Publications - Timo Teräsvirta

Building Multivariate Time-Varying Smooth Transition Correlation GARCH Models, with an Application to the Four Largest Australian Banks

Hall, A. D., Silvennoinen, A., Teräsvirta, T. — Sun, 01 Jan 2023 10:37:10 +0100

This paper proposes a methodology for building Multivariate Time-Varying STCC–GARCH models. The novel contributions in this area are the specification tests related to the correlation component, the extension of the general model to allow for additional correlation regimes, and a detailed exposition of the systematic, improved modelling cycle required for such nonlinear models. There is an R-package that includes the steps in the modelling cycle. Simulations demonstrate the robustness of the recommended model building approach. The modelling cycle is illustrated using daily return series for Australia’s four largest banks.

A parsimonious test of constancy of a positive definite correlation matrix in a multivariate time-varying GARCH model

Kang, J., Jakobsen, J. S., Silvennoinen, A., Teräsvirta, T., Wade, G. — Thu, 01 Sep 2022 10:37:10 +0200

We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are time-varying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example involving daily returns of 26 stocks included in the Dow Jones stock index is given.

Comprehensively testing linearity hypothesis using the smooth transition autoregressive model

Seong, D., Cho, J. S., Teräsvirta, T. — Fri, 01 Jul 2022 10:37:10 +0200

This article examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic for testing linearity condition against the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a multivariate Gaussian process under the null of linearity, which is done by resolving the issue of identification problem arises in two different ways under the null. In contrast with the Lagrange multiplier test that is widely employed for testing the linearity condition, the proposed QLR statistic has an omnibus power, and thus, it complements the existing testing procedure. We show the empirical relevance of our test by testing the neglected nonlinearity of the US fiscal multipliers and growth rates of US unemployment. These empirical examples demonstrate that the QLR test is useful for detecting the nonlinear structure among economic variables.

A parsimonious test of constancy of a positive definite correlation matrix in a multivariate time-varying GARCH model

Kang, J., Jakobsen, J. S., Silvennoinen, A., Teräsvirta, T., Wade, G. — Sat, 01 Jan 2022 10:37:10 +0100

Four Australian Banks and the Multivariate Time-Varying Smooth Transition Correlation GARCH model

Hall, A. D., Silvennoinen, A., Teräsvirta, T. — Tue, 28 Sep 2021 10:37:10 +0200

This paper looks at changes in the correlations of daily returns between the four major banks in Australia. Revelations from the analysis are of importance to investors, but also to government involvement, due to the large proportion of the highly concentrated financial sector relying on the stability of the Big Four. For this purpose, a methodology for building Multivariate Time-Varying STCC-GARCH models is developed. The novel contributions in this area are the specification tests related to the correlation component, the extension of the general model to allow for additional correlation regimes, and a detailed exposition of the systematic, improved modelling cycle required for such nonlinear models. There is an R-package that includes the steps in the modelling cycle. Simulations evidence the robustness of the recommended model building approach. The empirical analysis reveals an increase in correlations of the Australia's four largest banks that coincides with the stagnation of the home loan market, technology changes, the mining boom, and Basel II alignment, increasing the exposure of the Australian financial sector to shocks.

Transition from the Taylor rule to the zero lower bound

Hurn, S., Johnson, N., Silvennoinen, A., Teräsvirta, T. — Sat, 01 Jan 2022 10:37:10 +0100

This paper examines the Taylor rule in the context of United States monetary policy since 1965, particularly with respect to the zero-lower-bound era of the federal funds rate from 2009 to 2016. A nonlinear Taylor rule is developed which features smooth transitions in the first two moments of the federal funds rate. This flexible specification is found to usefully capture observed nonlinearity, while accounting for the well-documented structural changes in monetary policy formation at the Federal Reserve in the last 50 years, and especially in the recent zero-lower-bound era.

Comparing long monthly Chinese and selected European temperature series using the Vector Seasonal Shifting Mean and Covariance Autoregressive model

He, C., Kang, J., Teräsvirta, T., Zhang, S. — Sat, 01 May 2021 10:37:10 +0200

The purpose of this paper is to study differences in long monthly Asian and European temperature series. The longest available Asian series are those of Beijing and Shanghai, and they are compared with the ones for St Petersburg, Dublin and Uccle that have a rather different climate. The comparison is carried out in the Vector Shifting Mean and Covariance Autoregressive model that the authors have previously used to analyse 20 long European temperature series. This model gives information about mean shifts in these five temperature series as well as (error) correlations between them. The results suggest, among other things, that warming has begun later in China than in Europe, but that the change in the summer months in both Beijing and Shanghai has been quite rapid.

