Performance of periodic time series models in forecasting

The paper provides a comparison of alternative univariate time series models that are advocated for the analysis of seasonal data. Consumption and income series from (West-) Germany, United Kingdom, Japan and Sweden are investigated. The performance of competing models in forecasting is used to assess the adequacy of a specific model. To account for nonstationarity first and annual differences of the series are investigated. In addition, time series models assuming periodic integration are evaluated. To describe the stationary dynamics (standard) time invariant parametrizations are compared with periodic time series models conditioning the data generating process on the season. Periodic models improve the in-sample fit considerably but in most cases under study this model class involves a loss in ex-ante forecasting relative to nonperiodic models. Inference on unit-roots indicates that the nonstationary characteristics of consumption and income data may differ. For German and Swedish data forecasting exercises yield a unique recommendation of unit roots in consumption and income data which is an important (initial) result for multivariate analysis. Time series models assuming periodic integration are parsimonious to specify but often involve correlated one-step-ahead forecast errors. First version received: April 1996/final version received: January 1998     

Multivariate time series models for Austrian interest rates

Zusammenfassung Fünf monatliche österreichische Zinszeitreihen, die Habenzinsen, die Sollzinsen sowie die Zinssätze für Dreimonatsgelder, der täglich fälligen Gelder und der Anleihen (i. w. S.) werden für den Zeitraum 1972 bis 1980 mit Hilfe multivariater (oder vektor-)autoregressiver (AR) Prozesse untersucht.Nachdem die Zeitreihen mittels der Methode vonKitagawa-Akaike (1982) auf Ausreißer geprüft und korrigiert wurden, zeigt sich, daß die korrigierte Zeitreihe der Sollzinsen bessere Prognoseeigenschaften erzielt. Obwohl die Stationaritätsvoraussetzungen für alle Zeitreihen etwas problematisch sind, bringen auch einfache Transformationen wie Differenzenbildung keine Hilfe bezüglich Stationarität. Die Schätzung eines simultanen fünfdimensionalen AR-Prozesses allerZinsreihen ergibt, daß ein Aufbrechen dieses Systems in zwei Blöcke das beste Resultat im Sinne des InformationskriteriumsAIC ergibt. Der erste Block wird durch die Habenzinsen und die (korrigierten) Sollzinsen gebildet, die eine wechselseitige Dynamik bis zum Lag 2 aufweisen. Der zweite Block wird durch die Zinssätze für Dreimonatsgelder, täglich fällige Gelder und Anleihen gebildet. Als Nebenprodukt dieser multivariaten Zeitreihenanalyse können temporale Kausalitäts- (oder Feedback-)maße berechnet werden. Es wird jedoch gezeigt, daß das Zusammenwirken von bestimmten Schätzprozeduren mit dem InformationskriteriumAIC die Schätzung dieser Kausalitätsmaße nicht immer ermöglicht. Allgemein läßt sich sagen, daß die instantane Kausalität in den Modellen dominiert, was teilweise durch nichtstationäre Einflüsse und Ausreißer erklärt werden kann.     

The effects of small sample bias in Threshold Autoregressive models

This paper investigates Threshold Autoregressive (TAR) models that contain a limited number of observations in some regimes. Simulations show that within the context of the real exchange rate literature, parameter estimates exhibit significant small sample bias even with long time series data. These distortions create substantial power losses in attempting to identify values of coefficients from data.     

Adaptivity and stability of time series models

The effect of interventions on economic variables in the presence of a time dependent noise structure is modelled in this paper. Forecasts from such models are derived and it is disscussed whether forecasts from ARIMA time series models are adaptive with respect to interventions such as changes in the level or outliers.An overall criterion to test the stability of the parameters in ARIMA models is derived and applied to three Austrian macroeconomic sequences.

