Random Walk Forecasts Research Articles

Forecasting the 10‐year US Treasury rate

AbstractThis 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.

Evaluating the Forecasting Performance of Commodity Futures Prices

Commodity futures prices are frequently criticized as being uninformative for forecasting purposes because (1) they seem to do no better than a random walk or an extrapolation of recent trends and (2) futures prices for commodities often trace out a relatively flat trajectory even though global demand is steadily increasing. In this paper, we attempt to shed light on these concerns by discussing the theoretical relationship between spot and futures prices for commodities and by evaluating the empirical forecasting performance of futures prices relative to some alternative benchmarks. The key results of our analysis are that futures prices have generally outperformed a random walk forecast, but not by a large margin, while both futures and a random walk noticeably outperform a simple extrapolation of recent trends (a random walk with drift). Importantly, however, futures prices, on average, outperform a random walk by a considerable margin when there is a sizeable difference between spot and futures prices.

Regressive Oil Price Expectations Toward More Fundamental Values of the Oil Price

SummaryWe use oil price forecasts from the Consensus Economic Forecast poll for the time period Oct. 1989 - Dec. 2008 to analyze how forecasters form their expectations. Our findings indicate that the extrapolative as well as the regressive expectation formation hypothesis play a role. Standard measures of forecast accuracy reveal forecasters’ under performance relative to the random walk benchmark. We test the hypothesis of rational expectations by relying on the criteria of unbiasedness and orthogonality. Although both conditions are met, the forecast accuracy is significantly lower compared to naïve random walk forecast. The forecasters have problems to forecast the trends in the oil price. The recent roller-coaster movements in the international oil market have revealed forecasters’ inability to predict major trends in the spot oil price. As a consequence, some research institutes have stopped forecasting the oil price as an ingredient of their macroeconomic models and use a random walk forecast instead.

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Evaluating random walk forecasts of exchange rates

PurposeThe random walk forecast of exchange rate serves as a standard benchmark for forecast comparison. The purpose of this paper is to assess whether this benchmark is unbiased and directionally accurate under symmetric loss. The focus is on the random walk forecasts of the dollar/euro for 1999‐2007 and the dollar/pound for 1971‐2007.Design/methodology/approachA forecasting framework to generate the one‐ to four‐quarter‐ahead random walk forecasts at varying lead times is designed. This allows to compare forecast accuracy at different lead times and forecast horizons. Using standard evaluation methods, this paper further evaluates these forecasts in terms of unbiasedness and directional accuracy.FindingsThe paper shows that forecast accuracy improves with a reduction in the lead time but deteriorates with an increase in the forecast horizon. More importantly, the random walk forecasts are unbiased and accurately predict directional change under symmetric loss and thus are of value to a user who assigns similar cost to incorrect upward and downward move predictions in the exchange rates.Research limitations/implicationsThe one‐ to four‐quarter‐ahead random walk forecasts evaluated here are for averages of daily figures and not for the (end‐of‐quarter) rates in 3‐, 6‐, 9‐ and 12‐months. Thus, the framework is of value to a market participant who is interested in forecasting quarterly average rates rather than the end‐of‐quarter rates.Originality/valueThe exchange rate forecasting framework presented in this paper allows the evaluation of the random walk forecasts in terms of directional accuracy which (to the best of knowledge) has not been done before.

Inference on forward exchange rate risk premium: reviewing signal extraction methods

The existence of risk premium is thought to be the reason why forward exchange rate is not an unbiased predictor of future spot exchange rate. In this paper we review two methodologies for inferring this unobserved risk premium based upon signal extraction mechanism. One approach relies on the theory of derivatives pricing that relates historical and risk neutral measures via market price of risk. The other approach specifies the risk premium in the historical measure directly. We compare these two methods in predicting future spot exchange rates and contrast these with that of random walk forecast.

New evidence on nominal exchange rate predictability

The Meese–Rogoff puzzle, one of the well-known puzzles in international economics, concerns the weak relationship between nominal exchange rates and market fundamentals. The purpose of this paper is to show that market fundamentals do in fact matter in forecasting nominal exchange rates. In particular, we emphasize the importance of the Harrod–Balassa–Samuelson effect in modeling deviations from purchasing power parity. Based on the post-Bretton Woods period, we provide solid out-of-sample evidence that rejects the random walk forecast model at medium-term and long-term forecast horizons. We also find mild evidence for out-of-sample predictability of nominal exchange rates over the short term.

