Unemployment variation over the business cycles: a comparison of forecasting models

Asymmetry has been well documented in the business cycle literature. The asymmetric business cycle suggests that major macroeconomic series, such as a country's unemployment rate, are non‐linear and, therefore, the use of linear models to explain their behaviour and forecast their future values may not be appropriate. Many researchers have focused on providing evidence for the non‐linearity in the unemployment series. Only recently have there been some developments in applying non‐linear models to estimate and forecast unemployment rates. A major concern of non‐linear modelling is the model specification problem; it is very hard to test all possible non‐linear specifications, and to select the most appropriate specification for a particular model. Artificial neural network (ANN) models provide a solution to the difficulty of forecasting unemployment over the asymmetric business cycle. ANN models are non‐linear, do not rely upon the classical regression assumptions, are capable of learning the structure of all kinds of patterns in a data set with a specified degree of accuracy, and can then use this structure to forecast future values of the data. In this paper, we apply two ANN models, a back‐propagation model and a generalized regression neural network model to estimate and forecast post‐war aggregate unemployment rates in the USA, Canada, UK, France and Japan. We compare the out‐of‐sample forecast results obtained by the ANN models with those obtained by several linear and non‐linear times series models currently used in the literature. It is shown that the artificial neural network models are able to forecast the unemployment series as well as, and in some cases better than, the other univariate econometrics time series models in our test. Copyright © 2004 John Wiley & Sons, Ltd.     

Google's MIDAS Touch: Predicting UK Unemployment with Internet Search Data

Internet search data could be a useful source of information for policymakers when formulating decisions based on their understanding of the current economic environment. This paper builds on earlier literature via a structured value assessment of the data provided by Google Trends. This is done through two empirical exercises related to the forecasting of changes in UK unemployment. Firstly, economic intuition provides the basis for search term selection, with a resulting Google indicator tested alongside survey‐based variables in a traditional forecasting environment. Secondly, this environment is expanded into a pseudo‐time nowcasting framework which provides the backdrop for assessing the timing advantage that Google data have over surveys. The framework is underpinned by a MIDAS regression which allows, for the first time, the easy incorporation of Internet search data at its true sampling rate into a nowcast model for predicting unemployment. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust modelling of ARCH models

The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the conditional scale. We examine the L₁‐estimation of ARCH models and derive the limiting distributions of the estimators. A robust standardized absolute residual autocorrelation based on least absolute deviation estimation is proposed. Then a robust portmanteau statistic is constructed to test the adequacy of the model, especially the specification of the conditional scale. We obtain their asymptotic distributions under mild conditions. Examples show that the suggested L₁‐norm estimators and the goodness‐of‐fit test are robust against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright © 2001 John Wiley & Sons, Ltd.     

A new Bayesian formulation for Holt's exponential smoothing

In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two‐dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two‐dimensional grid, rather than applying a five‐variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd.     

Does Information Help Intra‐Day Volatility Forecasts?

While much research related to forecasting return volatility does so in a univariate setting, this paper includes proxies for information flows to forecast intra‐day volatility for the IBEX 35 futures market. The belief is that volume or the number of transactions conveys important information about the market that may be useful in forecasting. Our results suggest that augmenting a variety of GARCH‐type models with these proxies lead to improved forecasts across a range of intra‐day frequencies. Furthermore, our results present an interesting picture whereby the PARCH model generally performs well at the highest frequencies and shorter forecasting horizons, whereas the component model performs well at lower frequencies and longer forecast horizons. Both models attempt to capture long memory; the PARCH model allows for exponential decay in the autocorrelation function, while the component model captures trend volatility, which dominates over a longer horizon. These characteristics are likely to explain the success of each model. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting with a DSGE Model of a Small Open Economy within the Monetary Union

In this paper we lay out a two‐region dynamic stochastic general equilibrium (DSGE) model of an open economy within the European Monetary Union. The model, which is built in the New Keynesian tradition, contains real and nominal rigidities such as habit formation in consumption, price and wage stickiness as well as rich stochastic structure. The framework also incorporates the theory of unemployment, small open economy aspects and a nominal interest rate that is set exogenously by the area‐wide monetary authority. As an illustration, the model is estimated on Luxembourgish data. We evaluate the properties of the estimated model and assess its forecasting performance relative to reduced‐form model such as vector autoregression (VAR). In addition, we study the empirical validity of the DSGE model restrictions by applying a DSGE‐VAR approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting value‐at‐risk with a parsimonious portfolio spillover GARCH (PS‐GARCH) model