Comparing long monthly Chinese and selected European temperature series using the Vector Seasonal Shifting Mean and Covariance Autoregressive model

He, C., Kang, J., Teräsvirta, T., Zhang, S. — Mon, 04 Nov 2019 10:37:10 +0100

The purpose of this paper is to study differences in long monthly Asian and European temperature series. The longest available Asian series are those of Beijing and Shanghai, and they are compared with the ones for St Petersburg, Dublin and Uccle that have a rather different climate. The comparison is carried out in the Vector Shifting Mean and Covariance Autoregressive model that the authors have previously used to analysed 20 long European temperature series. This model gives information about mean shifts in these five temperature series as well as (error) correlations between them. The results suggest, among other things, that warming has begun later in China than in Europe, but that the change in the summer months in both Beijing and Shanghai has been quite rapid.

Long monthly temperature series and the Vector Seasonal Shifting Mean and Covariance Autoregressive model

He, C., Kang, J., Teräsvirta, T., Zhang, S. — Fri, 01 Nov 2019 10:37:10 +0100

We consider a vector version of the Shifting Seasonal Mean Autoregressive model. The model is used for describing dynamic behaviour of and contemporaneous dependence between a number of long monthly temperature series for 20 cities in Europe, extending from the second half of the 18th century until mid-2010s. The results indicate strong warming in the winter months, February excluded, and cooling followed by warming during the summer months. Error variances are mostly constant over time, but for many series there is systematic decrease between 1820 and 1850 in April. Error correlations are considered by selecting two small sets of series and modelling correlations within these sets. Some correlations do change over time, but a large majority remains constant. Not surprisingly, the correlations generally decrease with the distance between cities, but geography also plays a role.

Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model

Seong, D., Cho, J. S., Teräsvirta, T. — Fri, 01 Nov 2019 10:37:10 +0100

This paper examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic that tests linearity condition using the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a Gaussian stochastic process under the null of linearity by resolving the issue of twofold identification meaning that Davies’s (1977, 1987) identification problem arises in two different ways under the null. We illustrate our theory using the exponential STAR and logistic STAR models and also conduct Monte Carlo simulations. Finally, we test for neglected nonlinearity in the German money demand, growth rates of US unemployment, and German industrial production. These empirical examples also demonstrate that the QLR test statistic complements the linearity test of the Lagrange multiplier test statistic in Teräsvirta (1994).

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Central England Monthly Temperature Series, 1772-2016

He, C., Kang, J., Teräsvirta, T., Zhang, S. — Tue, 01 Jan 2019 10:37:10 +0100

A new autoregressive model with seasonal dummy variables in which coefficients of seasonal dummies vary smoothly and deterministically over time is introduced. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed as in ARCH models. This variance is also allowed to be smoothly and deterministically time-varying. Under regularity conditions, consistency and asymptotic normality of the maximum likelihood estimators of parameters of this model is proved. The purpose of the model is to find out how the average monthly temperatures in the well-known central England temperature series have been varying during the period of more than 240 years. The main result is that warming has occurred but that there are notable differences between months. In particular, no warming is found for February, April, May and June.

Global hemispheric temperatures and co-shifting

Holt, M. T., Terasvirta, T. — Wed, 01 Jan 2020 10:37:10 +0100

This paper examines local changes in annual temperature data for the northern and southern hemispheres (1850–2017) by using a multivariate generalization of the shifting-meanautoregressive model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the QuickShift methodology. Full information maximum likelihood estimates of a bivariate system of temperature equations are then obtained and asymptotic properties of the corresponding estimators considered. The system is then used to perform formal tests of co-movements, called co-shifting, in the series. The results show evidence of co-shifting in the two series.

