Jan G. De Gooijer

University of Amsterdam | UVA · Department of Economics

A test statistic for nonlinearity of a given heavy-tailed time series process is constructed, based on the sub-sample stability of Gini-based sample autocorrelations. The finite-sample performance of the proposed test is evaluated in a Monte Carlo study and compared to a similar test based on the sub-sample stability of a heavy-tailed analogue of t...

We propose a nonparametric method for estimating the conditional quantile function that admits a generalized additive specification with an unknown link function. This model nests single-index, additive, and multiplicative quantile regression models. Based on a full local linear polynomial expansion, we first obtain the asymptotic representation fo...

A general framework to devise portmanteau-type test statistics for a general class of multivariate nonlinear time series models with vector martingale difference errors is formulated. Based on this framework a suite of individual and mixed multivariate test statistics is considered. Two applications are developed: single- and multiple-lag test stat...

This study explores the multi-step ahead forecasting performance of a so-called hybrid conditional quantile method, which combines relevant conditional quantile forecasts from parametric and semiparametric methods. The focus is on lower (left) and upper (right) tail quantiles of the conditional distribution of the response variable. First, we evalu...

This paper addresses the problem of finding exact and explicit (closed-form) expressions for the stationary marginal distribution of threshold-type time series processes, their associated moments, autocovariance and autocorrelation coefficients. The innovation process of the models under consideration follows three central symmetric distribution fu...

A natural way to obtain conditional density estimates for time series processes is to adopt a kernel-based (nonparametric) conditional density estimation (KCDE) method. To this end, the data generating process is commonly assumed to be Markovian of finite order. Markov processes, however, have limited memory range so that only the most recent obser...

We propose the class of asymmetric vector moving average (asVMA) models. The asymmetry of these models is characterized by different MA filters applied to the components of vectors of lagged positive and negative innovations. This allows for a detailed investigation of the interrelationships among past model innovations of different sign. We derive...

For linear regression models, we propose and study a multi-step kernel density-based estimator that is adaptive to unknown error distributions. We establish asymptotic normality and almost sure convergence. An efficient EM algorithm is provided to implement the proposed estimator. We also compare its finite sample performance with five other adapti...

We propose a hybrid penalized averaging for combining parametric and non-parametric quan-tile forecasts when faced with a large number of predictors. This approach goes beyond the usual practice of combining conditional mean forecasts from parametric time series models with only a few predictors. The hybrid methodology adopts the adaptive LASSO reg...

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the "true" structure of the underlying conditional quantile function. In addition, we may have a large number of predictors. Mainly intended for such cases, we introduce a flexible and practical framework based on penalized high-dimensional quant...

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure usin...

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure usin...

Reliable forecasting methods increase the integration level of stochastic production and reduce cost of intermittence of photovoltaic production. This paper proposes a solar forecasting model for short time horizons, i.e. one to six hours ahead. In this time-range, machine learning methods have proven their efficiency. But their application require...

As we saw in Chapter 9, it is fairly straightforward to forecast future values of a time series process using semi- and nonparametric methods, given data up to a certain time t. In contrast, the situation becomes more complicated when real out-of-sample forecast are computed from parametric nonlinear time series models; in particular, as we explain...

Time-reversibility (TR) amounts to temporal symmetry in the probabilistic structure of a strictly stationary time series process. In other words, a stochastic process is said to be TR if its probabilistic structure is unaffected by reversing (“mirroring”) the direction of time. Otherwise, the process is said to be time-irreversible, or non-reversib...

Time-domain linearity test statistics are parametric; that is, they test the null hypothesis that a time series is generated by a linear process against a pre-chosen particular nonlinear alternative. Using the classical theory of statistical hypothesis testing, time-domain test nonlinearity tests can be based on three principles – the likelihood ra...

