Forecasting high‐frequency financial data with the ARFIMA–ARCH model

Financial data series are often described as exhibiting two non‐standard time series features. First, variance often changes over time, with alternating phases of high and low volatility. Such behaviour is well captured by ARCH models. Second, long memory may cause a slower decay of the autocorrelation function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA–ARCH model class has been suggested as a way of coping with both phenomena simultaneously. For estimation we implement the bias correction of Cox and Reid ( 1987 ). For daily data on the Swiss 1‐month Euromarket interest rate during the period 1986–1989, the ARFIMA–ARCH (5,d,2/4) model with non‐integer d is selected by AIC. Model‐based out‐of‐sample forecasts for the mean are better than predictions based on conditionally homoscedastic white noise only for longer horizons (τ > 40). Regarding volatility forecasts, however, the selected ARFIMA–ARCH models dominate. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting in the presence of level shifts

This article addresses the problem of forecasting time series that are subject to level shifts. Processes with level shifts possess a nonlinear dependence structure. Using the stochastic permanent breaks (STOPBREAK) model, I model this nonlinearity in a direct and flexible way that avoids imposing a discrete regime structure. I apply this model to the rate of price inflation in the United States, which I show is subject to level shifts. These shifts significantly affect the accuracy of out‐of‐sample forecasts, causing models that assume covariance stationarity to be substantially biased. Models that do not assume covariance stationarity, such as the random walk, are unbiased but lack precision in periods without shifts. I show that the STOPBREAK model outperforms several alternative models in an out‐of‐sample inflation forecasting experiment. Copyright © 2005 John Wiley & Sons, Ltd.     

The Informational Content of the Term Spread in Forecasting the US Inflation Rate: A Nonlinear Approach

The difficulty in modelling inflation and the significance in discovering the underlying data‐generating process of inflation is expressed in an extensive literature regarding inflation forecasting. In this paper we evaluate nonlinear machine learning and econometric methodologies in forecasting US inflation based on autoregressive and structural models of the term structure. We employ two nonlinear methodologies: the econometric least absolute shrinkage and selection operator (LASSO) and the machine‐learning support vector regression (SVR) method. The SVR has never been used before in inflation forecasting considering the term spread as a regressor. In doing so, we use a long monthly dataset spanning the period 1871:1–2015:3 that covers the entire history of inflation in the US economy. For comparison purposes we also use ordinary least squares regression models as a benchmark. In order to evaluate the contribution of the term spread in inflation forecasting in different time periods, we measure the out‐of‐sample forecasting performance of all models using rolling window regressions. Considering various forecasting horizons, the empirical evidence suggests that the structural models do not outperform the autoregressive ones, regardless of the model's method. Thus we conclude that the term spread models are not more accurate than autoregressive models in inflation forecasting. Copyright © 2016 John Wiley & Sons, Ltd.     

Exploring Survey‐Based Inflation Forecasts

This paper first shows that survey‐based expectations (SBE) outperform standard time series models in US quarterly inflation out‐of‐sample prediction and that the term structure of survey‐based inflation forecasts has predictive power over the path of future inflation changes. It then proposes some empirical explanations for the forecasting success of survey‐based inflation expectations. We show that SBE pool a large amount of heterogeneous information on inflation expectations and react more flexibly and accurately to macro conditions both contemporaneously and dynamically. We illustrate the flexibility of SBE forecasts in the context of the 2008 financial crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

Vector smooth transition regression models for US GDP and the composite index of leading indicators

In this paper, I extend to a multiple‐equation context the linearity, model selection and model adequacy tests recently proposed for univariate smooth transition regression models. Using this result, I examine the nonlinear forecasting power of the Conference Board composite index of leading indicators to predict both output growth and the business‐cycle phases of the US economy in real time. Copyright © 2004 John Wiley & Sons, Ltd.     

Bayesian Model Averaging under Regime Switching with Application to Cyclical Macro Variable Forecasting

Model uncertainty and recurrent or cyclical structural changes in macroeconomic time series dynamics are substantial challenges to macroeconomic forecasting. This paper discusses a macro variable forecasting methodology that combines model uncertainty and regime switching simultaneously. The proposed predictive regression specification permits both regime switching of the regression parameters and uncertainty about the inclusion of forecasting variables by employing Bayesian model averaging. In an empirical exercise involving quarterly US inflation, we observed that our Bayesian model averaging with regime switching leads to substantial improvements in forecast performance, particularly in the medium horizon (two to four quarters). Copyright © 2015 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.     

