Bayesian analysis of periodic unit roots in the presence of a break

A Bayesian testing approach for a periodic unit root in quarterly and monthly data is presented. Further a Bayesian test is introduced to test for unit roots at (non)seasonal spectral frequencies. All procedures admit one structural break in the periodic trend function, where the occurrence of a break and the associated timing are treated as additional model parameters. A Bayesian model averaging (BMA) approach is proposed and power functions of the tests are computed. Overall the results indicate that the BMA periodic unit root test exhibits favourable test properties even in small samples. In an empirical application the presented testing procedures are used to test for (non)seasonal forms of unemployment persistence among OECD countries.     

Threshold models for trended time series

This paper presents the theoretical development of a new threshold autoregressive model based on trended time series. The theoretical arguments underlying the model are outlined and a nonlinear economic model is used to derive the specification of the empirical econometric model. Estimation and testing issues are considered and analysed. Additionally we apply the model to the empirical investigation of U.S. GDP.This paper is the result of work carried out for the author's Ph.D. thesis. I would like to thank Hashem Pesaran for his help, encouragement and insights during the preparation of this paper. I also thank Gary Koop and Sean Holly for helpful comments. Financial assistance from the Economic and Social Research Council is gratefully acknowledged.     

The order of integration for quarterly macroeconomic time series: A simple testing strategy

An empirical example and a simulation study show that much more attention should be devoted to the practical issue of selecting the maximum admissible order of integration for quarterly macroeconomic time series. In fact, it is shown that when that order is too high, one may get (spurious) evidence for an excessive number of unit roots, resulting in an overdifferenced series. Besides introducing a simple and intuitive definition for the order of integration of quarterly time series, this paper also presents a simple testing strategy to determine that order for the case of macroeconomic data.Helpful comments and suggestions from João Santos Silva and Paulo Rodrigues are gratefully acknowledged. I am also grateful to two anonymous referees, whose comments and suggestions helped improving this paper. Obviously, the usual disclaimer applies. This work has also benefited from financial support from Fundação para a Ciência e Tecnologia (FCT), through Programa POCTI (ECO/33778/2000). A previous version of this paper was presented at the Royal Economic Society Conference, March 2002, Warwick.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost

A main drawback of existing fuzzy time series forecasting methods is that they lack persuasiveness in determining universe of discourse and the length of intervals. Two approaches are proposed for overcoming the problem, and the proposed approaches are more objective and reasonable to improve the persuasiveness in determining the universe of discourse, length of intervals and membership functions of fuzzy time series. The first approach is using Minimize Entropy Principle Approach (MEPA) to partition the universe of discourse and build membership functions, and the second is using Trapezoid Fuzzification Approach (TFA). Monthly amount data of IT project expenditure of a company are used to evaluate the performance of the proposed approaches. The forecasting accuracies of the proposed approaches are better than those of previous methods.     

Equilibrium-correction vs. differencing in macroeconometric forecasting

Recent work by Clements and Hendry elucidate why forecasting systems that are in terms of differences, dVARs, can be more accurate than econometric models that include levels variables, EqCMs. For example, dVAR forecasts are in some cases insulated from parameter non-constancies in the long run mean of the cointegration relationships. In this paper, the practical relevance of these issues are investigated for RIMINI, the quarterly macroeconometric model used in Norges Bank (Central Bank of Norway), an example of an EqCM forecasting model. We develop two dVAR versions of the full RIMINI model and compare EqCM and dVAR forecasts for the period 1992.1–1994.4. We also include forecasts from univariate dVAR type models. The results seem to confirm the relevance of the theoretical results. First, dVAR forecasts appear to provide some immunity against parameter non-constancies that could seriously bias the EqCM forecasts. Second, the misspecification resulting from omitting levels information generates substantial biases in the dVAR forecasts 8 and 12 quarters ahead.     

A vector error-correction forecasting model of the US economy

Any research or policy analysis in economics must be consistent with the time-series properties of observed macroeconomic data. Numerous previous studies reinforce the need to specify correctly a model’s multivariate stochastic structure. This paper discusses in detail the specification of a vector error correction forecasting model that is anchored by long-run equilibrium relationships suggested by economic theory. The model includes six variables––the CPI, the GDP price index, real money balances (M1), the federal funds rate, the yield on long-term (10-year) government bonds, and real GDP––and four cointegrating vectors. The accuracy of VECM model forecasts for individual, univariate time series during for the 1990s is comparable to forecasts made by government agencies and private forecasters, perhaps because many forecasters share a similar implicit, long-run steady-state growth model of the economy. Judged by multivariate statistics that account for forecast-error covariance, VECM forecasts are found to be somewhat more accurate than a naïve random-walk alternative.     

