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.     

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.     

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 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.     

The asymmetry of judgemental confidence intervals in time series forecasting

In forecasting a time series, one may be asked to communicate the likely distribution of the future actual value, often expressed as a confidence interval. Whilst the accuracy (calibration) of these intervals has dominated most studies to date, this paper is concerned with other possible characteristics of the intervals. It reports a study in which the prevalence and determinants of the symmetry of judgemental confidence intervals in time series forecasting was examined. Most prior work has assumed that this interval is symmetrically placed around the forecast. However, this study shows that people generally estimate asymmetric confidence intervals where the forecast is not the midpoint of the estimated interval. Many of these intervals are grossly asymmetric. Results indicate that the placement of the forecast in relation to the last actual value of a time series is a major determinant of the direction and size of the asymmetry.     

Comments on “An analysis of the international tourism demand in Spain” by P. González and P. Moral

Although the state-space, unobserved component approach to forecasting has many advantages, it must be applied carefully in practice and should not be used in an uncritical, ‘black box’ fashion. In particular, such an approach to the modelling and forecasting of Spanish tourism data is inappropriate and leads to misleading conclusions, particularly in relation to the uncritical selection and use of explanatory regression variables.     

A two–stage approach to additive time series models

For nonlinear additive time series models, an appealing approach used in the literature to estimate the nonparametric additive components is the projection method. In this paper, it is demonstrated that the projection method might not be efficient in an asymptotic sense. To estimate additive components efficiently, a two–stage approach is proposed together with a local linear fitting and a new bandwidth selector based on the nonparametric version of the Akaike information criterion. It is shown that the two–stage method not only achieves efficiency but also makes bandwidth selection relatively easier. Also, the asymptotic normality of the resulting estimator is established. A small simulation study is carried out to illustrate the proposed methodology and the two–stage approach is applied to a real example from econometrics.     

Production technologies in stochastic continuous time models

Properties of dynamic stochastic general equilibrium models can be revealed by either using numerical solutions or qualitative analysis. Very precise and intuition-building results are obtained by working with models which provide closed-form solutions. Closed-form solutions are known for a large class of models some of which, however, have some undesirable features such as potentially negative output. This paper offers closed-form solutions for models which are just as tractable but do not suffer from these shortcomings.     

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     

When was the U.S. housing downturn predictable? A comparison of univariate forecasting methods

This paper uses three classes of univariate time series techniques (ARIMA type models, switching regression models, and state-space/structural time series models) to forecast, on an ex post basis, the downturn in U.S. housing prices starting around 2006. The performance of the techniques is compared within each class and across classes by out-of-sample forecasts for a number of different forecast points prior to and during the downturn. Most forecasting models are able to predict a downturn in future home prices by mid 2006. Some state-space models can predict an impending downturn as early as June 2005. State-space/structural time series models tend to produce the most accurate forecasts, although they are not necessarily the models with the best in-sample fit.     

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.     

Testing of unit root and other nonstationary hypotheses in macroeconomic time series

Recently proposed tests for unit root and other nonstationarity of Robinson (1994a) are applied to an extended version of the data set used by Nelson and Plosser (1982). Unusually, the tests are efficient (against appropriate parametric alternatives), the null can be any member of the I(d) class, and the null limit distribution is chi-squared. The conclusions vary substantially across the 14 series, and across different models for the disturbances (which, also unusually, include the Bloomfield spectral model). Overall, the consumer price index and money stock seem the most nonstationary, while industrial production and unemployment rate seem the closest to stationarity.     

Detecting shocks: Outliers and breaks in time series

A single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares. An equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question. Similarly, for unobserved components or structural time-series models, the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter, such as trend or level changes. Because such time-series models contain more than one variance, the effect of the intervention is measured by the change in individual variances.We examine the effect on the estimated parameters of moving various kinds of intervention along the series. The horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing. Interpretation of the resulting time-series plots of diagnostics is aided by simulation envelopes.Our procedures, illustrated with four example, permit keen insights into the fragility of inferences to specific shocks, such as outliers and level breaks. Although the emphasis is mostly on parameter estimation, forecast are also considered. Possible extensions include seasonal adjustment and detrending of series.     

Forecasting the New York State economy: The coincident and leading indicators approach

Currently there are no reliable summary indicators of the economic and fiscal condition of states and localities. This deficiency has hampered the efforts of policy makers at the sub-national level to monitor changes in the economic environment and predict how those changes will impact the fiscal health of governments. This paper attempts to fill this analytical vacuum by providing summary indicators of economic and fiscal health for New York State. The models developed are based on the single-index methodology developed by Stock and Watson [(1991). A probability model of the coincident economic indicators. In K. Lahiri and G. H. Moore (eds.), Leading economic indicators: new approaches and forecasting records (pp. 63–85). New York: Cambridge University Press]. This approach allows us to date New York business cycles and compare local cyclical behavior with the nation as a whole. We develop a leading index of economic indicators which predicts future movements in the coincident indicator. The Stock and Watson approach is used to create a fiscal indicator which acts as a summary indicator of revenue performance for New York. In addition, we explore the ability of our economic indicator series to predict future changes in state revenues. We find that changes in the leading indicator series have significant predictive power in forecasting changes in our revenue index.     

Equilibria in the spatial stochastic model of voting with party activists

Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. Empirical analyses discussed in this paper suggest that convergence of this kind is rarely observed. Here we examine a stochastic electoral model where parties differ in their valences – the electorally perceived, non-policy “quality” of the party leader. It is assumed that valence may either be exogenous, in the sense of being an intrinsic characteristic of the leader, or may be due to the contributions of party activists, who donate time and money and thus enhance electoral support for the party. Theorem 1 shows that vote maximization depends on balancing these two opposed effects. Theorem 2 provides the necessary and sufficient conditions for convergence to the electoral mean when activist valence is zero. The paper then examines empirical electoral models for the Netherlands circa 1980 and Britain in 1979, 1992 and 1997 and shows that party divergence from the electoral mean cannot be accounted for by exogenous valence alone. The balance condition suggests that the success of the Labour party in the election of 1997 can be attributed to a combination of high exogenous valence and pro-Europe activist support.     

Signal Extraction Problems in Seismology*

The earth's surface is under continuous influence of a variety of natural forces such as the effect of past earthquakes, wave, wind, tide, air pressure, precipitation and a variety of human induced sources. Since it is almost impossible to describe the response to these noise inputs precisely, for automatic processing of seismic data, proper statistical modeling is necessary. In this paper, we describe four specific examples of time series modeling for signal extraction problems related to seismology. Namely, we consider 1) the estimation of the arrival time of a seismic signal, 2) the extraction of small seismic signal from noisy data, 3) the detection of the coseismic effect in groundwater level data contaminated by various effects from air pressure etc., and 4) the estimation of changing spectral characteristic of seismic record.     

Extracting a common stochastic trend: Theory with some applications

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models—those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models we explicitly consider comprise a special–yet useful–class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.