Random Walk Forecasts Research Articles

Forecasting the Nominal Brent Oil Price with VARs-One Model Fits All?

We carry out an ex post assessment of popular models used to forecast oil prices and propose a host of alternative VAR models based on traditional global macroeconomic and oil market aggregates. While the exact specification of VAR models for nominal oil price prediction is still open to debate, the bias and underprediction in futures and random walk forecasts are larger across all horizons in relation to a large set of VAR specifications. The VAR forecasts generally have the smallest average forecast errors and the highest accuracy, with most specifications outperforming futures and random walk forecasts for horizons up to two years. This calls for caution in reliance on futures or the random walk for forecasting, particularly for near term predictions. Despite the overall strength of VAR models, we highlight some performance instability, with small alterations in specifications, subsamples or lag lengths providing widely different forecasts at times. Combining futures, random walk and VAR models for forecasting have merit for medium term horizons.

Forecasting the Nominal Brent Oil Price with VARs-One Model Fits All?

We carry out an ex post assessment of popular models used to forecast oil prices and propose a host of alternative VAR models based on traditional global macroeconomic and oil market aggregates. While the exact specification of VAR models for nominal oil price prediction is still open to debate, the bias and underprediction in futures and random walk forecasts are larger across all horizons in relation to a large set of VAR specifications. The VAR forecasts generally have the smallest average forecast errors and the highest accuracy, with most specifications outperforming futures and random walk forecasts for horizons up to two years. This calls for caution in reliance on futures or the random walk for forecasting, particularly for near term predictions. Despite the overall strength of VAR models, we highlight some performance instability, with small alterations in specifications, subsamples or lag lengths providing widely different forecasts at times. Combining futures, random walk and VAR models for forecasting have merit for medium term horizons.

Fast Kalman filter using hierarchical matrices and a low-rank perturbative approach

We develop a fast algorithm for a Kalman filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time step as a weighted sum of two contributions—the process noise covariance matrix and a low-rank term computed from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the preceding terms and the computation of eigenmodes of the generalized eigenvalue problem. The resulting algorithm for the Kalman filter with a random walk forecast model scales as in memory and in computational cost, where N is the number of grid points. We show how to efficiently compute measures of uncertainty and conditional realizations from the state distribution at each time step. An extension to the case with nonlinear measurement operators is also discussed. Numerical experiments demonstrate the performance of our algorithms, which are applied to a synthetic example from monitoring CO2 in the subsurface using travel-time tomography.

On the accuracy of Blue Chip forecasts of interest rates and country risk premiums

We examine the accuracy of Blue Chip forecasts of short- and long-term interest rates and country risk premiums for the Eurozone and six other industrial countries for 1999–2008. In so doing, we utilize comparable random walk forecasts as benchmarks. Consistent with the efficient market hypothesis, the long-term interest rate forecasts fail to outperform the random walk. Our findings on the accuracy of short-term interest rate forecasts are, however, mixed. Further results reveal that Blue Chip is more (less) accurate in predicting country risk premiums associated with short-term (long-term) interest rates. Such evidence is reasonable since the short-term country risk premiums contain only the perceived default risk, while the long-term risk premiums, in addition, can contain the perceived inflation and exchange rate differentials.

Is it Possible to Beat the Random Walk Model in Exchange Rate Forecasting? More Evidence for the Brazilian Case

The seminal study of Meese and Rogoff (1983) on exchange rate forecastability had a great impact on the international finance literature. The authors showed that exchange rate forecasts based on structural models are worse than a naive random walk. This result is known as the Meese-Rogoff (MR) puzzle. Although the validity of this result has been checked for many currencies, studies for the Brazilian currency are not common. In 1999, Brazil adopted the dirty floating exchange rate regime. The country is one of the most dynamic emerging market economies. Rossi (2013) ran an extensive study on the MR puzzle but did not analyse Brazilian data. Our goal is to run a “pseudo real-time experiment” to investigate whether forecasts based on econometric models that use the fundamentals suggested by the exchange rate monetary theory of the 80s can beat the random model for the case of the Brazilian currency. Our work has three main differences with respect to Rossi (2013). We use a bias correction technique and forecast combination in an attempt to improve the forecast accuracy of our projections. We also combine the random walk projections with the projections of the structural models to investigate if it is possible to further improve the accuracy of the random walk forecasts. However, our results are quite in line with Rossi (2013). We show that it is not difficult to beat the forecasts generated by the random walk with drift using Brazilian data, but that it is quite difficult to beat the random walk without drift. Our results suggest that it is advisable to use the random walk without drift, not only the random walk with drift, as a benchmark in exercises that claim the MR result is not valid.