Transition from the Taylor rule to the zero lower bound

Hurn, S., Johnson, N., Silvennoinen, A., Terasvirta, T. — Mon, 03 Dec 2018 10:37:10 +0100

Univariate and multivariate GARCH type models with multiplicative decomposition of the variance to short and long run components are surveyed. The latter component can be either deterministic or stochastic. Examples of both types are studied.

Models with Multiplicative Decomposition of Conditional Variances and Correlations

Amado, C., Silvennoinen, A., Terasvirta, T. — Tue, 01 Jan 2019 10:37:10 +0100

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Central England Monthly Temperature Series, 1772-2016

He, C., Kang, J., Terasvirta, T., Zhang, S. — Wed, 25 Apr 2018 10:37:10 +0200

In this paper we introduce an autoregressive model with seasonal dummy variables in which coefficients of seasonal dummies vary smoothly and deterministically over time. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed, the decomposition being similar to that in well known ARCH and GARCH models. This variance is also allowed to be smoothly and deterministically time-varying. Under regularity conditions, consistency and asymptotic normality of the maximum likelihood estimators of parameters of this model is proved. A test of constancy of the seasonal coefficients is derived. The test is generalised to specifying the parametric structure of the model. A test of constancy over time of the heteroskedastic error variance is presented. The purpose of building this model is to use it for describing changing seasonality in the well-known monthly central England temperature series. More specifically, the idea is to find out in which way and by how much the monthly temperatures are varying over time during the period of more than 240 years, if they do. Misspecification tests are applied to the estimated model and the findings discussed.

Models with Multiplicative Decomposition of Conditional Variances and Correlations

Amado, C., Silvennoinen, A., Terasvirta, T. — Wed, 25 Apr 2018 10:37:10 +0200

Nonlinear models in macroeconometrics

Terasvirta, T. — Thu, 28 Jun 2018 10:37:10 +0200

Modelling nonlinear economic relationships

Granger, C. W.J., Terasvirta, T. — Tue, 01 Aug 2017 10:37:10 +0200

Modelling nonlinear economic time series

Terasvirta, T., Tjøstheim, D., Granger, C. W.J. — Tue, 01 Aug 2017 10:37:10 +0200

Panel Smooth Transition Regression Models

González, A., Terasvirta, T., Dijk, D. v., Yang, Y. — Thu, 19 Oct 2017 10:37:10 +0200

We introduce the panel smooth transition regression model. This new model is intended for characterizing heterogeneous panels, allowing the regression coefficients to vary both across individuals and over time. Specifically, heterogeneity is allowed for by assuming that these coefficients are bounded continuous functions of an observable variable and fluctuate between a limited number of "extreme regimes". The model can be viewed as a generalization of the threshold panel model of Hansen (1999). We extend the modelling strategy originally designed for univariate smooth transition regression models to the panel context. The strategy consists of model specification based on homogeneity tests, parameter estimation, and model evaluation, including tests of parameter constancy and no remaining heterogeneity. The model is applied to describing firms' investment decisions in the presence of capital market imperfections.

Nonlinear models in macroeconometrics

Terasvirta, T. — Mon, 02 Oct 2017 10:37:10 +0200

This article contains a short review of nonlinear models that are applied to modelling macroeconomic time series. Brief descriptions of relevant models, both univariate, dynamic single-equation, and vector autoregressive ones are presented. Their application is illuminated by a number of selected examples.

Modelling and forecasting WIG20 daily returns

Amado, C., Silvennoinen, A., Terasvirta, T. — Mon, 04 Sep 2017 10:37:10 +0200

The purpose of this paper is to model daily returns of the WIG20 index. The idea is to consider a model that explicitly takes changes in the amplitude of the clusters of volatility into account. This variation is modelled by a positive-valued deterministic component. A novelty in specification of the model is that the deterministic component is specified before estimating the multiplicative conditional variance component. The resulting model is subjected to misspecification tests and its forecasting performance is compared with that of commonly applied models of conditional heteroskedasticity.

Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model

Silvennoinen, A., Terasvirta, T. — Mon, 04 Sep 2017 10:37:10 +0200

A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations are deterministically time-varying. Parameters of the model are estimated jointly using maximum likelihood. Consistency and asymptotic normality of maximum likelihood estimators is proved. Numerical aspects of the estimation algorithm are discussed. A bivariate empirical example is provided.