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Zusammenfassung Bei der Schätzung und vorhersage von ökonomischen Zeitreihen werden in der Regel konstante Parameter unterstellt. In dieser Arbeit werden verschiedene Aspekte dieser Annahme untersucht.Zuerst werden Modelle beschrieben, durch die die Wirkung von Interventionen auf ökonomische Zeitreihen dargestellt werden kann. Es wird mit Hilfe dieser Modelle untersucht, in wie weit die Vorhersagen von ARIMA Zeitreihenmodellen gegenüber Interventionen (wie Ausreißer und Änderungen im Niveau) adaptiv sind. Ferner wird ein statistisches Kriterium abgeleitet, das die Stabilität der Parameter in ARIMA Zeitreihenmodellen testet. Dieser Test wird an Hand von drei ökonomischen Reihen beschrieben. Es wird gezeigt, daß sich die Parameter in den mit Daten bis 1974/3 geschätzten Zeitreihenmodellen für privaten Konsum und Brutto-Anlageinvestitionen über die folgenden 9 Quartale nich geändert haben. Für das Brutto-Nationalprodukt kann die Annahme konstanter Parameter verworfen werden. Die Vorhersagefehler der letzten 9 Quartale ermöglichen es jedoch, ein einfaches Interventionsmodell zu spezifizieren.

     

Out-of-sample forecasting of the Canadian unemployment rates using univariate models

This article investigates the out-of-sample forecasting performance of some linear and nonlinear univariate time series models on the monthly seasonally adjusted Canadian unemployment rates during the 1980–2013 period. The findings reveal that nonlinear time series models better capture the asymmetry present in the unemployment rate series at short and long forecast horizons.     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

Estimating time-dependent means in dynamic models for cross-sections of time series

This paper considers a dynamic extension of the classical error components model based on the ideas of structural time series models. The study concentrates on the mean square error estimation of time-dependent means by using the Kalman filter, and on the relative efficiency of these estimators as a function of both the number of observations across units and time.     

Signs of impact effects in time series regression models

In this paper we consider the problem of interpreting the signs of the estimated coefficients in multivariate time series regressions where the regressors are correlated. Using a continuous time model, we argue that focusing on the signs of individual coefficients in such regressions could be misleading and argue in favour of allowing for the indirect effects that arise due to the historical correlations amongst the regressors. For estimation from discrete time data we show that the sign of the total impact, including the direct and indirect effects, of a regressor can be obtained using a simple regression that only includes the regressor of interest.     

Estimating leisure goods models on time series of cross sections

This paper analyses the joint modelling of labour supply and consumer expenditure in a utility maximizing framework. A recent demand system (AIDS) is augmented to include labour supply and incorporate time series/cross section wage rate variation and, then, estimated on pooled F.E.S. data [Family Expenditure Surveys]. A method of non linear FIML is applied. The paper questions the near unanimous ‘evidence’ on backward bending labour supply in previous studies and, using counter evidence, argues that such a bend could have been partly due to the restrictive utility forms usually employed. In addition, hypotheses relating to effects of price/wage movements on composition of ‘full income’ are tested, and the welfare implications of the estimated parameter estimates worked out.     

Calendar effects in structural time series models with trend and season

Calendar effects are analysed in the class of structural time series models one of the two main model based approaches in time series decomposition. While Bell and Hillmer (1983) modeled calendar variation in the ARIMA model based approach, we represent structural models in the generalized regression form which allows to apply classical estimation and test procedures. It turns out that the expected high computaional complexity 0(T ³) in the generalized regression model can be reduced to 0(T). As all parameters are estimated by maximizing the likelihood the Likelihood Ratio statistics can be used to test effects of the calendar composition.     

Unemployment and growth: some empirical evidence from structural time series models

This study investigates the empirical relationship between unemployment and growth in a number of OECD economies. A structural time series model is used for labour productivity growth to demonstrate that, in most economies, there seems to be a negative correlation between unemployment and labour productivity growth. The results provide little support for the theory that recessions may stimulate productivity growth. The use of a structural time series approach allows an attempt to model the underlying dynamics of productivity growth jointly with the effect of unemployment.     