Arbitrage-Free Prediction of the Implied Volatility Smile

This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to n strikes (with n large, e.g. n ≥ 40) and the same maturity, is a difficult task due to the fact that option prices at any moment in time satisfy non-linear and non-explicit no-arbitrage restrictions. Hence any n-dimensional time series model also has to satisfy these implicit restrictions at each time step, a condition that is impossible to meet since the model innovations can take arbitrary values. We solve this problem for any n ∈ N in the context of Foreign Exchange (FX) by first encoding the option prices at each time step in terms of the parameters of the corresponding risk-neutral measure and then performing the time series analysis in the parameter space. The option price predictions are obtained from the predicted risk neutral measure by effectively integrating it against the corresponding option payoffs. The non-linear transformation between option prices and the risk-neutral parameters applied here is not arbitrary: it is the standard mapping used by market makers in the FX option markets (the SABR parameterisation) and is given explicitly in closed form. Our method is not restricted to the FX asset class nor does it depend on the type of parameterisation used. Statistical analysis of FX market data illustrates that our arbitrage-free predictions outperform the naive random walk forecasts, suggesting a potential for building management strategies for portfolios of derivative products, akin to the ones widely used in the underlying equity and futures markets.

Adaptive learning and survey data

This paper investigates the ability of the adaptive learning approach to replicate the expectations of professional forecasters. For a range of macroeconomic and financial variables, we compare constant and decreasing gain learning models to simple, yet powerful benchmark models. We find that constant gain models provide a better fit for the expectations of professional forecasters. For macroeconomic series they usually perform significantly better than a naïve random walk forecast. In contrast, we find it difficult to beat the no-change benchmark using the adaptive learning models to forecast financial variables.

Inflation expectations and energy price forecasting

AbstractIn this study, we ask whether US consumers' inflation expectations provide useful information for accurately predicting the direction of change in energy prices. As such, we set up a forecasting model to generate the one‐, two‐ and three‐quarter‐ahead random walk forecasts of crude oil, gasoline and heating oil prices. For the period 1987–2012, our test results reveal that the forecasts are free of systematic bias and thus imply symmetric loss. Also, they are generally efficient, where efficiency means the forecast error is uncorrelated with its own past values. The random walk forecast errors are, however, correlated with the change in inflation expectations (measured by the data from the Michigan Surveys of Consumers). Thus, we conclude such expectations may contain useful predictive information for crude oil, gasoline and heating oil prices. Consistent with this conclusion, we show that the change in inflation expectations accurately predicts the direction of change in such energy prices for 1987–2012.

Adaptive Learning and Survey Data

This paper investigates the ability of the adaptive learning approach to replicate the expectations of professional forecasters. For a range of macroeconomic and financial variables, we compare constant and decreasing gain learning models to simple, yet powerful benchmark models. We find that constant gain models provide a better fit for the expectations of professional forecasters. For macroeconomic series they usually perform significantly better than a naive random walk forecast. In contrast, we find it difficult to beat the no-change benchmark using the adaptive learning models to forecast financial variables.

Exchange Rate Predictability

The main goal of this article is to provide an answer to the question: does anything forecast exchange rates, and if so, which variables? It is well known that exchange rate fluctuations are very difficult to predict using economic models, and that a random walk forecasts exchange rates better than any economic model (the Meese and Rogoff puzzle). However, the recent literature has identified a series of fundamentals/methodologies that claim to have resolved the puzzle. This article provides a critical review of the recent literature on exchange rate forecasting and illustrates the new methodologies and fundamentals that have been recently proposed in an up-to-date, thorough empirical analysis. Overall, our analysis of the literature and the data suggests that the answer to the question: “Are exchange rates predictable?” is, “It depends”—on the choice of predictor, forecast horizon, sample period, model, and forecast evaluation method. Predictability is most apparent when one or more of the following hold: the predictors are Taylor rule or net foreign assets, the model is linear, and a small number of parameters are estimated. The toughest benchmark is the random walk without drift. (JEL C53, F31, F37, E43, E52)

Exchange Rate Predictability

The main goal of this article is to provide an answer to the question: Does anything forecast exchange rates, and if so, which variables?. It is well known that exchange rate fluctuations are very difficult to predict using economic models, and that a random walk forecasts exchange rates better than any economic model (the Meese and Rogoff puzzle). However, the recent literature has identified a series of fundamentals/methodologies that claim to have resolved the puzzle. This article provides a critical review of the recent literature on exchange rate forecasting and illustrates the new methodologies and fundamentals that have been recently proposed in an up-to-date, thorough empirical analysis.

Beating the random walk: a performance assessment of long-term interest rate forecasts

This article 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 outside sample forecast errors, where a random walk forecast acts as benchmark. It is found that for five major Organization for Economic Co-operation and Development (OECD) countries, namely the US, Germany, UK, The Netherlands and Japan, the other forecasting approaches do not outperform the random walk on a 3-month forecast horizon. On a 12-month forecast horizon, the random walk model is outperformed by a model that combines economic data and expert forecasts. Several methods of combination are considered: equal weights, optimized weights and weights based on the forecast error. It seems that the additional information contents of the structural models and expert knowledge adds considerably to the performance of forecasting 12 months ahead.