Quite often it is not possible to postulate an appropriate parametric form for the DGP under study. In such cases, semi- and nonparametric methods are called for. Certain of these methods introduced in Chapter 9 can be easily extended to the multivariate (vector) framework. Specifically, let \(Y_t\;=\;(Y_{1,t},\ldots,Y_{m,t})\prime\) denote an m-di...

In this chapter, we extend the univariate nonlinear parametric time series framework to encompass multiple, related time series exhibiting nonlinear behavior. Over the past few years, many multivariate (vector) nonlinear time series models have been proposed. Some of them are “ad - hoc”, with a special application in mind. Others are direct multiva...

The time series methods we have discussed so far can be loosely classified as parametric (see, e.g., Chapter 5), and semi- and nonparametric (see, e.g., Chapter 7). For the parametric methods, usually a quite flexible but well-structured family of finitedimensional models are considered (Chapter 2), and the modeling process typically consists of th...

Model estimation, selection, and diagnostic checking are three interwoven components of time series analysis. If, within a specified class of nonlinear models, a particular linearity test statistics indicates that the DGP underlying an observed time series is indeed a nonlinear process, one would ideally like to be able to select the correct lag st...

From the previous two chapters we have seen that the richness of nonlinear models is fascinating: they can handle various nonlinear phenomena met in practice. However, before selecting a particular nonlinear model we need tools to fully understand the probabilistic and statistical characteristics of the underlying DGP. For instance, precise informa...

The specification and estimation of a nonlinear model may be difficult in practice and sometimes no substantial improvements in forecasting accuracy can be achieved by using a nonlinear model instead of a familiar ARMA model. Therefore, one may wish to start the model building from a linear model and abandon it only if sufficiently strong evidence...

Testing for randomness of a given finite time series is one of the basic problems of statistical analysis. For instance, in many time series models the noise process is assumed to consist of i.i.d. random variables, and this hypothesis should be testable. Also, it is the first issue that gets raised when checking the adequacy of a fitted time serie...

Informally, a time series is a record of a fluctuating quantity observed over time that has resulted from some underlying phenomenon. The set of times at which observations are measured can be equally spaced. In that case, the resulting series is called discrete. Continuous time series, on the other hand, are obtained when observations are taken co...

In Section 1.1, we discussed in some detail the distinction between linear and nonlinear time series processes. In order to make this distinction as clear as possible, we introduce in this chapter a number of classic parametric univariate nonlinear models. By “classic” we mean that during the relatively brief history of nonlinear time series analys...

This book provides an overview of the current stat-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a "theorem-proof" format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time seri...

We propose two non parametric portmanteau test statistics for serial dependence in high dimensions using the correlation integral. One test depends on a cutoff threshold value, while the other test is freed of this dependence. Although these tests may each be viewed as variants of the classical Brock, Dechert, and Scheinkman (BDS) test statistic, t...

In classical Bayesian inference the prior is treated as fixed and its effects are ignored asymptotically, and useful information, if any, is wasted. However, in practice often an informative prior is summarized from previous similar or the same kind of studies, which contains useful cumulative information for the current study. We treat such prior...

The paper suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks and exogenous variables. The model is employed to study the three closely related Baltic States’ stock exchanges and the influence exerted by the Russi...

The paper suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks and exogenous variables. The model is employed to study the three closely related Baltic States’ stock exchanges and the influence exerted by the Russi...

This paper describes a forecasting exercise of close-to-open returns on major global stock indices, based on price patterns from foreign markets that have become available overnight. As the close-to-open gap is a scalar response variable to a functional variable, it is natural to focus on functional data analysis. Both parametric and non-parametric...

Socio-economic variables are often measured on a discrete scale or rounded to protect confidentiality. Nevertheless, when exploring the effect of a relevant covariate on the outcome distribution of a discrete response variable, virtually all common quantile regression methods require the distribution of the covariate to be continuous. This paper de...

In classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of studies, which contains non-negligible information for...

  In this paper, two non-parametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a more viable alternative to existing kernel-based approaches. The second estimator involves sequential fitting by univariate local po...