The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve

The class of functional signal plus noise (FSN) models is introduced that provides a new, general method for modeling and forecasting time series of economic functions. The underlying, continuous economic function (or “signal”) is a natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates (or “y-values”) at the knots of the spline. The natural cubic spline provides flexible cross-sectional fit and results in a linear state-space model. This FSN model achieves dimension reduction, provides a coherent description of the observed yield curve and its dynamics as the cross-sectional dimension N becomes large, and can be feasibly estimated and used for forecasting when N is large. The integration and cointegration properties of the model are derived. The FSN models are then applied to forecasting 36-dimensional yield curves for U.S. Treasury bonds at the 1-month-ahead horizon. The method consistently outperforms the dynamic Nelson–Siegel and random walk forecasts on the basis of both mean squared forecast error criteria and economically relevant loss functions derived from the realized profits of pairs trading algorithms. The analysis also highlights in a concrete setting the dangers of attempting to infer the relative economic value of model forecasts on the basis of their associated mean squared forecast errors.

Forecasting in efficient bond markets: Do experts know better?

Term structure theory suggests that bond rates in efficient markets approximately follow a random walk. We show that the random walk forecasts of 10-year U.S. Treasury and Moody's Aaa corporate bond rates for 1988–2005 are generally unbiased. Blue Chip forecasts, however, are both biased and inferior to random walk forecasts. Both models produce unbiased forecasts of the default spread, with the random walk again outperforming the Blue Chip. In addition, Blue Chip fails to accurately predict directional change. Emphasizing that the success of the random walk model is theoretically expected, we discuss why experts fail to beat random walk predictions.

Forecasting the past: the case of US interest rate forecasts

This study evaluates 10-year US government bond yield forecasts and three-month US Treasury bill rate forecasts for the period between October 1989 and December 2004. In total, 136 forecast time series with approximately 13,800 forecast data were scrutinized, making this the most extensive analysis of interest rate forecasts to date. Not one of the forecast time series proved to be unbiased. In the majority of cases, information from the past was not efficiently integrated into the forecasts. The sign accuracy is significantly better than random walk forecasts in only a very few of the forecast time series. The modified Diebold-Mariano test for forecast encompassing reveals that the information content of most of the forecast time series is lower than that of the naive forecasts, the simple ARIMA models, the implicit forward rates, or average interest rate expectations. The forecasting process is dominated by the present and past market situation.

Bayesian Model Averaging and exchange rate forecasts

Abstract Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3–24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that effectively combine the information in a large number of time series. In this paper, I apply one such method for pooling forecasts from several different models, Bayesian Model Averaging, to the problem of pseudo out-of-sample exchange rate predictions. For most currency–horizon pairs, the Bayesian Model Averaging forecasts using a sufficiently high degree of shrinkage, give slightly smaller out-of-sample mean square prediction error than the random walk benchmark. The forecasts generated by this model averaging methodology are however very close to, but not identical to, those from the random walk forecast.

Bayesian Model Averaging and Exchange Rate Forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff (1983) that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, has never really been overturned despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that combine the information in a large number of time series. One method that has been found to be remarkably useful for out-of-sample prediction is simple averaging of the forecasts of different models. This often seems to work better than the forecasts from any one model. Bayesian Model Averaging is a closely related method that has also been found to be useful for out-of-sample prediction. This starts out with many possible models and prior beliefs about the probability that each model is the true one. It then involves computing the posterior probability that each model is the true one, and averages the forecasts from the different models, weighting them by these posterior probabilities. This is effectively a shrinkage methodology, but with shrinkage over models not just over parameters. I apply this Bayesian Model Averaging approach to pseudo-out-of-sample exchange rate forecasting over the last ten years. I find that it compares quite favorably to a driftless random walk forecast. Depending on the currency-horizon pair, the Bayesian Model Averaging forecasts sometimes do quite a bit better than the random walk benchmark (in terms of mean square prediction error), while they never do much worse. The forecasts generated by this model averaging methodology are however very close to (but not identical to) those from the random walk forecast.

A random walk approach to predicting US 30-year home mortgage rates

Following the implications of term structure theory in an efficient bond market, this study formulates a random walk model that produces unbiased and efficient forecasts of the 30-year mortgage rate for 1987–2006. Forecast accuracy improves with a reduction in lead time but deteriorates with an increase in the forecast horizon. We find, however, no clear trend indicating that forecast accuracy has improved over time. From a more practical perspective, the random walk forecasts of the 30-year mortgage rate and prepayment premium (the spread between 30-year mortgage and 10-year Treasury rates) accurately predict directional change and thus are of value to a user. In exploring the view that the 30-year mortgage rate often moves in tandem with the 10-year Treasury rate, we further find that these rates are cointegrated and thus converge to an equilibrium relation in the long-run.

Consensus vs. Time‐series Forecasts of US 30‐year Home Mortgage Rates

Accurate forecasts of the 30‐year home mortgage rate (HMR) are important to both US housing market participants and policymakers. This study compares the consensus forecasts of the HMR from the Blue Chip panel of experts with two benchmarks: the random walk forecasts (which are basically the most recent HMR available at the time of the survey) and the augmented‐autoregressive (A‐A) forecasts (which contain the past information in both the HMR and trend rate of inflation). For 1992–2005, the Blue Chip forecasts are unbiased and accurately predict directional change at the shorter but not longer forecast horizons. The random walk and A‐A forecasts, in addition to outperforming the Blue Chip, are unbiased and accurately predict directional change at all forecast horizons. Further findings indicate that the A‐A forecasts encompass those of the random walk, implying that the predictive information in the trend rate of inflation helps improve forecast accuracy. Therefore, one with access to these HMR forecasts would clearly prefer the A‐A over the Blue Chip and random walk forecasts in decision‐making.

