Estimating the codifference function of linear time series models with infinite variance

We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetric α-stable innovations, 0 < α ≤ 2. In addition, we derive their limiting distribution. We present a simulation study showing the dependence of the estimator on certain design parameters. Finally, we provide an empirical example using some stocks from Indonesia Stock Exchange.     

Forecasting tourist arrivals using time-varying parameter structural time series models

Empirical evidence has shown that seasonal patterns of tourism demand and the effects of various influencing factors on this demand tend to change over time. To forecast future tourism demand accurately requires appropriate modelling of these changes. Based on the structural time series model (STSM) and the time-varying parameter (TVP) regression approach, this study develops the causal STSM further by introducing TVP estimation of the explanatory variable coefficients, and therefore combines the merits of the STSM and TVP models. This new model, the TVP-STSM, is employed for modelling and forecasting quarterly tourist arrivals to Hong Kong from four key source markets: China, South Korea, the UK and the USA. The empirical results show that the TVP-STSM outperforms all seven competitors, including the basic and causal STSMs and the TVP model for one- to four-quarter-ahead ex post forecasts and one-quarter-ahead ex ante forecasts.     

Bayesian inference in time series models using kernel quasi likelihoods

The paper takes up Bayesian inference in time series models when essentially nothing is known about the distribution of the dependent variable given past realizations or other covariates. It proposes the use of kernel quasi likelihoods upon which formal inference can be based. Gibbs sampling with data augmentation is used to perform the computations related to numerical Bayesian analysis of the model. The method is illustrated with artificial and real data sets.     

Estimating the commuting cost and commuting time property price gradients

In this paper, we estimate the property price gradients in Hong Kong. We distinguish our effort from previous studies on the subject by directly measuring the economic distance, i.e., the monetary commuting cost and commuting time, instead of merely the physical distance. Our results are generally supportive of the prediction of a negative property price gradient. In one specification, the estimated capitalization of the savings of commuting cost in property prices appears to be just right. The expected negative effect of commuting time on property values, however, can only be detected among observations with larger commuting times. Nevertheless, over the range where the effect of commuting time has the expected negative sign, the values of time implied by the estimates agree well with the results reported in the transportation economics literature.     

Forecasting economic time series using score-driven dynamic models with mixed-data sampling

We introduce a mixed-frequency score-driven dynamic model for multiple time series where the score contributions from high-frequency variables are transformed by means of a mixed-data sampling weighting scheme. The resulting dynamic model delivers a flexible and easy-to-implement framework for the forecasting of low-frequency time series variables through the use of timely information from high-frequency variables. We verify the in-sample and out-of-sample performances of the model in an empirical study on the forecasting of U.S. headline inflation and GDP growth. In particular, we forecast monthly headline inflation using daily oil prices and quarterly GDP growth using a measure of financial risk. The forecasting results and other findings are promising. Our proposed score-driven dynamic model with mixed-data sampling weighting outperforms competing models in terms of both point and density forecasts.     

Estimation of copula-based semiparametric time series models

This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric marginal distributions and parametric copula functions, while the copulas capture all the scale-free temporal dependence of the processes. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. These results are used to obtain root-n consistent and asymptotically normal estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles. The semiparametric conditional quantile estimators are automatically monotonic across quantiles, which is attractive for portfolio conditional value-at-risk calculations.     

Distribution-free tests for time series models specification

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box–Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.     

Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models

In this paper we review an approach to estimating the causal effect of a time-varying treatment on time to some event of interest. This approach is designed for a situation where the treatment may have been repeatedly adapted to patient characteristics, which themselves may also be time-dependent. In this situation the effect of the treatment cannot simply be estimated by conditioning on the patient characteristics, as these may themselves be indicators of the treatment effect. This so-called time-dependent confounding is typical in observational studies. We discuss a new class of failure time models, structural nested failure time models, which can be used to estimate the causal effect of a time-varying treatment, and present methods for estimating and testing the parameters of these models.     

Distributed ARIMA models for ultra-long time series

Providing forecasts for ultra-long time series plays a vital role in various activities, such as investment decisions, industrial production arrangements, and farm management. This paper develops a novel distributed forecasting framework to tackle the challenges of forecasting ultra-long time series using the industry-standard MapReduce framework. The proposed model combination approach retains the local time dependency. It utilizes a straightforward splitting across samples to facilitate distributed forecasting by combining the local estimators of time series models delivered from worker nodes and minimizing a global loss function. Instead of unrealistically assuming the data generating process (DGP) of an ultra-long time series stays invariant, we only make assumptions on the DGP of subseries spanning shorter time periods. We investigate the performance of the proposed approach with AutoRegressive Integrated Moving Average (ARIMA) models using the real data application as well as numerical simulations. Our approach improves forecasting accuracy and computational efficiency in point forecasts and prediction intervals, especially for longer forecast horizons, compared to directly fitting the whole data with ARIMA models. Moreover, we explore some potential factors that may affect the forecasting performance of our approach.     