A bottom-up approach for forecasting GDP in a data-rich environment

In an increasingly data-rich environment, the use of factor models for forecasting purposes has gained prominence in the literature and among practitioners. Herein, we assess the forecasting behaviour of factor models to predict several GDP components and investigate the performance of a bottom-up approach to forecast GDP growth in Portugal, which was one of the hardest hit economies during the latest economic and financial crisis. We find supporting evidence of the usefulness of factor models and noteworthy forecasting gains when conducting a bottom-approach drawing on the main aggregates of GDP.     

Forecasting electricity spot prices using time-series models with a double temporal segmentation

The French wholesale market is set to expand in the next few years under European pressure and national decisions. In this article, we assess the forecasting ability of several classes of time-series models for electricity wholesale spot prices at a day-ahead horizon in France. Electricity spot prices display a strong seasonal pattern, particularly in France, given the high share of electric heating in housing during winter time. To deal with this pattern, we implement a double temporal segmentation of the data. For each trading period and season, we use a large number of specifications based on market fundamentals: linear regressions, Markov-switching (MS) models and threshold models with a smooth transition. An extensive evaluation on French data shows that modelling each season independently leads to better results. Among nonlinear models, MS models designed to capture the sudden and fast-reverting spikes in the price dynamics yield more accurate forecasts. Finally, pooling forecasts give more reliable results.     

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.     

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.     

A comparison of Logistic and Harvey models for electricity consumption in New Zealand

There have been a number of forecasting models based on various forms of the logistic growth curve. This paper investigates the effectiveness of two forms of Harvey models and a Logistic model for forecasting electricity consumption in New Zealand. The three growth curve models are applied to the Domestic and Non-Domestic sectors and Total electricity consumption in New Zealand. The developed models are compared using their goodness of fit to historical data and forecasting accuracy over a period of 19 years. The comparison revealed that the Harvey model is a very appropriate candidate for forecasting electricity consumption in New Zealand. The developed models are also compared with some available national forecasts.     

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.

     

Price convergence of peripheral European countries on the way to the EMU: A time series approach

This paper examines price and inflation convergence between three European countries (Italy, Spain and the U.K.) and a European average and, alternatively, between them and Germany from the beginning of the 80's.  For this purpose the long-run stochastic relationships on prices derived from the convergence criteria agreed in the Maastricht Treaty are analyzed. In order to do this, some recent unit root tests have been applied as well as time-varying parameters models.  The results reject the long-run convergence hypothesis in all the cases but allow us to accept the existence of catching-up with the European average and Germany in some cases depending on the nature of the prices and on the countries considered. First version received: March 1997/final version received: May 1999     

The cyclical behaviour of prices in the U.K.: Some structural time series evidence

The cyclical behaviour of prices in the U.K. is investigated using a sample of annual observations covering the period 1886–1993. A structural time series model relating consumer prices to output is estimated over four sub-periods. The results indicate that prices were procyclical in the inter-war period, countercyclical in the post-1973 period and acyclical otherwise. The proposition that the cyclical behaviour of prices is determined by the dominance of supply or demand shocks alone is disputed on the basis of empirical evidence and theoretical reasoning. It is concluded that the cyclical behaviour of prices cannot be explained just by analysing time series on output and prices and that due attention should be paid to the institutional and policy changes occurring during the period under study. It is demonstrated that the empirical results are consistent with the events experienced by the U.K. economy in the most recent period. First version received: November 1998/final version accepted: October 1999     

Modelling time series properties of Australian lending interest rates

The purpose of this paper is to examine the time series properties of Australian residential mortgage interest rates, and in doing so, establish whether or not selected home loan rates （product-level monthly home loan interest rates for CBA） exhibit the expected cyclical and seasonal variations and whether seasonality, if present, is stochastic or deterministic. In particular, due to a well established presence of cyclicality in financial markets＇ interest rates and strong correlation between financial markets＇ interest rates and home loan interest rates, the paper presumes that cyclicality is also to be found in home loan interest rates. Furthermore, the paper tests the hypothesis that home loan interest rates, for selected products, exhibit the three identified （＂Spring＂, ＂Autumn＂ and ＂The end of the Financial Year＂） season-related interest rate reductions. The paper uses a structural time series modelling approach and product-level home loan interest rates data from one of the biggest banks in Australia, Commonwealth Bank of Australia （CBA）. As expected, the results overall confirm the existence of cyclicality in home loan interest rates. With respect to the seasonality of home loan interest rate, although most of the analysed variables show the presence of statistically significant seasonal factors, the majority of the statistically significant seasonal factors observed cannot be attributed to any of the three considered seasonal effects.     

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 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.     

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.