ARFIMA approximation and forecasting of the limiting aggregate structure of long‐memory process

This article studies Man and Tiao's (2006) low‐order autoregressive fractionally integrated moving‐average (ARFIMA) approximation to Tsai and Chan's (2005b) limiting aggregate structure of the long‐memory process. In matching the autocorrelations, we demonstrate that the approximation works well, especially for larger d values. In computing autocorrelations over long lags for larger d value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, d, d?₁) model provides a useful alternative to compute the autocorrelations as a really close approximation. In forecasting future aggregates, we demonstrate the close performance of using the ARFIMA(0, d, d?₁) model and the exact aggregate structure. In practice, this provides a justification for the use of a low‐order ARFIMA model in predicting future aggregates of long‐memory process. Copyright © 2008 John Wiley & Sons, Ltd.     

Semi‐Structural Forecasting of UK Inflation Based on the Hybrid New Keynesian Phillips Curve

We develop a semi‐structural model for forecasting inflation in the UK in which the New Keynesian Phillips curve (NKPC) is augmented with a time series model for marginal cost. By combining structural and time series elements we hope to reap the benefits of both approaches, namely the relatively better forecasting performance of time series models in the short run and a theory‐consistent economic interpretation of the forecast coming from the structural model. In our model we consider the hybrid version of the NKPC and use an open‐economy measure of marginal cost. The results suggest that our semi‐structural model performs better than a random‐walk forecast and most of the competing models (conventional time series models and strictly structural models) only in the short run (one quarter ahead) but it is outperformed by some of the competing models at medium and long forecast horizons (four and eight quarters ahead). In addition, the open‐economy specification of our semi‐structural model delivers more accurate forecasts than its closed‐economy alternative at all horizons. Copyright © 2014 John Wiley & Sons, Ltd.     

Long‐memory forecasting of US monetary indices

Several studies have tested for long‐range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long‐memory models as forecast‐generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out‐of‐sample fractional forecasts to benchmark forecasts. The long‐memory parameter is estimated using Robinson's Gaussian semi‐parametric and multivariate log‐periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out‐of‐sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive learning from model space

Dynamic model averaging (DMA) is used extensively for the purpose of economic forecasting. This study extends the framework of DMA by introducing adaptive learning from model space. In the conventional DMA framework all models are estimated independently and hence the information of the other models is left unexploited. In order to exploit the information in the estimation of the individual time‐varying parameter models, this paper proposes not only to average over the forecasts but, in addition, also to dynamically average over the time‐varying parameters. This is done by approximating the mixture of individual posteriors with a single posterior, which is then used in the upcoming period as the prior for each of the individual models. The relevance of this extension is illustrated in three empirical examples involving forecasting US inflation, US consumption expenditures, and forecasting of five major US exchange rate returns. In all applications adaptive learning from model space delivers improvements in out‐of‐sample forecasting performance.     

Forecasting inflation using univariate continuous-time stochastic models

In this paper we investigate the applicability of several continuous-time stochastic models to forecasting inflation rates with horizons out to 20 years. While the models are well known, new methods of parameter estimation and forecasts are supplied, leading to rigorous testing of out-of-sample inflation forecasting at short and long time horizons. Using US consumer price index data we find that over longer forecasting horizons—that is, those beyond 5 years—the log-normal index model having Ornstein–Uhlenbeck drift rate provides the best forecasts.     

Forecasting the 10‐year US Treasury rate

This study compares the performance of two forecasting models of the 10‐year Treasury rate: a random walk (RW) model and an augmented‐autoregressive (A‐A) model which utilizes the information in the expected inflation rate. For 1993–2008, the RW and A‐A forecasts (with different lead times and forecast horizons) are generally unbiased and accurately predict directional change under symmetric loss. However, the A‐A forecasts outperform the RW, suggesting that the expected inflation rate (as a leading indicator) helps improve forecast accuracy. This finding is important since bond market efficiency implies that the RW forecasts are optimal and cannot be improved. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting interest rate swap spreads using domestic and international risk factors: evidence from linear and non‐linear models

This paper explores the ability of factor models to predict the dynamics of US and UK interest rate swap spreads within a linear and a non‐linear framework. We reject linearity for the US and UK swap spreads in favour of a regime‐switching smooth transition vector autoregressive (STVAR) model, where the switching between regimes is controlled by the slope of the US term structure of interest rates. We compare the ability of the STVAR model to predict swap spreads with that of a non‐linear nearest‐neighbours model as well as that of linear AR and VAR models. We find some evidence that the non‐linear models predict better than the linear ones. At short horizons, the nearest‐neighbours (NN) model predicts better than the STVAR model US swap spreads in periods of increasing risk conditions and UK swap spreads in periods of decreasing risk conditions. At long horizons, the STVAR model increases its forecasting ability over the linear models, whereas the NN model does not outperform the rest of the models. Copyright © 2007 John Wiley & Sons, Ltd.     

