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.     

Combination forecasts of output growth in a seven‐country data set

This paper uses forecast combination methods to forecast output growth in a seven‐country quarterly economic data set covering 1959–1999, with up to 73 predictors per country. Although the forecasts based on individual predictors are unstable over time and across countries, and on average perform worse than an autoregressive benchmark, the combination forecasts often improve upon autoregressive forecasts. Despite the unstable performance of the constituent forecasts, the most successful combination forecasts, like the mean, are the least sensitive to the recent performance of the individual forecasts. While consistent with other evidence on the success of simple combination forecasts, this finding is difficult to explain using the theory of combination forecasting in a stationary environment. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Yield curve forecast combinations based on bond portfolio performance

We propose an economically motivated forecast combination strategy in which model weights are related to portfolio returns obtained by a given forecast model. An empirical application based on an optimal mean–variance bond portfolio problem is used to highlight the advantages of the proposed approach with respect to combination methods based on statistical measures of forecast accuracy. We compute average net excess returns, standard deviation, and the Sharpe ratio of bond portfolios obtained with nine alternative yield curve specifications, as well as with 12 different forecast combination strategies. Return‐based forecast combination schemes clearly outperformed approaches based on statistical measures of forecast accuracy in terms of economic criteria. Moreover, return‐based approaches that dynamically select only the model with highest weight each period and discard all other models delivered even better results, evidencing not only the advantages of trimming forecast combinations but also the ability of the proposed approach to detect best‐performing models. To analyze the robustness of our results, different levels of risk aversion and a different dataset are considered.     

Out‐of‐sample equity premium prediction: A scenario analysis approach

We propose two methods of equity premium prediction with single and multiple predictors respectively and evaluate their out‐of‐sample performance using US stock data with 15 popular predictors for equity premium prediction. The first method defines three scenarios in terms of the expected returns under the scenarios and assumes a Markov chain governing the occurrence of the scenarios over time. It employs predictive quantile regressions of excess return on a predictor for three quantiles to estimate the occurrence of the scenarios over an in‐sample period and the transition probabilities of the Markov chain, predicts the expected returns under the scenarios, and generates an equity premium forecast by combining the predicted expected returns under three scenarios with the estimated transition probabilities. The second method generates an equity premium forecast by combining the individual forecasts from the first method across all predictors. For most of predictors, the first method outperforms the benchmark method of historical average and the traditional predictive linear regression with a single predictor both statistically and economically, and the second method consistently performs better than several competing methods used in the literature. The performance of our methods is further examined under different scenarios and economic conditions, and is robust for two different out‐of‐sample periods and specifications of the scenarios.     

On forecasting counts

Forecasting for a time series of low counts, such as forecasting the number of patents to be awarded to an industry, is an important research topic in socio‐economic sectors. Recently (2004), Freeland and McCabe introduced a Gaussian type stationary correlation model‐based forecasting which appears to work well for the stationary time series of low counts. In practice, however, it may happen that the time series of counts will be non‐stationary and also the series may contain over‐dispersed counts. To develop the forecasting functions for this type of non‐stationary over‐dispersed data, the paper provides an extension of the stationary correlation models for Poisson counts to the non‐stationary correlation models for negative binomial counts. The forecasting methodology appears to work well, for example, for a US time series of polio counts, whereas the existing Bayesian methods of forecasting appear to encounter serious convergence problems. Further, a simulation study is conducted to examine the performance of the proposed forecasting functions, which appear to work well irrespective of whether the time series contains small or large counts. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Mixed‐Frequency Time Series with ECM‐MIDAS Models

This paper proposes a mixed‐frequency error correction model for possibly cointegrated non‐stationary time series sampled at different frequencies. We highlight the impact, in terms of model specification, of the choice of the particular high‐frequency explanatory variable to be included in the cointegrating relationship, which we call a dynamic mixed‐frequency cointegrating relationship. The forecasting performance of aggregated models and several mixed‐frequency regressions are compared in a set of Monte Carlo experiments. In particular, we look at both the unrestricted mixed‐frequency model and at a more parsimonious MIDAS regression. Whereas the existing literature has only investigated the potential improvements of the MIDAS framework for stationary time series, our study emphasizes the need to include the relevant cointegrating vectors in the non‐stationary case. Furthermore, it is illustrated that the choice of dynamic mixed‐frequency cointegrating relationship does not matter as long as the short‐run dynamics are adapted accordingly. Finally, the unrestricted model is shown to suffer from parameter proliferation for samples of relatively small size, whereas MIDAS forecasts are robust to over‐parameterization. We illustrate our results for the US inflation rate. Copyright © 2014 John Wiley & Sons, Ltd.     

The impact of measurement errors on ARMA prediction

Measurement errors can have dramatic impact on the outcome of empirical analysis. In this article we quantify the effects that they can have on predictions generated from ARMA processes. Lower and upper bounds are derived for differences in minimum mean squared prediction errors (MMSE) for forecasts generated from data with and without errors. The impact that measurement errors have on MMSE and other relative measures of forecast accuracy are presented for a variety of model structures and parameterizations. Based on these results the need to set up the models in state space form to extract the signal component appears to depend upon whether processes are nearly non‐invertible or non‐stationary or whether the noise‐to‐signal ratio is very high. Copyright © 1999 John Wiley & Sons, Ltd.     

Filters for short non‐stationary sequences

This paper describes a methodology for implementing bidirectional frequency‐selective filters in cases where the data sequence is short and non‐stationary. A simple method is proposed for dealing with the start‐up problem. The method has a firm theoretical basis and it is computationally efficient. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting Volatility with Many Predictors

This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.     

