Forecast Evaluation of Nonlinear Models: The Case of Long‐Span Real Exchange Rates

This paper deals with the nonlinear modeling and forecasting of the dollar–sterling and franc–sterling real exchange rates using long spans of data. Our contribution is threefold. First, we provide significant evidence of smooth transition dynamics in the series by employing a battery of recently developed in‐sample statistical tests. Second, we investigate the small‐sample properties of several evaluation measures for comparing recursive forecasts when one of the competing models is nonlinear. Finally, we run a forecasting race for the post‐Bretton Woods era between the nonlinear real exchange rate model, the random walk, and the linear autoregressive model. The nonlinear model outperforms all rival models in the dollar–sterling case but cannot beat the linear autoregressive in the franc–sterling. Copyright © 2011 John Wiley & Sons, Ltd.     

Why do regime‐switching models forecast so badly?

Most non‐linear techniques give good in‐sample fits to exchange rate data but are usually outperformed by random walks or random walks with drift when used for out‐of‐sample forecasting. In the case of regime‐switching models it is possible to understand why forecasts based on the true model can have higher mean squared error than those of a random walk or random walk with drift. In this paper we provide some analytical results for the case of a simple switching model, the segmented trend model. It requires only a small misclassification, when forecasting which regime the world will be in, to lose any advantage from knowing the correct model specification. To illustrate this we discuss some results for the DM/dollar exchange rate. We conjecture that the forecasting result is more general and describes limitations to the use of switching models for forecasting. This result has two implications. First, it questions the leading role of the random walk hypothesis for the spot exchange rate. Second, it suggests that the mean square error is not an appropriate way to evaluate forecast performance for non‐linear models. Copyright © 1999 John Wiley & Sons, Ltd.     

Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory

This paper presents an autoregressive fractionally integrated moving‐average (ARFIMA) model of nominal exchange rates and compares its forecasting capability with the monetary structural models and the random walk model. Monthly observations are used for Canada, France, Germany, Italy, Japan and the United Kingdom for the period of April 1973 through December 1998. The estimation method is Sowell's (1992) exact maximum likelihood estimation. The forecasting accuracy of the long‐memory model is formally compared to the random walk and the monetary models, using the recently developed Harvey, Leybourne and Newbold (1997) test statistics. The results show that the long‐memory model is more efficient than the random walk model in steps‐ahead forecasts beyond 1 month for most currencies and more efficient than the monetary models in multi‐step‐ahead forecasts. This new finding strongly suggests that the long‐memory model of nominal exchange rates be studied as a viable alternative to the conventional models. Copyright © 2006 John Wiley & Sons, Ltd.     

Google Trends and the forecasting performance of exchange rate models

In this paper, we use Google Trends data for exchange rate forecasting in the context of a broad literature review that ties the exchange rate movements with macroeconomic fundamentals. The sample covers 11 OECD countries’ exchange rates for the period from January 2004 to June 2014. In out‐of‐sample forecasting of monthly returns on exchange rates, our findings indicate that the Google Trends search query data do a better job than the structural models in predicting the true direction of changes in nominal exchange rates. We also observed that Google Trends‐based forecasts are better at picking up the direction of the changes in the monthly nominal exchange rates after the Great Recession era (2008–2009). Based on the Clark and West inference procedure of equal predictive accuracy testing, we found that the relative performance of Google Trends‐based exchange rate predictions against the null of a random walk model is no worse than the purchasing power parity model. On the other hand, although the monetary model fundamentals could beat the random walk null only in one out of 11 currency pairs, with Google Trends predictors we found evidence of better performance for five currency pairs. We believe that these findings necessitate further research in this area to investigate the extravalue one can get from Google search query data.     

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.     

Structural,VAR and BVAR models of exchange rate determination: A comparison of their forecasting performance

This paper compares the out-of-sample forecasting accuracy of a wide class of structural, BVAR and VAR models for major sterling exchange rates over different forecast horizons. As representative structural models we employ a portfolio balance model and a modified uncovered interest parity model, with the latter producing the more accurate forecasts. Proper attention to the long-run properties and the short-run dynamics of structural models can improve on the forecasting performance of the random walk model. The structural model shows substantial improvement in medium-term forecasting accuracy, whereas the BVAR model is the more accurate in the short term. BVAR and VAR models in levels strongly out predict these models formulated in difference form at all forecast horizons.     

