Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

An aggregate sales model for consumer durables incorporating a time-varying mean replacement age

Forecasting category or industry sales is a vital component of a company's planning and control activities. Sales for most mature durable product categories are dominated by replacement purchases. Previous sales models which explicitly incorporate a component of sales due to replacement assume there is an age distribution for replacements of existing units which remains constant over time. However, there is evidence that changes in factors such as product reliability/durability, price, repair costs, scrapping values, styling and economic conditions will result in changes in the mean replacement age of units. This paper develops a model for such time-varying replacement behaviour and empirically tests it in the Australian automotive industry. Both longitudinal census data and the empirical analysis of the replacement sales model confirm that there has been a substantial increase in the average aggregate replacement age for motor vehicles over the past 20 years. Further, much of this variation could be explained by real price increases and a linear temporal trend. Consequently, the time-varying model significantly outperformed previous models both in terms of fitting and forecasting the sales data. Copyright (C) 2001 John Wiley & Sons, Ltd.

Comparative analysis of time-frequency methods estimating the time-varying microstructure of sleep EEG spindles

Proceedings of the Information Technology Applications in Biomedicine, Ioannina - Epirus, Greece, October 26-28, 2006

Potential dementia biomarkers based on the time-varying microstructure of sleep EEG spindles

Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007

Structural time series models and the Kalman filter: A concise review

The continued increase in availability of economic data in recent years and, more importantly, the possibility to construct larger frequency time series, have fostered the use (and development) of statistical and econometric techniques to treat them more accurately. This paper presents an exposition of structural time series models by which a time series can be decomposed as the sum of a trend, seasonal and irregular components. In addition to a detailled analysis of univariate speci fications we also address the SUTSE multivariate case and the issue of cointegration. Finally, the recursive estimation and smoothing by means of the Kalman filter algorithm is described taking into account its different stages, from initialisation to parameter s estimation.

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Model Switching and Model Averaging in Time- Varying Parameter Regression Models

This paper investigates the usefulness of switching Gaussian state space models as a tool for implementing dynamic model selecting (DMS) or averaging (DMA) in time-varying parameter regression models. DMS methods allow for model switching, where a different model can be chosen at each point in time. Thus, they allow for the explanatory variables in the time-varying parameter regression model to change over time. DMA will carry out model averaging in a time-varying manner. We compare our exact approach to DMA/DMS to a popular existing procedure which relies on the use of forgetting factor approximations. In an application, we use DMS to select different predictors in an in ation forecasting application. We also compare different ways of implementing DMA/DMS and investigate whether they lead to similar results.

Time Varying Dimension Models

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP models are parameter-rich and risk over-fitting unless the dimension of the model is small. Motivated by this worry, this paper proposes several Time Varying dimension (TVD) models where the dimension of the model can change over time, allowing for the model to automatically choose a more parsimonious TVP representation, or to switch between different parsimonious representations. Our TVD models all fall in the category of dynamic mixture models. We discuss the properties of these models and present methods for Bayesian inference. An application involving US inflation forecasting illustrates and compares the different TVD models. We find our TVD approaches exhibit better forecasting performance than several standard benchmarks and shrink towards parsimonious specifications.

Hierarchical Shrinkage in Time-Varying Parameter Models

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Sequential estimation of time-varying multipath channel for MIMO-OFDM systems

In this paper, we introduce a pilot-aided multipath channel estimator for Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems. Typical estimation algorithms assume the number of multipath components and delays to be known and constant, while theiramplitudes may vary in time. In this work, we focus on the more realistic assumption that also the number of channel taps is unknown and time-varying. The estimation problem arising from this assumption is solved using Random Set Theory (RST), which is a probability theory of finite sets. Due to the lack of a closed form of the optimal filter, a Rao-Blackwellized Particle Filter (RBPF) implementation of the channel estimator is derived. Simulation results demonstrate the estimator effectiveness.

Measuring time-varying economic fears with consumption-based stochastic discount factors

This paper analyzes empirically the volatility of consumption-based stochastic discount factors as a measure of implicit economic fears by studying its relationship with future economic and stock market cycles. Time-varying economic fears seem to be well captured by the volatility of stochastic discount factors. In particular, the volatility of recursive utility-based stochastic discount factor with contemporaneous growth explains between 9 and 34 percent of future changes in industrial production at short and long horizons respectively. They also explain ex-ante uncertainty and risk aversion. However, future stock market cycles are better explained by a similar stochastic discount factor with long-run consumption growth. This specification of the stochastic discount factor presents higher volatility and lower pricing errors than the specification with contemporaneous consumption growth.

Time-Varying Benefits of International Diversification for Finnish Investor: Country-Specific Strategy Concentrating on Emerging Markets

The main objective of this study is to investigate whether the Finnish investors’ country-specific strategy concentrating on emerging markets provides diversification benefits. We also analyze whether the benefits of international diversification has been diminished after periods of high volatility caused by different market crisis. The objective is investigated with three methods: Correlation coefficients, rolling correlations added with OLS trend-lines and Box’s M statistic. All the empirical tests are analyzed and calculated with logarithmic returns of weekly time series data from Friday closing values between January 1995 and December 2007. The number of weekly observations is 678. The data type is total return indices of different countries. Data is collected from DataStream and provided by Datastream Financial. Countries investigated are Finland, Argentina, Brazil, Chile, China, India, Mexico, Poland, Russia, South Africa, South Korea, Thailand and Turkey. The current data is quoted both in U.S. Dollars and local currencies. The empirical results of this thesis show that the correlation coefficients are time-varying across Finland and 12 emerging market countries. Although the correlations have risen from 1995 to 2007, there can be found sub-periods where the correlation has declined from earlier period. The results also indicate that a Finnish investor constructing a portfolio of emerging market countries cannot rely on the correlation coefficients estimated from historical data because of the instability of correlation matrices.

Time-varying Risk Premiums and Conditional Market Risk: Empirical Evidence from European Stock Markets

This study investigates the relationship between the time-varying risk premiums and conditional market risk in the stock markets of the ten member countries of Economy and Monetary Union. Second, it examines whether the conditional second moments change over time and are there asymmetric effects in the conditional covariance matrix. Third, it analyzes the possible effects of the chosen testing framework. Empirical analysis is conducted using asymmetric univariate and multivariate GARCH-in-mean models and assuming three different degrees of market integration. For a daily sample period from 1999 to 2007, the study shows that the time-varying market risk alone is not enough to explain the dynamics of risk premiums and indications are found that the market risk is detected only when its price is allowed to change over time. Also asymmetric effects in the conditional covariance matrix, which is found to be time-varying, are clearly present and should be recognized in empirical asset pricing analyses.