A bayesian approach to modelling stochastic cycles

This article deals with a fully Bayesian approach to describe the cyclical behaviour of a univariate time series. A damped sine wave where both the period and the damping factor are time varying is assumed as the underlying mathematical model for the cyclical component. The model is applied to two real data sets; the annual rainfall observations in Fortaleza, Brazil, and the annual Wolf sunspot numbers.     

Forecasting economic time series that require a power transformation: Case of state tax receipts

In this study, time series analysis is applied to the problem of forecasting state income tax receipts. The data series is of special interest since it exhibits a strong trend with a high multiplicative seasonal component. An appropriate model is identified by simultaneous estimation of the parameters of the power transformation and the ARMA model using the Schwarz (1978) Bayesian information criterion. The forecasting performance of the time series model obtained from this procedure is compared with alternative time series and regression models. The study illustrates how an information criterion can be employed for identifying time series models that require a power transformation, as exemplified by state tax receipts. It also establishes time series analysis as a viable technique for forecasting state tax receipts.     

Composite leading indicators of underlying inflation for seven EU countries

This paper presents short‐ and long‐term composite leading indicators (CLIs) of underlying inflation for seven EU countries, namely Belgium, Germany, France, Italy, the Netherlands, Sweden and the UK. CLI and CPI reference series are calculated in terms of both growth rates and in deviations from its trend. The composite leading indicators are based on leading basic series, such as sources of inflation, series containing information on inflation expectations and prices of intermediate goods and services. Neftci's decision rule approach has been applied to transfer movements in the CLIs into a measure of the probability of a cyclical turning point, which enables the screening out of false turning point predictions. Finally, CLIs have been used to analyse the international coherence of price cycles. The forecast performance of CLIs of inflation over the past raises hope that this forecast instrument can be useful in predicting future price movements. Copyright © 1999 John Wiley & Sons, Ltd.     

Long‐Run and Cyclical Dynamics in the US Stock Market

This paper uses fractional integration to examine the long‐run dynamics and cyclical structure of US inflation, real risk‐free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 2000. It implements a procedure which allows consideration of unit roots with possibly fractional orders of integration both at zero (long‐run) and cyclical frequencies. When focusing exclusively on the former, the estimated order of integration varies considerably, and non‐stationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long‐run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, six different criteria are applied to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results, based on a 15‐year horizon, show that the former outperforms the others in a number of cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Causal forces: Structuring knowledge for time-series extrapolation

This paper examines a strategy for structuring one type of domain knowledge for use in extrapolation. It does so by representing information about causality and using this domain knowledge to select and combine forecasts. We use five categories to express causal impacts upon trends: growth, decay, supporting, opposing, and regressing. An identification of causal forces aided in the determination of weights for combining extrapolation forecasts. These weights improved average ex ante forecast accuracy when tested on 104 annual economic and demographic time series. Gains in accuracy were greatest when (1) the causal forces were clearly specified and (2) stronger causal effects were expected, as in longer-range forecasts. One rule suggested by this analysis was: ‘Do not extrapolate trends if they are contrary to causal forces.’ We tested this rule by comparing forecasts from a method that implicitly assumes supporting trends (Holt's exponential smoothing) with forecasts from the random walk. Use of the rule improved accuracy for 20 series where the trends were contrary; the MdAPE (Median Absolute Percentage Error) was 18% less for the random walk on 20 one-year ahead forecasts and 40% less for 20 six-year-ahead forecasts. We then applied the rule to four other data sets. Here, the MdAPE for the random walk forecasts was 17% less than Holt's error for 943 short-range forecasts and 43% less for 723 long-range forecasts. Our study suggests that the causal assumptions implicit in traditional extrapolation methods are inappropriate for many applications.     