Accurate modelling of volatility (or risk) is important in finance, particularly as it relates to the modelling and forecasting of value‐at‐risk (VaR) thresholds. As financial applications typically deal with a portfolio of assets and risk, there are several multivariate GARCH models which specify the risk of one asset as depending on its own past as well as the past behaviour of other assets. Multivariate effects, whereby the risk of a given asset depends on the previous risk of any other asset, are termed spillover effects. In this paper we analyse the importance of considering spillover effects when forecasting financial volatility. The forecasting performance of the VARMA‐GARCH model of Ling and McAleer (2003), which includes spillover effects from all assets, the CCC model of Bollerslev (1990), which includes no spillovers, and a new Portfolio Spillover GARCH (PS‐GARCH) model, which accommodates aggregate spillovers parsimoniously and hence avoids the so‐called curse of dimensionality, are compared using a VaR example for a portfolio containing four international stock market indices. The empirical results suggest that spillover effects are statistically significant. However, the VaR threshold forecasts are generally found to be insensitive to the inclusion of spillover effects in any of the multivariate models considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparing the DSGE model with the factor model: an out‐of‐sample forecasting experiment

In this paper, we put dynamic stochastic general equilibrium DSGE forecasts in competition with factor forecasts. We focus on these two models since they represent nicely the two opposing forecasting philosophies. The DSGE model on the one hand has a strong theoretical economic background; the factor model on the other hand is mainly data‐driven. We show that incorporating a large information set using factor analysis can indeed improve the short‐horizon predictive ability, as claimed by many researchers. The micro‐founded DSGE model can provide reasonable forecasts for US inflation, especially with growing forecast horizons. To a certain extent, our results are consistent with the prevailing view that simple time series models should be used in short‐horizon forecasting and structural models should be used in long‐horizon forecasting. Our paper compares both state‐of‐the‐art data‐driven and theory‐based modelling in a rigorous manner. Copyright © 2008 John Wiley & Sons, Ltd.     

Can cointegration‐based forecasting outperform univariate models? An application to Asian exchange rates

Conventional wisdom holds that restrictions on low‐frequency dynamics among cointegrated variables should provide more accurate short‐ to medium‐term forecasts than univariate techniques that contain no such information; even though, on standard accuracy measures, the information may not improve long‐term forecasting. But inconclusive empirical evidence is complicated by confusion about an appropriate accuracy criterion and the role of integration and cointegration in forecasting accuracy. We evaluate the short‐ and medium‐term forecasting accuracy of univariate Box–Jenkins type ARIMA techniques that imply only integration against multivariate cointegration models that contain both integration and cointegration for a system of five cointegrated Asian exchange rate time series. We use a rolling‐window technique to make multiple out of sample forecasts from one to forty steps ahead. Relative forecasting accuracy for individual exchange rates appears to be sensitive to the behaviour of the exchange rate series and the forecast horizon length. Over short horizons, ARIMA model forecasts are more accurate for series with moving‐average terms of order >1. ECMs perform better over medium‐term time horizons for series with no moving average terms. The results suggest a need to distinguish between ‘sequential’ and ‘synchronous’ forecasting ability in such comparisons. Copyright © 2002 John Wiley & Sons, Ltd.     

Term premia and the maturity composition of the Federal debt: new evidence from the term structure of interest rates

This paper models bond term premia empirically in terms of the maturity composition of the federal debt and other observable economic variables in a time‐varying framework with potential regime shifts. We present regression and out‐of sample forecasting results demonstrating that information on the age composition of the Federal debt is useful for forecasting term premia. We show that the multiprocess mixture model, a multi‐state time‐varying parameter model, outperforms the commonly used GARCH model in out‐of‐sample forecasts of term premia. The results underscore the importance of modelling term premia, as a function of economic variables rather than just as a function of asset covariances as in the conditional heteroscedasticity models. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting daily foreign exchange rates using genetically optimized neural networks