A new methodology for the logistic analysis of evolutionary S-shaped processes: Application to historical time series and forecasting

A new multi-logistic methodology to analyze long range time series of evolutionary S-shaped processes is presented. It conceptually innovates over the traditional logistic approach. The ansatz includes computing the residuals to an optimized multi-logistic trend curve least squares fitted to the time-series data. The elements of the residuals series are checked for autocorrelations and once detected the residuals series is further analyzed to search for eventual presence of underlying periodic structures using a truncated Fourier sine series. The method foundations ensures both a universal applicability and a capacity to disclose the existence of active clocks that can be possibly traced to the driving motors of the evolutionary character of the time series, due to the responsiveness of corresponding process to the development of economic cycles. On associating these two views, it is found that the methodology has a strong potential to improve the quality of short-term forecasts. These findings have been put to test through applications of the methodology to studying the time evolution of two commodities of strong economic and social importance (corn and steel) and good results were consistently obtained for both the analytical and forecasting aspects.     

The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US

This article provides out-of-sample forecasts of linear and nonlinear models of US and four Census subregions’ housing prices. The forecasts include the traditional point forecasts, but also include interval and density forecasts, of the housing price distributions. The nonlinear smooth-transition autoregressive model outperforms the linear autoregressive model in point forecasts at longer horizons, but the linear autoregressive and nonlinear smooth-transition autoregressive models perform equally at short horizons. In addition, we generally do not find major differences in performance for the interval and density forecasts between the linear and nonlinear models. Finally, in a dynamic 25-step ex-ante and interval forecasting design, we, once again, do not find major differences between the linear and nonlinear models. In sum, we conclude that when forecasting regional housing prices in the United States, generally the additional costs associated with nonlinear forecasts outweigh the benefits for forecasts only a few months into the future.     

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.First version received: September 2002/Final version received : October 2003I would like to thank Cees Diks, Cars Hommes and an anonymous referee for useful comments that significantly improved the paper.     

Deterministic and stochastic trends in the time series models: a guide for the applied economist

Applied economists working with time series data face a dilemma in selecting between models with deterministic and stochastic trends. While models with deterministic trends are widely used, models with stochastic trends are not so well known. In an influential paper Harvey (1997 Harvey, AC. 1997. Trends, cycles and autoregression. Economic Journal, 107: 192–201. [Crossref] , [Google Scholar]) strongly advocates a structural time series approach with stochastic trends in place of the widely used autoregressive models based on unit root tests and cointegration techniques. Therefore, it is important to understand their relative merits. This article suggests that both methodologies are useful and they may perform differently in different models. This article provides a few guidelines to the applied economists to understand these alternative methods.     

Forecasting tourism demand to Catalonia: Neural networks vs. time series models

The increasing interest aroused by more advanced forecasting techniques, together with the requirement for more accurate forecasts of tourism demand at the destination level due to the constant growth of world tourism, has lead us to evaluate the forecasting performance of neural modelling relative to that of time series methods at a regional level. Seasonality and volatility are important features of tourism data, which makes it a particularly favourable context in which to compare the forecasting performance of linear models to that of nonlinear alternative approaches. Pre-processed official statistical data of overnight stays and tourist arrivals from all the different countries of origin to Catalonia from 2001 to 2009 is used in the study. When comparing the forecasting accuracy of the different techniques for different time horizons, autoregressive integrated moving average models outperform self-exciting threshold autoregressions and artificial neural network models, especially for shorter horizons. These results suggest that the there is a trade-off between the degree of pre-processing and the accuracy of the forecasts obtained with neural networks, which are more suitable in the presence of nonlinearity in the data. In spite of the significant differences between countries, which can be explained by different patterns of consumer behaviour, we also find that forecasts of tourist arrivals are more accurate than forecasts of overnight stays.     