Removing Forecasting Errors with White Gaussian Noise after Square Root Transformation

An analytical model has been developed in the present paper based on a square root transformation of white Gaussian noise. The mathematical expectation and variance of the new asymmetric distribution generated by white Gaussian noise after a square root transformation are analytically deduced from the preceding four terms of the Taylor expansion. The model was first evaluated against numerical experiments and a good agreement was obtained. The model was then used to predict time series of wind speeds and highway traffic flows. The simulation results from the new model indicate that the prediction accuracy could be improved by 0.1–1% by removing the mean errors. Further improvement could be obtained for non‐stationary time series, which had large trends. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting the Antwerp maritime steel traffic flow: A case study

This paper uses multivariate time series models to specify the maritime steel traffic flow in the port of Antwerp. The time series considered are the total outgoing and total incoming maritime steel traffic and the total steel production in the EEC. The obtained time series models provide useful insight into the general behaviour of the maritime steel traffic flow during the period 1971–82. In particular, they provide a quantitative interpretation of important changes which took place in the European steel industry during that period. The multivariate time series models produce forecasts which are a substantial improvement over those obtained by univariate time series models. This is especially the case for the series of total incoming maritime steel traffic in the port of Antwerp, when differencing and transformation of the original data are applied.     

The Effects of Disaggregation on Forecasting Nonstationary Time Series

This paper focuses on the effects of disaggregation on forecast accuracy for nonstationary time series using dynamic factor models. We compare the forecasts obtained directly from the aggregated series based on its univariate model with the aggregation of the forecasts obtained for each component of the aggregate. Within this framework (first obtain the forecasts for the component series and then aggregate the forecasts), we try two different approaches: (i) generate forecasts from the multivariate dynamic factor model and (ii) generate the forecasts from univariate models for each component of the aggregate. In this regard, we provide analytical conditions for the equality of forecasts. The results are applied to quarterly gross domestic product (GDP) data of several European countries of the euro area and to their aggregated GDP. This will be compared to the prediction obtained directly from modeling and forecasting the aggregate GDP of these European countries. In particular, we would like to check whether long‐run relationships between the levels of the components are useful for improving the forecasting accuracy of the aggregate growth rate. We will make forecasts at the country level and then pool them to obtain the forecast of the aggregate. The empirical analysis suggests that forecasts built by aggregating the country‐specific models are more accurate than forecasts constructed using the aggregated data. Copyright © 2014 John Wiley & Sons, Ltd.     

A multi-country dynamic factor model with stochastic volatility for euro area business cycle analysis

This paper develops a dynamic factor model that uses euro area country-specific information on output and inflation to estimate an area-wide measure of the output gap. Our model assumes that output and inflation can be decomposed into country-specific stochastic trends and a common cyclical component. Comovement in the trends is introduced by imposing a factor structure on the shocks to the latent states. We moreover introduce flexible stochastic volatility specifications to control for heteroscedasticity in the measurement errors and innovations to the latent states. Carefully specified shrinkage priors allow for pushing the model towards a homoscedastic specification, if supported by the data. Our measure of the output gap closely tracks other commonly adopted measures, with small differences in magnitudes and timing. To assess whether the model-based output gap helps in forecasting inflation, we perform an out-of-sample forecasting exercise. The findings indicate that our approach yields superior inflation forecasts, both in terms of point and density predictions.     

Bicorrelations and cross‐bicorrelations as non‐linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross‐bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non‐linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high‐frequency exchange rate returns, and their out‐of‐sample forecasting performance is compared to that of other time series models. Copyright © 2001 John Wiley & Sons, Ltd.     

Short‐term forecasting of industrial electricity consumption in Brazil

This paper presents short‐term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non‐linear models and econometric models. The first method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves non‐observable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy‐consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S‐PLUS. Copyright © 1999 John Wiley & Sons, Ltd.     

On a dynamic mixture GARCH model

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non‐stationary volatility component. The VaR based on the new model performs better than traditional GARCH‐based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.     

The use of canonical correlation analysis to identify the order of multivariate ARMA models: simulation and application

This paper is concerned with how canonical correlation can be used to identify the structure of a linear multivariate time series model. We describe briefly methods that use the canonical correlation technique and present simulation results in order to compare and evaluate the performance of these methods. The methods are also applied to a well‐known multivariate time series. Copyright © 2000 John Wiley & Sons, Ltd.     