Forecasting currency exchange rates is an important financial problem that has received much attention especially because of its intrinsic difficulty and practical applications. The statistical distribution of foreign exchange rates and their linear unpredictability are recurrent themes in the literature of international finance. Failure of various structural econometric models and models based on linear time series techniques to deliver superior forecasts to the simplest of all models, the simple random walk model, have prompted researchers to use various non‐linear techniques. A number of non‐linear time series models have been proposed in the recent past for obtaining accurate prediction results, in an attempt to ameliorate the performance of simple random walk models. In this paper, we use a hybrid artificial intelligence method, based on neural network and genetic algorithm for modelling daily foreign exchange rates. A detailed comparison of the proposed method with non‐linear statistical models is also performed. The results indicate superior performance of the proposed method as compared to the traditional non‐linear time series techniques and also fixed‐geometry neural network models. Copyright © 2002 John Wiley & Sons, Ltd.     

A Bayesian nonlinear support vector machine error correction model

The use of linear error correction models based on stationarity and cointegration analysis, typically estimated with least squares regression, is a common technique for financial time series prediction. In this paper, the same formulation is extended to a nonlinear error correction model using the idea of a kernel‐based implicit nonlinear mapping to a high‐dimensional feature space in which linear model formulations are specified. Practical expressions for the nonlinear regression are obtained in terms of the positive definite kernel function by solving a linear system. The nonlinear least squares support vector machine model is designed within the Bayesian evidence framework that allows us to find appropriate trade‐offs between model complexity and in‐sample model accuracy. From straightforward primal–dual reasoning, the Bayesian framework allows us to derive error bars on the prediction in a similar way as for linear models and to perform hyperparameter and input selection. Starting from the results of the linear modelling analysis, the Bayesian kernel‐based prediction is successfully applied to out‐of‐sample prediction of an aggregated equity price index for the European chemical sector. Copyright © 2006 John Wiley & Sons, Ltd.     

Neural model identification,variable selection and model adequacy

In recent years an impressive array of publications has appeared claiming considerable successes of neural networks in modelling financial data but sceptical practitioners and statisticians are still raising the question of whether neural networks really are ‘a major breakthrough or just a passing fad’. A major reason for this is the lack of procedures for performing tests for misspecified models, and tests of statistical significance for the various parameters that have been estimated, which makes it difficult to assess the model's significance and the possibility that any short‐term successes that are reported might be due to ‘data mining’. In this paper we describe a methodology for neural model identification which facilitates hypothesis testing at two levels: model adequacy and variable significance. The methodology includes a model selection procedure to produce consistent estimators, a variable selection procedure based on statistical significance and a model adequacy procedure based on residuals analysis. We propose a novel, computationally efficient scheme for estimating sampling variability of arbitrarily complex statistics for neural models and apply it to variable selection. The approach is based on sampling from the asymptotic distribution of the neural model's parameters (‘parametric sampling’). Controlled simulations are used for the analysis and evaluation of our model identification methodology. A case study in tactical asset allocation is used to demonstrate how the methodology can be applied to real‐life problems in a way analogous to stepwise forward regression analysis. Neural models are contrasted to multiple linear regression. The results indicate the presence of non‐linear relationships in modelling the equity premium. Copyright © 1999 John Wiley & Sons, Ltd.     

Do professional forecasters believe in the Phillips curve? evidence from the G7 countries

This paper uses monthly survey data for the G7 countries for the time period 1989–2007 to explore the link between expectations on nominal wages, prices and unemployment rates as suggested by the wage and price Phillips curves. Four major findings stand out. First, we find that survey participants trust in both types of Phillips curve relationships. Second, we find evidence in favor of nonlinearities in the price Phillips curve. Third, we take into account a kink in the price Phillips curve to indicate that the slope of the Phillips curve differs during the business cycle. We find strong evidence of this feature in the data which confirms recent theoretical discussions. Fourth, we employ our data to the expectations‐augmented Phillips curve model. The results suggest that professional forecasters adopt this model when forecasting macroeconomic variables. Copyright © 2010 John Wiley & Sons, Ltd.     