The use of encompassing tests for forecast combinations

This paper proposes an algorithm that uses forecast encompassing tests for combining forecasts when there are a large number of forecasts that might enter the combination. The algorithm excludes a forecast from the combination if it is encompassed by another forecast. To assess the usefulness of this approach, an extensive empirical analysis is undertaken using a US macroeconomic dataset. The results are encouraging; the algorithm forecasts outperform benchmark model forecasts, in a mean square error (MSE) sense, in a majority of cases. The paper also compares the empirical performance of different approaches to forecast combination, and provides a rule‐of‐thumb cut‐off point for the thick‐modeling approach. Copyright © 2009 John Wiley & Sons, Ltd.     

The accuracy of IMF and OECD forecasts for G7 countries

This paper analyses the size and nature of the errors in GDP forecasts in the G7 countries from 1971 to 1995. These GDP short‐term forecasts are produced by the Organization for Economic Cooperation and Development and by the International Monetary Fund, and published twice a year in the Economic Outlook and in the World Economic Outlook, respectively. The evaluation of the accuracy of the forecasts is based on the properties of the difference between the realization and the forecast. A forecast is considered to be accurate if it is unbiased and efficient. A forecast is unbiased if its average deviation from the outcome is zero, and it is efficient if it reflects all the information that is available at the time the forecast is made. Finally, we also examine tests of directional accuracy and offer a non‐parametric method of assessment. Copyright © 2000 John Wiley & Sons, Ltd.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

Combining expert‐adjusted forecasts

It is well known that a combination of model‐based forecasts can improve upon each of the individual constituent forecasts. Most forecasts available in practice are, however, not purely based on econometric models but entail adjustments, where experts with domain‐specific knowledge modify the original model forecasts. There is much evidence that expert‐adjusted forecasts do not necessarily improve the pure model‐based forecasts. In this paper we show, however, that combined expert‐adjusted model forecasts can improve on combined model forecasts, in the case when the individual expert‐adjusted forecasts are not better than their associated model‐based forecasts. We discuss various implications of this finding.     

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.     

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.     

Forecast Combination for Euro Area Inflation: A Cure in Times of Crisis?

The period of extraordinary volatility in euro area headline inflation starting in 2007 raised the question whether forecast combination methods can be used to hedge against bad forecast performance of single models during such periods and provide more robust forecasts. We investigate this issue for forecasts from a range of short‐term forecasting models. Our analysis shows that there is considerable variation of the relative performance of the different models over time. To take that into account we suggest employing performance‐based forecast combination methods—in particular, one with more weight on the recent forecast performance. We compare such an approach with equal forecast combination that has been found to outperform more sophisticated forecast combination methods in the past, and investigate whether it can improve forecast accuracy over the single best model. The time‐varying weights assign weights to the economic interpretations of the forecast stemming from different models. We also include a number of benchmark models in our analysis. The combination methods are evaluated for HICP headline inflation and HICP excluding food and energy. We investigate how forecast accuracy of the combination methods differs between pre‐crisis times, the period after the global financial crisis and the full evaluation period, including the global financial crisis with its extraordinary volatility in inflation. Overall, we find that forecast combination helps hedge against bad forecast performance and that performance‐based weighting outperforms simple averaging. Copyright © 2017 John Wiley & Sons, Ltd.     

A comparison between linear and nonlinear forecasts for nonlinear AR models

In this paper the relative forecast performance of nonlinear models to linear models is assessed by the conditional probability that the absolute forecast error of the nonlinear forecast is smaller than that of the linear forecast. The comparison probability is explicitly expressed and is shown to be an increasing function of the distance between nonlinear and linear forecasts under certain conditions. This expression of the comparison probability may not only be useful in determining the predictor, which is either a more accurate or a simpler forecast, to be used but also provides a good explanation for an odd phenomenon discussed by Pemberton. The relative forecast performance of a nonlinear model to a linear model is demonstrated to be sensitive to its forecast origins. A new forecast is thus proposed to improve the relative forecast performance of nonlinear models based on forecast origins. © 1997 John Wiley & Sons, Ltd.     

Optimal sampling frequency for volatility forecast models for the Indian stock markets

This paper evaluates the performance of conditional variance models using high‐frequency data of the National Stock Index (S&P CNX NIFTY) and attempts to determine the optimal sampling frequency for the best daily volatility forecast. A linear combination of the realized volatilities calculated at two different frequencies is used as benchmark to evaluate the volatility forecasting ability of the conditional variance models (GARCH (1, 1)) at different sampling frequencies. From the analysis, it is found that sampling at 30 minutes gives the best forecast for daily volatility. The forecasting ability of these models is deteriorated, however, by the non‐normal property of mean adjusted returns, which is an assumption in conditional variance models. Nevertheless, the optimum frequency remained the same even in the case of different models (EGARCH and PARCH) and different error distribution (generalized error distribution, GED) where the error is reduced to a certain extent by incorporating the asymmetric effect on volatility. Our analysis also suggests that GARCH models with GED innovations or EGRACH and PARCH models would give better estimates of volatility with lower forecast error estimates. Copyright © 2008 John Wiley & Sons, Ltd.     

Bootstrap prediction bands for forecast paths from vector autoregressive models

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non‐Bayesian approaches use either asymptotic approximations or bootstrapping to evaluate the uncertainty associated with the forecast. The practice in the empirical literature has been to assess the uncertainty of multi‐step forecasts by connecting the intervals constructed for individual forecast periods. This paper proposes a bootstrap method of constructing prediction bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications using an optimization procedure to find the envelope of the most concentrated paths. From extensive Monte Carlo study, it is found that the proposed method provides more accurate assessment of predictive uncertainty from the vector autoregressive model than its competitors. Copyright © 2010 John Wiley & Sons, Ltd.