler and Gilchrist (1999) into a medium-scale Dynamic General Equilibrium model and evaluate the relative importance of financial frictions in explaining monetary transmission. Specifically, we match the impulse responses generated by the model with empirical impulse response functions obtained from a vector autoregression on US time series data. This allows us to provide estimates for the structural parameters of our model and judge the relevance of different model features. In addition, we propose a set of simple and instructive specification tests that can be used to assess the relative fit of various restricted models. Although our point estimates suggest some role for financial accelerator effects, they are actually of minor importance for the descriptive success of the model. JEL Classification: E32, E44, E51Financial Frictions, Minimum Distance Estimation, monetary policy, Output Composition

Government Spending Shocks in Quarterly and Annual U.S. Time-Series

Government spending shocks are frequently identi?ed in quarterly time-series data by ruling out a contemporaneous response of government spending to other macroeconomic aggregates. We provide evidence that this assumption may not be too restrictive for U.S. annual time-series data.Government spending shocks, Annual Data, Identi?cation

How do fiscal and technology shocks affect real exchange rates? : New evidence for the United States

Using vector autoregressions on U.S. time series relative to an aggregate of industrialized countries, this paper provides new evidence on the dynamic effects of government spending and technology shocks on the real exchange rate and the terms of trade. To achieve identification, we derive robust restrictions on the sign of several impulse responses from a two-country general equilibrium model. We find that both the real exchange rate and the terms of trade – whose responses are left unrestricted – depreciate in response to expansionary government spending shocks and appreciate in response to positive technology shocks

Productivity shocks, budget deficits and the current account

Currently the U.S. is experiencing record budget and current account deficits, a phenomenon familiar from the "Twin Deficits" discussion of the 1980s. In contrast, during the 1990s productivity growth has been identified as the primary cause of the US current account deficit. We suggest a theoretical framework which allows to evaluate empirically the relative importance of budget deficits and productivity shocks for the determination of the current account. Using a sample of 21 OECD countries and time series data from 1960 to 2003 we find little evidence for a contemporaneous effect of budget deficits on the current account, while country-specific productivity shocks appear to play a key role. JEL Classification: E62, F32, F41budget deficit, current account, Investment, productivity