Non‐linear,non‐parametric,non‐fundamental exchange rate forecasting

This paper employs a non‐parametric method to forecast high‐frequency Canadian/US dollar exchange rate. The introduction of a microstructure variable, order flow, substantially improves the predictive power of both linear and non‐linear models. The non‐linear models outperform random walk and linear models based on a number of recursive out‐of‐sample forecasts. Two main criteria that are applied to evaluate model performance are root mean squared error (RMSE) and the ability to predict the direction of exchange rate moves. The artificial neural network (ANN) model is consistently better in RMSE to random walk and linear models for the various out‐of‐sample set sizes. Moreover, ANN performs better than other models in terms of percentage of correctly predicted exchange rate changes. The empirical results suggest that optimal ANN architecture is superior to random walk and any linear competing model for high‐frequency exchange rate forecasting. Copyright © 2006 John Wiley & Sons, Ltd.     

Conditional predictability of daily exchange rates

At what forecast horizon is one time series more predictable than another? This paper applies the Diebold–Kilian conditional predictability measure to assess the out‐of‐sample performance of three alternative models of daily GBP/USD and DEM/USD exchange rate returns. Predictability is defined as a non‐linear statistic of a model's relative expected losses at short and long forecast horizons, allowing flexible choice of both the estimation procedure and loss function. The long horizon is set to 2 weeks and one month ahead and forecasts evaluated according to MSE loss. Bootstrap methodology is used to estimate the data's conditional predictability using GARCH models. This is then compared to predictability under a random walk and a model using the prediction bias in uncovered interest parity (UIP). We find that both exchange rates are less predictable using GARCH than using a random walk, but they are more predictable using UIP than a random walk. Predictability using GARCH is relatively higher for the 2‐weeks‐than for the 1‐month long forecast horizon. Comparing the results using a random walk to that using UIP reveals ‘pockets’ of predictability, that is, particular short horizons for which predictability using the random walk exceeds that using UIP, or vice versa. Overall, GBP/USD returns appear more predictable than DEM/USD returns at short horizons. Copyright © 2002 John Wiley & Sons, Ltd.     

Forecasting the price of crude oil via convenience yield predictions

The paper develops an oil price forecasting technique which is based on the present value model of rational commodity pricing. The approach suggests shifting the forecasting problem to the marginal convenience yield, which can be derived from the cost‐of‐carry relationship. In a recursive out‐of‐sample analysis, forecast accuracy at horizons within one year is checked by the root mean squared error as well as the mean error and the frequency of a correct direction‐of‐change prediction. For all criteria employed, the proposed forecasting tool outperforms the approach of using futures prices as direct predictors of future spot prices. Vis‐à‐vis the random‐walk model, it does not significantly improve forecast accuracy but provides valuable statements on the direction of change. Copyright © 2007 John Wiley & Sons, Ltd.     

Beating the random walk in Central and Eastern Europe

We compare the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian error correction (BVEC) models in forecasting the exchange rates of five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Slovak Koruna, Slovenian Tolar and Polish Zloty) against the US Dollar and the Euro. Although these models tend to outperform the random walk model for long‐term predictions (6 months ahead and beyond), even the best models in terms of average prediction error fail to reject the test of equality of forecasting accuracy against the random walk model in short‐term predictions. Copyright © 2005 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.     

A threshold model for the French franc/deutschmark exchange rate

The behaviour of the French franc/deutschmark exchange rate is examined in this paper. During the time period studied, these currencies were constrained to lie within prescribed bands relative to one another and the usual random walk explanation of the exchange rate may not be appropriate. The data are examined for evidence of non-linear structure and it is shown that a piecewise linear SETAR model provides a better explanation and superior forecasting performance than a random walk.     

Forecasting the dollar/euro exchange rate: are international parities useful?

In this paper we assess the empirical relevance of an expectations version of purchasing power parity in forecasting the dollar/euro exchange rate. This version is based on the differential of inflation expectations derived from inflation‐indexed bonds for the euro area and the USA. Using the longest daily data for both the dollar/euro exchange rate and for the inflation expectations, our results suggest that, with few exceptions, our predictors behave significantly better than a random walk in forecasts up to five days, both in terms of prediction errors and in directional forecasts. Copyright © 2005 John Wiley & Sons, Ltd.     

Intrinsic bubbles revisited: evidence from nonlinear cointegration and forecasting

This paper offers strong further empirical evidence to support the intrinsic bubble model of stock prices, developed by Froot and Obstfeld (American Economic Review, 1991), in two ways. First, our results suggest that there is a long‐run nonlinear relationship between stock prices and dividends for the US stock market during the period 1871–1996. Second, we find that the out‐of‐sample forecasting performance of the intrinsic bubbles model is significantly better than the performance of two alternatives, namely the random walk and the rational bubbles model. Copyright © 2004 John Wiley & Sons, Ltd.     

Do Long‐Run Theory Restrictions Help in Forecasting?