Modelling and forecasting WIG20 daily returns

Amado, C., Silvennoinen, A., Terasvirta, T. — Sun, 01 Jan 2017 10:37:10 +0100

Global Hemispheric Temperatures and Co–Shifting: A Vector Shifting–Mean Autoregressive Analysis

Holt, M. T., Terasvirta, T. — Tue, 31 Jan 2017 10:37:10 +0100

This paper examines local changes in annual temperature data for the northern and southern hemispheres (1850-2014) by using a multivariate generalisation of the shifting-mean autoregressive model

of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the QuickShift methodology. Full information maximum likelihood estimates of a bivariate system of temperature

equations are then obtained and asymptotic properties of the corresponding estimators considered. The system is then used to perform formal tests of co-movements, called co-shifting, in the series. The

results show evidence of co-shifting in the two series. Forecasting this pair of series is considered as well.

Sir Clive Granger’s contributions to nonlinear time series and econometrics

Terasvirta, T. — Tue, 31 Jan 2017 10:37:10 +0100

Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger’s

contributions to a few other aspects of nonlinearity are reviewed as well.

Sir Clive Granger's contributions to nonlinear time series and econometrics

Terasvirta, T. — Sun, 01 Jan 2017 10:37:10 +0100

A Lagrange Multiplier test for testing the adequacy of the Constant Conditional Correlation GARCH model

Catani, P., Terasvirta, T., Yin, M. — Sun, 01 Jan 2017 10:37:10 +0100

A Lagrange multiplier test for testing the parametric structure of a constant conditional correlation-generalized autoregressive conditional heteroskedasticity (CCC-GARCH) model is proposed. The test is based on decomposing the CCC-GARCH model multiplicatively into two components, one of which represents the null model, whereas the other one describes the misspecification. A simulation study shows that the test has good finite sample properties. We compare the test with other tests for misspecification of multivariate GARCH models. The test has high power against alternatives where the misspecification is in the GARCH parameters and is superior to other tests. The test is not greatly affected by misspecification in the conditional correlations and is therefore well suited for considering misspecification of GARCH equations.

Testing constancy of unconditional variance in volatility models by misspecification and specification tests

Silvennoinen, A., Terasvirta, T. — Fri, 01 Jan 2016 10:37:10 +0100

The topic of this paper is testing the hypothesis of constant unconditional variance in GARCH models against the alternative that the unconditional variance changes deterministically over time. Tests of this hypothesis have previously been performed as misspecification tests after fitting a GARCH model to the original series. It is found by simulation that the positive size distortion present in these tests is a function of the kurtosis of the GARCH process. Adjusting the size by numerical methods is considered. The possibility of testing the constancy of the unconditional variance before fitting a GARCH model to the data is discussed. The power of the ensuing test is vastly superior to that of the misspecification test and the size distortion minimal. The test has reasonable power already in very short time series. It would thus serve as a test of constant variance in conditional mean models. An application to exchange rate returns is included.

Testing constancy of unconditional variance in volatility models by misspecification and specification tests

Silvennoinen, A., Terasvirta, T. — Tue, 27 Oct 2015 10:37:10 +0100

Specification and testing of Multiplicative Time-Varying GARCH models with applications

Amado, C., Teräsvirta, T. — Sun, 01 Jan 2017 10:37:10 +0100

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.

Forecasting macroeconomic variables using neural network models and three automated model selection techniques

Kock, A. B., Teräsvirta, T. — Fri, 01 Jan 2016 10:37:10 +0100

When forecasting with neural network models one faces several problems, all of which influence the accuracy of the forecasts. First, neural networks are often hard to estimate due to their highly nonlinear structure. To alleviate the problem, White (2006) presented a solution (QuickNet) that converts the specification and nonlinear estimation problem into a linear model selection and estimation problem. We shall compare its performance to that of two other procedures building on the linearization idea: the Marginal Bridge Estimator and Autometrics. Second, one must decide whether forecasting should be carried out recursively or directly. This choice is investigated in this work. The economic time series used in this study are the consumer price indices for the G7 and the Scandinavian countries. In addition, a number of simulations are carried out and results reported in the article.