Testing for (common) stochastic trends in the presence of structural breaks

This paper considers the problem of testing for the presence of stochastic trends in multivariate time series with structural breaks. The breakpoints are assumed to be known. The testing framework is the multivariate locally best invariant test and the common trend test of Nyblom and Harvey (2000). The asymptotic distributions of the test statistics are derived under a specification of the deterministic component which allows for structural breaks. Asymptotic critical values are provided for the case of a single breakpoint. A modified statistic is then proposed, the asymptotic distribution of which is independent of the breakpoint location and belongs to the Cramér‐von Mises family. This modification is particularly advantageous in the case of multiple breakpoints. It is also shown that the asymptotic distributions of the test statistics are unchanged when seasonal dummy variables and/or weakly dependent exogenous regressors are included. Finally, as an example, the tests are applied to UK macroeconomic data and to data on road casualties in Great Britain. Copyright © 2002 John Wiley & Sons, Ltd.     

Forecasting and signal extraction with misspecified models

This paper evaluates multistep estimation for the purposes of signal extraction, and in particular the separation of the trend from the cycle in economic time series, and long‐range forecasting, in the presence of a misspecified, but simply parameterized model. Our workhorse models are two popular unobserved components models, namely the local level and the local linear model. The paper introduces a metric for assessing the accuracy of the unobserved components estimates and concludes that multistep estimation can be valuable. However, its performance depends crucially on the properties of the series and the paper explores the role of the order of integration and the relative size of the cyclical variation. On the contrary, cross‐validation is usually not suitable for the purposes considered. Copyright © 2005 John Wiley & Sons, Ltd.     

Predictive power and unbiasedness of implied forward charter rates

This paper examines the efficiency and predictive power of implied forward shipping charter rates. In particular, we examine whether implied forward 6‐month time‐charter rates, which are derived through the difference between time‐charters with different maturities based on the term structure model, are efficient and unbiased predictors of actual future time‐charter rates. Using a dataset for the period January 1989 to June 2003, results of different statistical tests, including the cointegration approach, suggest that implied forward rates are in fact unbiased predictors of future time‐charter rates in the dry bulk freight market. In addition, it is found that implied forward rates yield superior forecasts compared to alternative univariate and multivariate time series models. However, while the unbiasedness hypothesis is found to hold, on average, we find that chartering strategies based on simple trend‐following trading rules in this cyclical market are able to generate economic profits even out‐of‐sample. This highlights how standard tests for unbiasedness do not always capture cyclical predictable components in the market behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Forward Rates,Monetary Policy and the Economic Cycle

The short end of the yield curve incorporates essential information to forecast central banks' decisions, but in a biased manner. This article proposes a new method to forecast the Fed and the European Central Bank's decision rate by correcting the swap rates for their cyclical economic premium, using an affine term structure model. The corrected yields offer a higher out‐of‐sample forecasting power than the yields themselves. They also deliver forecasts that are either comparable or better than those obtained with a factor‐augmented vector autoregressive model, underlining the fact that yields are likely to contain at least as much information regarding monetary policy as a dataset composed of economic data series. Copyright © 2015 John Wiley & Sons, Ltd.     

Monetary Aggregates to Improve Early Output Gap Estimates in the Euro Area: An Empirical Assessment

Output gap estimates at the current edge are subject to severe revisions. This study analyzes whether monetary aggregates can be used to improve the reliability of early output gap estimates as proposed by several theoretical models. A real‐time experiment shows that real M1 can improve output gap estimates for euro area data. For many periods the cyclical component of real M1 shows good results, while a forecasting strategy based on projecting GDP series seems to be more robust and provides superior results during the Great Recession. Broader monetary aggregates provide no superior information for output gap estimates. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting time series which are inherently discontinuous

Commonly used forecasting methods often produce meaningless forecasts when time series display abrupt changes in level. Measuring and accounting for the effect of discontinuities can have a significant impact on forecasting accuracy. In addition, if discontinuities are considered non-random and their cause is known, then adjustments can be made to more reliably represent the trend, seasonal and random component. This paper concerns a computational method used in forecasting inherently discontinuous time series. The method provides screening to determine the locations and types of discontinuities. The paper includes analyses of actual time series which are typical of certain types of inherently discontinuous processes.     

Exponential smoothing of seasonal data: a comparison

A parsimonious method of exponential smoothing is introduced for time series generated from a combination of local trends and local seasonal effects. It is compared with the additive version of the Holt–Winters method of forecasting on a standard collection of real time series. Copyright © 2001 John Wiley & Sons, Ltd.