Functional-coefficient models for nonstationary time series data

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean squared error. When the coefficient function is a function of a nonstationary variable, the new findings are that the asymptotic bias of its nonparametric estimator is the same as the stationary covariate case but convergence rate differs, and further, the asymptotic distribution is a mixed normal, associated with the local time of a standard Brownian motion. The asymptotic behavior at boundaries is also investigated.     

Forecasting football match results in national league competitions using score-driven time series models

We develop a new dynamic multivariate model for the analysis and forecasting of football match results in national league competitions. The proposed dynamic model is based on the score of the predictive observation mass function for a high-dimensional panel of weekly match results. Our main interest is in forecasting whether the match result is a win, a loss or a draw for each team. The dynamic model for delivering such forecasts can be based on three different dependent variables: the pairwise count of the number of goals, the difference between the numbers of goals, or the category of the match result (win, loss, draw). The different dependent variables require different distributional assumptions. Furthermore, different dynamic model specifications can be considered for generating the forecasts. We investigate empirically which dependent variable and which dynamic model specification yield the best forecasting results. We validate the precision of the resulting forecasts and the success of the forecasts in a betting simulation in an extensive forecasting study for match results from six large European football competitions. Finally, we conclude that the dynamic model for pairwise counts delivers the most precise forecasts while the dynamic model for the difference between counts is most successful for betting, but that both outperform benchmark and other competing models.     

Forecasting the NN5 time series with hybrid models

We propose a simple way of predicting time series with recurring seasonal periods. Missing values of the time series are estimated and interpolated in a preprocessing step. We combine several forecasting methods by taking the weighted mean of forecasts that were generated with time-domain models which were validated on left-out parts of the time series. The hybrid model is a combination of a neural network ensemble, an ensemble of nearest trajectory models and a model for the 7-day cycle. We apply this approach to the NN5 time series competition data set.     

Estimating yield spreads volatility using GARCH-type models

The primary focus of this study is on modeling the relationship between the volatility of corporate bond yield spreads and other covariates, including interest rate volatility, equity volatility, and rating. The purpose of this article is to apply various GARCH models to estimate the volatility of corporate bond yield spreads. This attempt is, to the best of our knowledge, the first to analyze the volatility of the yield spreads. In particular, this study utilizes standard GARCH and various asymmetric GARCH models, including E-GARCH, T-GARCH, P-GARCH, Q-GARCH, and I-GARCH models. We select the best fitting models for the noncallable (callable) case based on AIC, and it turns out Q-GARCH (T-GARCH) is the best fitting model. The estimation results indicate that our explanatory variables are statistically significant even at the 1% significance level when we apply the best fitting models. They are generally consistent, but we observe the presence of apparent differences. Our findings should be beneficial to practitioners, including investors.     

Graphical interaction models for multivariate time series1

In this paper we extend the concept of graphical models for multivariate data to multivariate time series. We define a partial correlation graph for time series and use the partial spectral coherence between two components given the remaining components to identify the edges of the graph. As an example we consider multivariate autoregressive processes. The method is applied to air pollution data. Received: June 1999     

Fully Bayesian analysis of ARMA time series models

Statistical analysis of autoregressive-moving average (ARMA) models is an important non-standard problem. No classical approach is widely accepted; legitimacy for most classical approaches is based solely on asymptotic grounds, while small sample sizes are common. The only obstacle to the Bayesian approach are designing a structure through which prior information can be incorporated and designing a practical computational method. The objective of this work is to overcome these two obstacles. In addition to the standard results, the Bayesian approach gives a different method of determining the order of the ARMA model, that is (p, q).     

Kernel-weighted GMM estimators for linear time series models

This paper analyzes the higher-order asymptotic properties of generalized method of moments (GMM) estimators for linear time series models using many lags as instruments. A data-dependent moment selection method based on minimizing the approximate mean squared error is developed. In addition, a new version of the GMM estimator based on kernel-weighted moment conditions is proposed. It is shown that kernel-weighted GMM estimators can reduce the asymptotic bias compared to standard GMM estimators. Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments. A feasible procedure similar to optimal bandwidth selection is proposed for the kernel-weighted GMM estimator.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Bayesian inference for nonlinear structural time series models

We consider efficient methods for likelihood inference applied to structural models. In particular, we introduce a particle filter method which concentrates upon disturbances in the Markov state of the approximating solution to the structural model. A particular feature of such models is that the conditional distribution of interest for the disturbances is often multimodal. We provide a fast and effective method for approximating such distributions. We estimate a neoclassical growth model using this approach. An asset pricing model with persistent habits is also considered. The methodology we employ allows many fewer particles to be used than alternative procedures for a given precision.