A smooth transition logit model of the effects of deregulation in the electricity market

Hurn, A. S., Silvennoinen, A., Teräsvirta, T. — Fri, 01 Jan 2016 10:37:10 +0100

This paper introduces the smooth transition logit (STL) model that is designed to detect and model situations in which there is structural change in the behaviour underlying the latent index from which the binary dependent
variable is constructed. The maximum likelihood estimators of the parameters of the model are derived along with their asymptotic properties, together with a Lagrange multiplier test of the null hypothesis of linearity in the underlying latent index. The development of the STL model is motivated by the desire to assess the impact of deregulation in the Queensland electricity market and ascertain whether increased competition has resulted in significant changes in the behaviour of the spot price of electricity, specifically with respect to the occurrence of periodic abnormally high prices. The model allows the timing of any change to be endogenously determined and also market participants’ behaviour to change gradually over time. The main results provide clear evidence in support of a structural change in the nature of price events, and the endogenously determined timing of the change is consistent with the process of deregulation in Queensland.

A Smooth Transition Logit Model of the Effects of Deregulation in the Electricity Market

Hurn, A.S., Silvennoinen, A., Teräsvirta, T. — Fri, 28 Mar 2014 10:37:10 +0100

We consider a nonlinear vector model called the logistic vector smooth transition autoregressive model. The bivariate single-transition vector smooth transition regression model of Camacho (2004) is generalised to a multivariate and multitransition one. A modelling strategy consisting of specification, including testing linearity, estimation and evaluation of these models is constructed. Nonlinear least squares estimation of the parameters of the model is discussed. Evaluation by misspecification tests is carried out using tests derived in a companion paper. The use of the modelling strategy is illustrated by two applications. In the first one, the dynamic relationship between the US gasoline price and consumption is studied and possible asymmetries in it considered. The second application consists of modelling two well known Icelandic riverflow series, previously considered by many hydrologists and time series analysts.

Specification, Estimation and Evaluation of Vector Smooth Transition Autoregressive Models with Applications

Teräsvirta, T., Yang, Y. — Fri, 28 Mar 2014 10:37:10 +0100

Clive William John Granger 1934-2009

Hendry, D. F., Teräsvirta, T. — Tue, 01 Jan 2013 10:37:10 +0100

Linearity and Misspecification Tests for Vector Smooth Transition Regression Models

Teräsvirta, T., Yang, Y. — Mon, 17 Feb 2014 10:37:10 +0100

In this paper, we derive Lagrange multiplier and Lagrange multiplier type specification and misspecification tests for vector smooth transition models. We report results from simulation studies in which the size and power properties of the proposed tests in small samples are considered. The results show that these asymptotic tests generally suffer from size distortion. We find thatWilks’s lambda and Rao’s F statistic both have satisfactory size properties and can be recommended for empirical use. Bootstrapping the standard asymptotic LM statistic offers another solution to the problem.

A Lagrange Multiplier Test for Testing the Adequacy of the Constant Conditional Correlation GARCH Model

Catani, P., Teräsvirta, T., Yin, M. — Mon, 03 Feb 2014 10:37:10 +0100

A Lagrange multiplier test for testing the parametric structure of a constant conditional correlation generalized autoregressive conditional heteroskedasticity (CCC-GARCH) model is proposed. The test is based on decomposing the CCC-GARCH model multiplicatively into two components, one of which represents the null model, whereas the other one describes the misspeci…cation. A simulation study shows that the test has good …nite sample properties. We compare the test with other tests for misspeci…cation of multivariate GARCH models. The test has high power against alternatives where the misspeci…cation is in the GARCH parameters and is superior to other tests. The test is not greatly affected by misspeci…cation in the conditional correlations and is therefore well suited for considering misspeci…cation of GARCH equations.

Thresholds and smooth transitions in vector autoregressive models

Hubrich, K., Teräsvirta, T. — Tue, 01 Jan 2013 10:37:10 +0100

Book Review of "Dynamic Models for Volatility and Heavy Tails: with Applications to Financial and Economic Time Series" by Andrew C. Harvey

Teräsvirta, T. — Sun, 01 Dec 2013 10:37:10 +0100

Modelling changes in the unconditional variance of long stock return series

Amado, C., Teräsvirta, T. — Wed, 01 Jan 2014 10:37:10 +0100

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long daily return series. For this purpose we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2012, 2013). The latter component is modelled such that the unconditional time-varying component evolves slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to 22,986 daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the apparent long memory property in volatility may be interpreted as changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecasting accuracy of the new model over the GJR-GARCH model at all horizons for eight subsets of the long return series.