Item response theory is one of the modern test theory with many applications in the educational and psychological testing field. Recent developments made it possible to characterize some desired latent properties in terms of a collection of manifest ones, so that hypothesis tests on these latent traits can, in principle, be performed. But the exist...

Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is bas...

Under the condition that the observations, which come from a high-dimensional population (X, Y), are strongly stationary and strongly mixing, through using the local linear method, we investigate in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg min a𝔼(ρ (a, Y)|X=x), where the loss f...

In this paper two kernel-based nonparametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a viable alternative to the method of De Gooijer and Zerom (2003). With the aim to reduce variance of the first estimator, a...

We study the problem of selecting the optimal functional form among a set of non-nested nonlinear mean functions for a semiparametric kernel based regression model. To this end we consider Rissanen's minimum description length (MDL) principle. We prove the consistency of the proposed MDL criterion. Its performance is examined via simulated data set...

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987–2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time...

Partial sums of lagged cross-products of AR residuals are defined. By studying the sample paths of these statistics, changes in residual dependence can be detected that might be missed by statistics using only the total sum of cross-products. Also, a test statistic for white noise is proposed. It is shown that the limiting distribution of the test...

In this paper the use of three kernel-based nonparametric forecasting methods - the conditional mean, the conditional median, and the conditional mode -is explored in detail. Several issues related to the estimation of these methods are discussed, including the choice of the bandwidth and the type of kernel function. The out-of-sample forecasting p...

Motivated by Chaudhuri's work [1996. On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91, 862–872] on unconditional geometric quantiles, we explore the asymptotic properties of sample geometric conditional quantiles, defined through kernel functions, in high-dimensional spaces. We establish a Bahadur-type linear re...

We compare and investigate Neyman's smooth test, its components, and the Kolmogorov-Smirnov (KS) goodness-of-fit test for testing the uniformity of multivariate forecast densities. Simulations indicate that the KS test lacks power when the forecast distributions are misspecified, especially for correlated sequences of random variables. Neyman's smo...

We propose and study a class of regression models, in which the mean function is specified parametrically as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric reg...

An affine equivariant version of the nonparametric spatial conditional median (SCM) is constructed, using an adaptive transformation–retransformation (TR) procedure. The relative performance of SCM estimates, computed with and without applying the TR-procedure, are compared through simulations. Also included is the vector of coordinate conditional,...

The paper suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks and an outside stock exchange. Using daily data 2000-2006 for the Baltic state stock exchanges and that of Moscow we find recursive structures with Riga...

We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982–1985 and International Journal of Forecasting 1985–2005). During this period, over one third of all papers publish...

A general test statistic for detecting change-points in multidimensional stochastic processes with unknown parameters is proposed. The test statistic is specialized to the case of detecting changes in sequences of covariance matrices. Large-sample distributional results are presented for the test statistic under the null hypothesis of no-change. Th...

Under the condition that the observations, which come from a high-dimensional population ( X,Y ), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M -estimator for the unknown function m(x) =arg min<SUB>a</SUB> IE( r (a,Y) | X=x)...

Using simulations, the paper shows that there is a trade-off in using CLS and 2SLS on the one hand and ML on the other when estimating the parameters of a bivariate threshold vector equilibrium correction model with regime-specific cointegration vectors.

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We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also revi...

Motivated by Chaudhuri's work (1996) on unconditional geometric quantiles, we explore the asymptotic properties of sample geometric conditional quantiles, defined through kernel functions, in high dimensional spaces. We establish a Bahadur type linear representation for the geometric conditional quantile estimator and obtain the convergence rate fo...

We propose a nonlinear time series model where both the conditional mean and the conditional variance are asymmetric functions of past information. The model is particularly useful for analysing financial time series where it has been noted that there is an asymmetric impact of good news and bad news on volatility (risk) transmission. We introduce...