The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve

The class of Functional Signal plus Noise (FSN) models is introduced that provides a new, general method for modelling and forecasting time series of economic functions. The underlying, continuous economic function (or `signal') is a natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates (or 'y-values') at the knots of the spline. The natural cubic spline provides flexible cross-sectional fit and results in a linear, state space model. This FSN model achieves dimension reduction, provides a coherent description of the observed yield curve and its dynamics as the cross-sectional dimension N becomes large, and can feasibly be estimated and used for forecasting when N is large. The integration and cointegration properties of the model are derived. The FSN models are then applied to forecasting 36-dimensional yield curves for US Treasury bonds at the one month ahead horizon. The method consistently outperforms the Diebold and Li (2006) and random walk forecasts on the basis of both mean square forecast error criteria and economically relevant loss functions derived from the realised profits of pairs trading algorithms. The analysis also highlights in a concrete setting the dangers of attempts to infer the relative economic value of model forecasts on the basis of their associated mean square forecast errors.

Beating the Random Walk: A Performance Assessment of Long-Term Interest Rate Forecasts

This paper assesses the performance of a number of long-term interest rate forecast approaches, namely time series models, structural economic models, expert forecasts and combinations thereof. The predictive performance of these approaches is compared using out of sample forecast errors, where a random walk forecast acts as benchmark. It is found that for five major OECD countries, namely United States, Germany, United Kingdom, The Netherlands and Japan, the other forecasting approaches do not outperform the random walk, or a somewhat more sophisticated time series model, on a 3 month forecast horizon. On a 12 month forecast horizon the random walk model can be outperformed by a model that combines economic data and expert forecasts. Here several methods of combination are considered: equal weights, optimized weights and weights based on forecast error. It appears that the additional information contents of the structural models and expert knowledge is only relevant for forecasting 12 months ahead.

Forecasting Euro Exchange Rates: How Much Does Model Averaging Help?

We analyze the performance of Bayesian model averaged exchange rate forecasts for euro/US dollar, euro/Japanese yen, euro/Swiss franc and euro/ British pound rates using weights based on the out-of-sample predictive likelihood. The paper also presents a simple stratified sampling procedure in the spirit of Sala i Martin et alia (2004) to obtain model weights based on predictive accuracy. Our results indicate that accounting explicitly for model uncertainty when constructing predictions of euro exchange rates leads to improvements in predictive accuracy as measured by the mean square forecast error. While the forecasting error of the combined forecast tends to be systematically smaller than that of the individual model that would have been chosen based on predictive accuracy in a test sample, random walk forecasts cannot be beaten significantly in terms of squared forecast errors. Direction of change statistics, on the other hand, are significantly improved by Bayesian model averaging.

Conventional and unconventional approaches to exchange rate modelling and assessment

AbstractWe examine the relative predictive power of the sticky price monetary model, uncovered interest parity, and a transformation of net exports and net foreign assets. In addition to bringing Gourinchas and Rey's new approach and more recent data to bear, we implement the Clark–West procedure for testing the significance of out‐of‐sample forecasts. The interest rate parity relation holds better at long horizons and the net exports variable does well in predicting exchange rates at short horizons in sample. In out‐of‐sample forecasts, we find evidence that our proxy for Gourinchas and Rey's measure of external imbalances outperforms a random walk at short horizons as do some of the other models, although no single model uniformly beats the random walk forecast. Copyright © 2007 John Wiley & Sons, Ltd.

An evaluation of professional forecasts of US corporate profits

We show that the one-year-ahead forecast of growth in US corporate profits from the Survey of Professional Forecasters, for 1983–2004, is unbiased and superior to the random walk forecast. Survey respondents, however, generally predicted positive growth and thus failed to accurately predict negative growth in corporate profits. This bias may be due to respondents assigning asymmetric costs to incorrect positive and negative growth predictions.

Using forecasts of forecasters to forecast

Quantification techniques are popular methods in empirical research for aggregating the qualitative predictions at the micro-level into a single figure. In this paper, we analyze the forecasting performance of various methods that are based on the qualitative predictions of financial experts for major financial variables and macroeconomic aggregates. Based on the Centre of European Economic Research's Financial Markets Survey, a monthly qualitative survey of around 330 financial experts, we analyze the out-of-sample predictive quality of probability methods and regression methods.Using the modified Diebold–Mariano test of Harvey, Leybourne and Newbold (Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13, 281–291.), we compare the forecasts based on survey methods with the forecasting performance of standard linear time series approaches and simple random walk forecasts.