How successful are dynamic factor models at forecasting output and inflation? A meta‐analytic approach

This paper uses a meta‐analysis to survey existing factor forecast applications for output and inflation and assesses what causes large factor models to perform better or more poorly at forecasting than other models. Our results suggest that factor models tend to outperform small models, whereas factor forecasts are slightly worse than pooled forecasts. Factor models deliver better predictions for US variables than for UK variables, for US output than for euro‐area output and for euro‐area inflation than for US inflation. The size of the dataset from which factors are extracted positively affects the relative factor forecast performance, whereas pre‐selecting the variables included in the dataset did not improve factor forecasts in the past. Finally, the factor estimation technique may matter as well. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models

We evaluate forecasting models of US business fixed investment spending growth over the recent 1995:1–2004:2 out‐of‐sample period. The forecasting models are based on the conventional Accelerator, Neoclassical, Average Q, and Cash‐Flow models of investment spending, as well as real stock prices and excess stock return predictors. The real stock price model typically generates the most accurate forecasts, and forecast‐encompassing tests indicate that this model contains most of the information useful for forecasting investment spending growth relative to the other models at longer horizons. In a robustness check, we also evaluate the forecasting performance of the models over two alternative out‐of‐sample periods: 1975:1–1984:4 and 1985:1–1994:4. A number of different models produce the most accurate forecasts over these alternative out‐of‐sample periods, indicating that while the real stock price model appears particularly useful for forecasting the recent behavior of investment spending growth, it may not continue to perform well in future periods. Copyright © 2007 John Wiley & Sons, Ltd.     

A markup model for forecasting inflation for the euro area

We develop a small model for forecasting inflation for the euro area using quarterly data over the period June 1973 to March 1999. The model is used to provide inflation forecasts from June 1999 to March 2002. We compare the forecasts from our model with those derived from six competing forecasting models, including autoregressions, vector autoregressions and Phillips‐curve based models. A considerable gain in forecasting performance is demonstrated using a relative root mean squared error criterion and the Diebold–Mariano test to make forecast comparisons. Copyright © 2006 John Wiley & Sons, Ltd.     

Choosing among competing econometric forecasts: Regression‐based forecast combination using model selection

Forecast combination based on a model selection approach is discussed and evaluated. In addition, a combination approach based on ex ante predictive ability is outlined. The model selection approach which we examine is based on the use of Schwarz (SIC) or the Akaike (AIC) Information Criteria. Monte Carlo experiments based on combination forecasts constructed using possibly (misspecified) models suggest that the SIC offers a potentially useful combination approach, and that further investigation is warranted. For example, combination forecasts from a simple averaging approach MSE‐dominate SIC combination forecasts less than 25% of the time in most cases, while other ‘standard’ combination approaches fare even worse. Alternative combination approaches are also compared by conducting forecasting experiments using nine US macroeconomic variables. In particular, artificial neural networks (ANN), linear models, and professional forecasts are used to form real‐time forecasts of the variables, and it is shown via a series of experiments that SIC, t‐statistic, and averaging combination approaches dominate various other combination approaches. An additional finding is that while ANN models may not MSE‐dominate simpler linear models, combinations of forecasts from these two models outperform either individual forecast, for a subset of the economic variables examined. Copyright © 2001 John Wiley & Sons, Ltd.     

ARARMA models for time series analysis and forecasting

Methods of time series forecasting are proposed which can be applied automatically. However, they are not rote formulae, since they are based on a flexible philosophy which can provide several models for consideration. In addition it provides diverse diagnostics for qualitatively and quantitatively estimating how well one can forecast a series. The models considered are called ARARMA models (or ARAR models) because the model fitted to a long memory time series (t) is based on sophisticated time series analysis of AR (or ARMA) schemes (short memory models) fitted to residuals Y(t) obtained by parsimonious‘best lag’non-stationary autoregression. Both long range and short range forecasts are provided by an ARARMA model Section 1 explains the philosophy of our approach to time series model identification. Sections 2 and 3 attempt to relate our approach to some standard approaches to forecasting; exponential smoothing methods are developed from the point of view of prediction theory (section 2) and extended (section 3). ARARMA models are introduced (section 4). Methods of ARARMA model fitting are outlined (sections 5,6). Since‘the proof of the pudding is in the eating’, the methods proposed are illustrated (section 7) using the classic example of international airline passengers.     

Forecasting US inflation by Bayesian model averaging

Recent empirical work has considered the prediction of inflation by combining the information in a large number of time series. One such method that has been found to give consistently good results consists of simple equal‐weighted averaging of the forecasts from a large number of different models, each of which is a linear regression relating inflation to a single predictor and a lagged dependent variable. In this paper, I consider using Bayesian model averaging for pseudo out‐of‐sample prediction of US inflation, and find that it generally gives more accurate forecasts than simple equal‐weighted averaging. This superior performance is consistent across subsamples and a number of inflation measures. Copyright © 2008 John Wiley & Sons, Ltd.