Forecasting with limited data: Combining ARIMA and diffusion models

Forecasting diffusion of new technologies is usually performed by the means of aggregate diffusion models, which tend to monopolize this area of research and practice, making the alternative approaches, like the Box-Jenkins, less favourable choices due to their lack of providing accurate long-term predictions. This paper presents a new methodology focusing on the improvement of the short-term prediction that combines the advantages of both approaches and that can be applied in the early stages of a diffusion process. An application of the methodology is also illustrated, providing short-term forecasts for the world broadband and mobile telecommunications' penetration. The results reveal that the methodology is capable of producing improved one-year-ahead predictions, after a certain level of penetration, as compared to the results of both methods individually. This methodology can find applications to all cases of the high-technology market, where a diffusion model is usually used for obtaining future forecasts. The paper concludes with the limitations of the methodology, the discussion on the application's results and the proposals for further research.     

Forecasting house prices for the four census regions and the aggregate US economy in a data-rich environment

This article considers the ability of large-scale (involving 145 fundamental variables) time-series models, estimated by dynamic factor analysis and Bayesian shrinkage, to forecast real house price growth rates of the four US census regions and the aggregate US economy. Besides the standard Minnesota prior, we also use additional priors that constrain the sum of coefficients of the VAR models. We compare 1- to 24-months-ahead forecasts of the large-scale models over an out-of-sample horizon of 1995:01–2009:03, based on an in-sample of 1968:02–1994:12, relative to a random walk model, a small-scale VAR model comprising just the five real house price growth rates and a medium-scale VAR model containing 36 of the 145 fundamental variables besides the five real house price growth rates. In addition to the forecast comparison exercise across small-, medium- and large-scale models, we also look at the ability of the ‘optimal’ model (i.e. the model that produces the minimum average mean squared forecast error) for a specific region in predicting ex ante real house prices (in levels) over the period of 2009:04 till 2012:02. Factor-based models (classical or Bayesian) perform the best for the North East, Mid-West, West census regions and the aggregate US economy and equally well to a small-scale VAR for the South region. The ‘optimal’ factor models also tend to predict the downward trend in the data when we conduct an ex ante forecasting exercise. Our results highlight the importance of information content in large number of fundamentals in predicting house prices accurately.     

Forecasting exchange rates in transition economies: A comparison of multivariate time series models

This article compares the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian vector error correction (BVEC) models in forecasting the exchange rates for five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Polish Zloty, Slovak Koruna and Slovenian Tolar) against the Euro and the US dollar. Among the specifications composing this battery of multivariate time series models, those with the smallest prediction error still fail to reject the test of equality of forecasting accuracy against the random walk model in short-term predictions, with the exception of the Slovenian Tolar/Euro exchange rate.First version received: October 2002/Final version received: September 2003The authors are grateful to two anonymous referees and the participants in the workshop Monetary and Exchange Rate Strategies Related to the Current European Unions Enlargement Processes, held in Leuven in September 2000, for very helpful comments.     

Between cointegration and multicointegration: Modelling time series dynamics by cumulative error correction models

This study proposes a cumulative error correction model where the summing weights follow a geometrically decreasing function of prior deviations from the equilibrium and are estimated from the data. It is shown that this approach nests both the traditional error correction model – where no weight is given to deviations from the steady state prior to the most recent period – and the error correction model based on the idea of multicointegration.The form of accumulation presented here does not change the order of integration of the series, as is the case in the multicointegration approach of Granger and Lee (1989). Furthermore, it is very parsimonious as only one or two parameters more have to be estimated. The assumption of geometrically decreasing weights can be tested by estimating the model in its unrestricted form.Based on this new model type, the relationship between private consumption and real disposable income of private households in the US is estimated. The short-term forces which set off the most recent period's deviations are much smaller than would be suggested by a VEC and a conventional single equation ECM, and the income elasticity is lower as well. The proposed model outperforms the other two with respect to its forecasting power.