Conditional correlation models of autoregressive conditional heteroscedasticity with nonstationary GARCH equations

Amado, C., Teräsvirta, T. — Wed, 01 Jan 2014 10:37:10 +0100

Forecasting the Finnish Consumer Price Inflation Using Artificial Neural Network Models and Three Automated Model Selection Techniques

Kock, A. B., Teräsvirta, T. — Tue, 01 Jan 2013 10:37:10 +0100

Thresholds and Smooth Transitions in Vector Autoregressive Models

Hubrich, K., Teräsvirta, T. — Mon, 10 Jun 2013 10:37:10 +0200

This survey focuses on two families of nonlinear vector time series models, the family of Vector Threshold Regression models and that of Vector Smooth Transition Regression models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary Vector Threshold Regression and Vector Smooth Transition Regression models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

Modelling volatility by variance decomposition

Amado, C., Teräsvirta, T. — Tue, 01 Jan 2013 10:37:10 +0100

Unit Roots, Non-linearities, and Structural Breaks

Haldrup, N., Kruse, R., Teräsvirta, T., Varneskov, R. T. — Tue, 01 Jan 2013 10:37:10 +0100

Forecasting performances of three automated modelling techniques during the economic crisis 2007-2009

Kock, A. B., Teräsvirta, T. — Wed, 01 Jan 2014 10:37:10 +0100

In this work we consider the forecasting of macroeconomic variables during an economic crisis. The focus is on a specific class of models, the so-called single hidden-layer feed-forward autoregressive neural network models. What makes these models interesting in the present context is the fact that they form a class of universal approximators and may be expected to work well during exceptional periods such as major economic crises. Neural network models are often difficult to estimate, and we follow the idea of White (2006) of transforming the specification and nonlinear estimation problem into a linear model selection and estimation problem. To this end, we employ three automatic modelling devices. One of them is White’s QuickNet, but we also consider Autometrics, which is well known to time series econometricians, and the Marginal Bridge Estimator, which is better known to statisticians. The performances of these three model selectors are compared by looking at the accuracy of the forecasts of the estimated neural network models. We apply the neural network model and the three modelling techniques to monthly industrial production and unemployment series from the G7 countries and the four Scandinavian ones, and focus on forecasting during the economic crisis 2007–2009. The forecast accuracy is measured using the root mean square forecast error. Hypothesis testing is also used to compare the performances of the different techniques.

Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis

Holt, M. T., Teräsvirta, T. — Thu, 29 Nov 2012 10:37:10 +0100

This paper examines trends in annual temperature data for the northern and southern hemisphere (1850-2010) by using variants of the shifting-mean autoregressive (SM-AR) model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the so called QuickShift methodology. Full information maximum likelihood (FIML) estimates of a bivariate system of temperature equations are then obtained. The system is then used to perform formal tests of co-system in the hemispheric series. The results show there is evidence of co-shifting in the temperature data, most notably since the early 1980s.

Unit roots, nonlinearities and structural breaks

Haldrup, N., Kruse, R., Teräsvirta, T., Varneskov, R. T. — Tue, 24 Apr 2012 10:37:10 +0200

One of the most influential research fields in econometrics over the past decades concerns unit root testing in economic time series. In macro-economics much of the interest in the area originate from the fact that when unit roots are present, then shocks to the time series processes have a persistent effect with resulting policy implications. From a statistical perspective on the other hand, the presence of unit roots has dramatic implications for econometric model building, estimation, and inference in order to avoid the so-called spurious regression problem. The present paper provides a selective review of contributions to the field of unit root testing over the past three decades. We discuss the nature of stochastic and deterministic trend processes, including break processes, that are likely to affect unit root inference. A range of the most popular unit root tests are presented and their modifications to situations with breaks are discussed. We also review some results on unit root testing within the framework of non-linear processes.

Modeling conditional correlations of asset returns

Silvennoinen, A., Teräsvirta, T. — Thu, 01 Jan 2015 10:37:10 +0100

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to a predetermined or exogenous transition variable. An LM-test is derived to test the constancy of correlations and LM- and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the S&P 500 stock index completes the paper.