Do long‐run equilibrium relations suggested by economic theory help to improve the forecasting performance of a cointegrated vector error correction model (VECM)? In this paper we try to answer this question in the context of a two‐country model developed for the Canadian and US economies. We compare the forecasting performance of the exactly identified cointegrated VECMs to the performance of the over‐identified VECMs with the long‐run theory restrictions imposed. We allow for model uncertainty and conduct this comparison for every possible combination of the cointegration ranks of the Canadian and US models. We show that the over‐identified structural cointegrated models generally outperform the exactly identified models in forecasting Canadian macroeconomic variables. We also show that the pooled forecasts generated from the over‐identified models beat most of the individual exactly identified and over‐identified models as well as the VARs in levels and in differences. Copyright © 2011 John Wiley & Sons, Ltd.     

A New‐Keynesian DSGE model for forecasting the South African economy

This paper develops a New‐Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model for forecasting the growth rate of output, inflation, and the nominal short‐term interest rate (91 days Treasury Bill rate) for the South African economy. The model is estimated via maximum likelihood technique for quarterly data over the period of 1970:1–2000:4. Based on a recursive estimation using the Kalman filter algorithm, out‐of‐sample forecasts from the NKDSGE model are compared with forecasts generated from the classical and Bayesian variants of vector autoregression (VAR) models for the period 2001:1–2006:4. The results indicate that in terms of out‐of‐sample forecasting, the NKDSGE model outperforms both the classical and Bayesian VARs for inflation, but not for output growth and nominal short‐term interest rate. However, differences in RMSEs are not significant across the models. Copyright © 2008 John Wiley & Sons, Ltd.     

Direction‐of‐Change Financial Time Series Forecasting using a Similarity‐Based Classification Model

A similarity‐based classification model is proposed whereby densities of positive and negative returns in a delay‐embedded input space are estimated from a graphical representation of the data using an eigenvector centrality measure, and subsequently combined under Bayes' theorem to predict the probability of upward/downward movements. Application to directional forecasting of the daily close price of the Dow Jones Industrial Average over a 20‐year out‐of‐sample period yields performance superior to random walk and logistic regression models, and on a par with that of multilayer perceptrons. A feature of the classifier is that it is parameter free, parameters entering the model only via the measure used to determine pairwise similarity between data points. This allows intuitions about the nature of time series to be elegantly integrated into the model. The recursive nature of eigenvector centrality makes it better able to deal with sparsely populated input spaces than conventional approaches based on density estimation. Copyright © 2013 John Wiley & Sons, Ltd.     

Predicting crypto‐currencies using sparse non‐Gaussian state space models

In this paper we forecast daily returns of crypto‐currencies using a wide variety of different econometric models. To capture salient features commonly observed in financial time series like rapid changes in the conditional variance, non‐normality of the measurement errors and sharply increasing trends, we develop a time‐varying parameter VAR with t‐distributed measurement errors and stochastic volatility. To control for overparametrization, we rely on the Bayesian literature on shrinkage priors, which enables us to shrink coefficients associated with irrelevant predictors and/or perform model specification in a flexible manner. Using around one year of daily data, we perform a real‐time forecasting exercise and investigate whether any of the proposed models is able to outperform the naive random walk benchmark. To assess the economic relevance of the forecasting gains produced by the proposed models we, moreover, run a simple trading exercise.     

Term Structure Forecasting of Government Bond Yields with Latent and Macroeconomic Factors: Do Macroeconomic Factors Imply Better Out‐of‐Sample Forecasts?

This study empirically examines the role of macroeconomic and stock market variables in the dynamic Nelson–Siegel framework with the purpose of fitting and forecasting the term structure of interest rate on the Japanese government bond market. The Nelson–Siegel type models in state‐space framework considerably outperform the benchmark simple time series forecast models such as an AR(1) and a random walk. The yields‐macro model incorporating macroeconomic factors leads to a better in‐sample fit of the term structure than the yields‐only model. The out‐of‐sample predictability of the former for short‐horizon forecasts is superior to the latter for all maturities examined in this study, and for longer horizons the former is still compatible to the latter. Inclusion of macroeconomic factors can dramatically reduce the autocorrelation of forecast errors, which has been a common phenomenon of statistical analysis in previous term structure models. Copyright © 2013 John Wiley & Sons, Ltd.     

Scalar BEKK and indirect DCC

The paper derives the scalar special case of the well‐known BEKK multivariate GARCH model using a multivariate extension of the random coefficient autoregressive (RCA) model. This representation establishes the relevant structural and asymptotic properties of the scalar BEKK model using the theoretical results available in the literature for general multivariate GARCH. Sufficient conditions for the (direct) DCC model to be consistent with a scalar BEKK representation are established. Moreover, an indirect DCC model that is consistent with the scalar BEKK representation is obtained, and is compared with the direct DCC model using an empirical example. The paper shows, within an asset allocation and risk measurement framework, that the two models are similar in terms of providing parameter estimates and forecasting value‐at‐risk thresholds for equally weighted and minimum variance portfolios. Copyright © 2008 John Wiley & Sons, Ltd.