A latent variable approach to forecasting the unemployment rate

A forecasting model for unemployment is constructed that exploits the time series properties of unemployment while satisfying the economic relationships specified by Okun's law and the Phillips curve. In deriving the model, we jointly consider the problem of obtaining estimates of the unobserved potential rate of unemployment consistent with Okun's law and the Phillips curve, and associating the potential rate of unemployment with actual unemployment. The empirical example shows that the model clearly outperforms alternative forecasting procedures typically used to forecast unemployment. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of GARCH models in forecasting stock market volatility

This paper studies the performance of GARCH model and its modifications, using the rate of returns from the daily stock market indices of the Kuala Lumpur Stock Exchange (KLSE) including Composite Index, Tins Index, Plantations Index, Properties Index, and Finance Index. The models are stationary GARCH, unconstrained GARCH, non‐negative GARCH, GARCH‐M, exponential GARCH and integrated GARCH. The parameters of these models and variance processes are estimated jointly using the maximum likelihood method. The performance of the within‐sample estimation is diagnosed using several goodness‐of‐fit statistics. We observed that, among the models, even though exponential GARCH is not the best model in the goodness‐of‐fit statistics, it performs best in describing the often‐observed skewness in stock market indices and in out‐of‐sample (one‐step‐ahead) forecasting. The integrated GARCH, on the other hand, is the poorest model in both respects. Copyright © 1999 John Wiley & Sons, Ltd.     

Monthly Employment Indicators of the Euro Area and Larger Member States: Real‐Time Analysis of Indirect Estimates

The paper presents a comparative real‐time analysis of alternative indirect estimates relative to monthly euro area employment. In the experiment quarterly employment is temporally disaggregated using monthly unemployment as related series. The strategies under comparison make use of the contribution of sectoral data of the euro area and its six larger member states. The comparison is carried out among univariate temporal disaggregations of the Chow and Lin type and multivariate structural time series models of small and medium size. Specifications in logarithms are also systematically assessed. All multivariate set‐ups, up to 49 series modelled simultaneously, are estimated via the EM algorithm. Main conclusions are that mean revision errors of disaggregated estimates are overall small, a gain is obtained when the model strategy takes into account the information by both sector and member state and that larger multivariate set‐ups perform very well, with several advantages with respect to simpler models.Copyright © 2014 John Wiley & Sons, Ltd.     

Prediction intervals for exponential smoothing using two new classes of state space models

Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non‐linear structure in the observation equation as well as heteroscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods. We use these classes to provide exact analytic (matrix) expressions for forecast error variances that can be used to construct prediction intervals one or multiple steps ahead. These formulas are reduced to non‐matrix expressions for 15 state space models that underlie the most common exponential smoothing methods. We discuss relationships between our expressions and previous suggestions for finding forecast error variances and prediction intervals for exponential smoothing methods. Simpler approximations are developed for the more complex schemes and their validity examined. The paper concludes with a numerical example using a non‐linear model. Copyright © 2005 John Wiley & Sons, Ltd.     

Correcting the January optimism effect

Each month, various professional forecasters give forecasts for next year's real gross domestic product (GDP) growth and unemployment. January is a special month, when the forecast horizon moves to the following calendar year. Instead of deleting the January data when analyzing forecast updates, I propose a periodic version of a test regression for weak-form efficiency. An application of this periodic model for many forecasts across a range of countries shows that in January GDP forecast updates are positive, whereas the forecast updates for unemployment are negative. I document that this January optimism about the new calendar year is detrimental to forecast accuracy. To empirically analyze Okun's law, I also propose a periodic test regression, and its application provides more support for this law.     

Can out‐of‐sample forecast comparisons help prevent overfitting?

This paper shows that out‐of‐sample forecast comparisons can help prevent data mining‐induced overfitting. The basic results are drawn from simulations of a simple Monte Carlo design and a real data‐based design similar to those used in some previous studies. In each simulation, a general‐to‐specific procedure is used to arrive at a model. If the selected specification includes any of the candidate explanatory variables, forecasts from the model are compared to forecasts from a benchmark model that is nested within the selected model. In particular, the competing forecasts are tested for equal MSE and encompassing. The simulations indicate most of the post‐sample tests are roughly correctly sized. Moreover, the tests have relatively good power, although some are consistently more powerful than others. The paper concludes with an application, modelling quarterly US inflation. Copyright © 2004 John Wiley & Sons, Ltd.