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Trend Inflation in Advanced Economies

We derive estimates of trend inflation for fourteen advanced economies from a framework in which trend shocks exhibit stochastic volatility. The estimated specification allows for time-variation in the degree to which longer-term inflation expectations are well anchored in each economy. Our results bring out the effect of changes in monetary regime (such as the adoption of inflation targeting in several countries) on the behavior of trend inflation. Our estimates expand on the previous literature in several dimensions: For each country, we employ a multivariate approach that pools different inflation series in order to identify their common trend. In addition, our estimates of the inflation gap—defined as the difference between trend and observed inflation—are allowed to exhibit considerable persistence. Consequently, the fluctuations in estimates of trend inflation are much lower than those reported in studies that use stochastic volatility models in which inflation gaps are serially uncorrelated. This specification also makes our estimates less sensitive than trend estimates in the literature to the effect of distortions to inflation arising from non-market influences on prices, such as tax changes. A forecast evaluation based on pseudo-real-time estimates documents improvements in inflation forecasts, even though it remains hard to outperform simple random walk forecasts to a statistically significant degree.

Small Trends and Big Cycles in Crude Oil Prices

In this paper, we employ an unobserved components model to disentangle the long-term trend from cyclical movements in international benchmark crude oil prices using data from 1861 to 2010. The in-sample estimation of the model identifies a deterministic quadratic trend and two types of cycles, with the short cycle having a period of 6 years and the long cycle of 29 years. Compared to the large amplitude of the cycles, the growth rate of the long-term trend is small. The out-of-sample forecasting performance of various competing models is compared to that of a “no change” random walk forecast. While the random walk forecast tends to be the most accurate in shorter horizons, it is outperformed by the trend-cycle models in longer horizons. The results provide evidence of predictability in the price of crude oil in longer horizons.

Forecasting government bond yields with large Bayesian vector autoregressions

We propose a new approach to forecasting the term structure of interest rates, which allows to efficiently extract the information contained in a large panel of yields. In particular, we use a large Bayesian Vector Autoregression (BVAR) with an optimal amount of shrinkage towards univariate AR models. The optimal shrinkage is chosen by maximizing the Marginal Likelihood of the model. Focusing on the US, we provide an extensive study on the forecasting performance of the proposed model relative to most of the existing alternative specifications. While most of the existing evidence focuses on statistical measures of forecast accuracy, we also consider alternative measures based on trading schemes and portfolio allocation. We extensively check the robustness of our results, using different datasets and Monte Carlo simulations. We find that the proposed BVAR approach produces competitive forecasts, systematically more accurate than random walk forecasts, even though the gains are small.

Weak-Form Efficiency Vs Semi-Strong Form Efficiency in Price Discovery: an Application to International Black Tea Markets

In this paper we study a fundamental issue related to the efficient price discovery process using time series data from seven international black tea markets. The major question studied is as follows: Is the price discovery process in black tea markets efficient? We use two statistical techniques as engines of analysis. First, we use time series methods to capture regularities in time lags among price series. Second, we forecast the tea prices in each market using the time series model we estimated followed by a comparison of the forecast with the forecasts from the random-walk (na&iuml;ve) model. Weekly time series data on black tea prices from seven markets around the world are studied using time series methods. The study follows two paths. We study these prices in a common currency, the US dollar. We also study prices in each country&rsquo;s local currency. Results from unit root tests suggest that prices from three Indian markets are not generated through random-walk like behavior. We conclude that the Indian markets are not weak-form efficient. However, prices from all non-Indian markets cannot be distinguished from random-walk like behavior. These latter markets are weak-form efficient. A Vector Autoregressions (VARs) on the non-Indian markets are studied in local currency and in US dollars. We use Theil&rsquo;s U-statistic to test the forecasting ability of the VAR models. We find that for most markets in either dollars or in local currencies, that a random walk forecast outperforms the VAR generated forecasts. This last result suggests the non-Indian markets are both weak-form and semi-strong form efficient. DOI: http://dx.doi.org/10.4038/sjae.v6i1.3467 <em>SJAE </em>2004; 6(1): 1-24

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.

Time-variation in term premia: International survey-based evidence

Using a large, previously unexplored data set of survey-based interest rate forecasts that covers a broad range of countries, this paper re-examines the expectations hypothesis of the term structure of interest rates. We find that survey-based interest rate forecasts outperform not only a random walk forecast, but also outperform forecasts from forward rates. When using these superior survey-based forecasts in a modified expectations hypothesis test, the expectations hypothesis is rejected for fewer countries, at lower significance levels, and has greater explanatory power than when using a traditional forward rates-based test. We furthermore document strong time-variation in the term premia, which is an important reason why the traditional expectations hypothesis test is rejected so frequently. This time-variation seems to arise from the changing attitudes towards risk among market participants and as a compensation for the change in liquidity in the term structure. Finally, we find that generalizing findings from earlier U.S. studies to other countries may lead to bias in the true economic relationships in these countries.

A Factor Model for Euro-area Short-term Inflation Analysis

Summary This paper develops a factor model for forecasting inflation in the euro area. The model can handle variables with different timeliness, sample size and frequency. We show that the forecasts based on the factor model outperform naïve random walk forecasts, a hard to beat benchmark for euro area inflation forecasts in recent years, at horizons of and beyond nine months ahead. They are also comparable, in terms of accuracy, to the judgemental forecasts prepared in the context of the Eurosystem macroeconomic projection exercises. The factor model is therefore a very suitable tool to extract the signal on current and future euro area inflation from new data releases.