We introduce a nonparametric quantile predictor for multivariate time series via generalizing the well-known univariate conditional quantile into a multivariate setting for dependent data. Applying the multivariate predictor to predicting tail conditional quantiles from foreign exchange daily returns, it is observed that the accuracy of extreme tai...

The cointegration literature suggests that forecast errors may be reduced by incorporating the knowledge of cointegrating relationships into linear models to generate forecasts. We show that the long-term (one- to sixty-steps ahead) forecasting performance can further be enhanced by applying nonlinear equilibrium correction models. In particular, w...

A modified multivariate adaptive regression splines method for modeling vector nonlinear time series is investigated. The method results in models that can capture certain types of vector self-exciting threshold autoregressive behavior, as well as provide good predictions for more general vector nonlinear time series. The effect of different model...

We investigate the estimation of the conditional quantile when many covariates are involved. In particular, we model the conditional quantile of a response as a nonlinear additive function of relevant covariates. For this setup, we propose a nonparametric smoother to estimate the unknown functions. The estimator provides direct computation of the n...

With the aim to mitigate the possible problem of negativity in the estimation of the conditional density function, we introduce a so-called re-weighted Nadaraya-Watson (RNW) estimator. The proposed RNW estimator is constructed by a slight modification of the well-known Nadaraya-Watson smoother. Because the estimator is explicitly defined in terms o...

The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynamic dependence on the level of the series and seaso...

GRASP is a Greedy Randomised Adaptive Sampling Procedure that has been proposed to estimate parameters of self-exciting autoregressive threshold models (SETARs) with mul-tivariate thresholds. We show that the GRASP procedure can often lead to an incorrect number of thresholds when estimating SETARs. Two simple modifications of the original GRASP pr...

We propose a kernel-based multi-stage conditional median predictor for α-mixing time series of Markovian structure. Mean squared error properties of single-stage and multi-stage conditional medians are derived and discussed.

Motivated by the problem of setting prediction intervals in time series analysis, this investigation is concerned with recovering a regression function m(X_{t}) on the basis of noisy observations taking at random design points X_{t}. It is presumed that the corresponding observations are corrupted by additive serially correlated noise and that the...

We present a multi-stage conditional quantile predictor for time series of Markovian structure. It is proved that at any quantile level, p 2 ð0, 1Þ, the asymptotic mean squared error (MSE) of the new predictor is smaller than the single-stage conditional quantile predictor. A simulation study confirms this result in a small sample situation. Becaus...

In this paper the class of discrete self-exciting threshold moving-average (SETMA) models is studied in some detail. In particular, we consider various problems associated with the identification, estimation and testing of these models. A simple method for distinguishing between low order moving average (MA) and low order SETMA models is presented....

This paper studies the problem of detecting multiple changes at unknown times in the mean level of elision in the trimeter sequences of the Orestes, a play written by the Ancient Greek dramatist Euripides (485-406 B.C.). Change-detection statistics proposed by MacNeill (1978) and Jandhayala and MacNeill (1991) are adopted for this purpose. Analysis...

Three cross-validation criteria, denoted by respectively C, Cc, and Cu, are proposed for selecting the orders of a self-exciting threshold autoregressive (SETAR) model when both the delay and the threshold value are unknown. The derivation of C is within a natural cross-validation framework. The criterion Cc is similar in spirit as AICc, a bias-cor...

In this paper, we present a new time series model, which describes self-exciting threshold autoregressive (SETAR) nonlinearity and seasonality simultaneously. The model is termed multiplicative seasonal SETAR (SEASETAR). It can be viewed as a special case of a general non-multiplicative SETAR model by imposing certain restrictions on the parameters...

The asymmetric moving average model (asMA) is extended to allow for asymmetric quadratic conditional heteroskedasticity (asQGARCH). The asymmetric parametrization of the conditional variance encompasses the quadratic GARCH model of Sentana (1995). We introduce a framework for testing asymmetries in the conditional mean and the conditional variance,...