Modified efficient importance sampling for partially non‐Gaussian state space models

The construction of an importance density for partially non‐Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom‐built procedure. For the class of partially non‐Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.     

Forecasting interest rates with shifting endpoints

We consider forecasting the term structure of interest rates with the assumption that factors driving the yield curve are stationary around a slowly time‐varying mean or ‘shifting endpoint’. The shifting endpoints are captured using either (i) time series methods (exponential smoothing) or (ii) long‐range survey forecasts of either interest rates or inflation and output growth, or (iii) exponentially smoothed realizations of these macro variables. Allowing for shifting endpoints in yield curve factors provides substantial and significant gains in out‐of‐sample predictive accuracy, relative to stationary and random walk benchmarks. Forecast improvements are largest for long‐maturity interest rates and for long‐horizon forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models in order to include macroeconomic factors. Our work benefits from recent developments in the dynamic factor literature related to the extraction of the common factors from a large panel of macroeconomic series and the estimation of the parameters in the model. We include these factors in a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study, we use a monthly time series panel of unsmoothed Fama–Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relationship between the macroeconomic factors and the yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts.     

Credit cycles and macro fundamentals

We use an intensity-based framework to study the relation between macroeconomic fundamentals and cycles in defaults and rating activity. Using Standard and Poor's U.S. corporate rating transition and default data over the period 1980–2005, we directly estimate the default and rating cycle from micro data. We relate this cycle to the business cycle, bank lending conditions, and financial market variables. In line with earlier studies, the macro variables appear to explain part of the default cycle. However, we strongly reject the correct dynamic specification of these models. The problem is solved by adding an unobserved dynamic component to the model, which can be interpreted as an omitted systematic credit risk factor. By accounting for this latent factor, many of the observed macro variables loose their significance. There are a few exceptions, but the economic impact of the observed macro variables for credit risk remains low. We also show that systematic credit risk factors differ over transition types, with risk factors for downgrades being noticeably different from those for upgrades. We conclude that portfolio credit risk models based only on observable systematic risk factors omit one of the strongest determinants of credit risk at the portfolio level. This has obvious consequences for current modeling and risk management practices.     

The multi-state latent factor intensity model for credit rating transitions

A new empirical reduced-form model for credit rating transitions is introduced. It is a parametric intensity-based duration model with multiple states and driven by exogenous covariates and latent dynamic factors. The model has a generalized semi-Markov structure designed to accommodate many of the stylized facts of credit rating migrations. Parameter estimation is based on Monte Carlo maximum likelihood methods for which the details are discussed in this paper. A simulation experiment is carried out to show the effectiveness of the estimation procedure. An empirical application is presented for transitions in a 7 grade rating system. The model includes a common dynamic component that can be interpreted as the credit cycle. Asymmetric effects of this cycle across rating grades and additional semi-Markov dynamics are found to be statistically significant. Finally, we investigate whether the common factor model suffices to capture systematic risk in rating transition data by introducing multiple factors in the model.     

Measuring Synchronization and Convergence of Business Cycles for the Euro area,UK and US*

This paper investigates business cycle relations among different economies in the Euro area. Cyclical dynamics are explicitly modelled as part of a time series model. We introduce mechanisms that allow for increasing or diminishing phase shifts and for time‐varying association patterns in different cycles. Standard Kalman filter techniques are used to estimate the parameters simultaneously by maximum likelihood. The empirical illustrations are based on gross domestic product (GDP) series of seven European countries that are compared with the GDP series of the Euro area and that of the US. The original integrated time series are band‐pass filtered. We find that there is an increasing resemblance between the business cycle fluctuations of the European countries analysed and those of the Euro area, although with varying patterns.     

Time Series Modelling of Daily Tax Revenues

We provide a detailed discussion of time series modelling of daily data in general and daily tax revenues in particular. The main feature of the daily tax revenue series is the pattern within calendar months. Standard time series methods for seasonal adjustment and forecasting cannot be used since the number of banking days per calendar month varies and because there are two levels of seasonality: between months and within months. We propose a daily time series model based on unobserved components that allows for the classic decomposition into trend, seasonal plus irregular, but it also includes components for intra-monthly, trading-day and length-of-month effects. Such components typically rely on stochastic cubic spline, polynomial and dummy variable functions. State space techniques are used for the recursive computation of the likelihood and forecasts functions with special allowance for irregular spacing. The model is operational for daily forecasting at the Dutch Ministry of Finance. We present the model specification and discuss estimation and forecasting results up to December 1999. A comparative forecast evaluation is also presented.     

Testing the assumptions behind importance sampling

Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumption is seldom checked. In this paper we use extreme value theory to empirically assess the appropriateness of this assumption. Our main application is the stochastic volatility model, where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model.     

Estimating systematic continuous-time trends in recidivism using a non-Gaussian panel data model

We model panel data of crime careers of juveniles from a Dutch Judicial Juvenile Institution. The data are decomposed into a systematic and an individual-specific component, of which the systematic component reflects the general time-varying conditions including the criminological climate. Within a model-based analysis, we treat (1) shared effects of each group with the same systematic conditions, (2) strongly non-Gaussian features of the individual time series, (3) unobserved common systematic conditions, (4) changing recidivism probabilities in continuous time and (5) missing observations. We adopt a non-Gaussian multivariate state-space model that deals with all these issues simultaneously. The parameters of the model are estimated by Monte Carlo maximum likelihood methods. This paper illustrates the methods empirically. We compare continuous time trends and standard discrete-time stochastic trend specifications. We find interesting common time variation in the recidivism behaviour of the juveniles during a period of 13 years, while taking account of significant heterogeneity determined by personality characteristics and initial crime records.