Naive Random Walk Research Articles

Oil Strikes Back: Trend Factors and Exchange Rates

AbstractA well‐known puzzle in international finance is that, to predict exchange rate returns, existing predictive models often perform worse than the naive random walk (RW) model. In this paper, we construct an oil trend factor which performs better than the RW model. More importantly, an oil‐trend‐based dynamic trading strategy can generate superior economic values. This result holds in both developed and emerging markets, with different forecasting horizons, with different specifications of trend factors, and across different currencies. Finally, we explore the economic link for the powerful predictability of the oil trend factor.

Quantitative easing effectiveness: Evidence from Euro private assets

AbstractProponents of quantitative easing (QE) unconventional policy have rather overstated some evidence that structural time series models do not predict long‐term asset prices and yields as well as naive random walk forecasts, implying that predictions of price reversals cannot be profitable and, therefore, that QE effects are not transitory. Indeed, in this work we present evidence that naive models do not outperform structural vector autoregressive and Markov switching models in out‐of‐sample forecasting of corporate bond yields purchased by the European Central Bank, when the information set includes base money growth. It turns out that structural time series models provide additional information regarding the likelihood of price reversals, thus motivating investors to offset the effects of QE interventions if they perceive unconventional monetary policy regimes as temporary.

Forecasting SGD-INR Exchange Return: An application of Autoregressive Integrated Moving Average

Predicting currency has always been open to doubt because in financial as well as in managerial decisions making process it plays a crucial role and it is not easy to forecast foreign rates with higher accuracy than a naive random walk model. The main goal of this paper is to use the Arima model to forecast the yearly exchange rate, here we use real foreign exchange data to check the suitable level of the Arima model for forecasting and it also shows how suitable the Arima model is to estimate foreign exchange. There has been considerable improvement in profitability of MNC which conducts substantial currency transfer in business courses and forecasts exchange rate accurately. The time series Arima model is applied to forecast the exchange return of SND to INR. To better understand how the Arima model applies within the period 1st February 2011 - 1st February 2021. In this report monthly or daily exchange returns are used for variable inputs. This model is based on a few observations on the Arima model to help predict and solve financial forecasting problems for the best and worst possible situations which results in demonstrating the predictive strength and potential but is still a problematic task.

Common factors and the dynamics of cereal prices. A forecasting perspective

This article investigates what determines the price dynamics of the main cereals: barley, maize, rice and wheat. Using an extensive dataset of monthly time series covering the years 1980–2019, we extract four different common factors explaining the dynamics of commodity prices, exchange rates, financial and macroeconomic indicators. Next, we examine whether these factors are useful in explaining the movements of cereal prices. We show that models incorporating all four factors outperform significantly the naive random walk model in out-of-sample forecasting competition, especially for longer horizons. However, they have only marginally better performance than a simpler model based on the commodity factor alone.

An evaluation of quantitative easing effectiveness based on out-of-sample forecasts

<abstract> <p>A line of defense of quantitative easing (QE) policies has been developed around empirical evidence that time series models do not predict long-term asset prices and yields as well as naive random walk forecasts, implying that predictions of price reversals cannot be profitable and, therefore, that QE effects are not reversed. However, in this work we present evidence that for the Eurozone, Sweden, and the UK, which have pursued QE interventions, a random walk does not beat a Markov switching regimes model in out-of-sample forecasting and, at the same time, the switching process provides additional information regarding the likelihood of price reversals, thus inducing market participants to offset the effects of QE interventions whenever they perceive unconventional monetary policy regimes as temporary.</p> </abstract>

Foreign Currency Forecasting: What Can Stock and Bond Markets Tell Us?

This paper provides a comprehensive statistical and economic evidence on the forecasting power of local-currency equity and bond returns in predicting exchange rate returns. We first construct out-of-sample (OOS) forecasts using various model specifications of equity and bond returns, and assess their statistical accuracy against the naive random walk (RW) model. Next, we test their economic value by designing a trading strategy based on the sign of our OOS forecasts. Using a sample of 28 countries, we find three key results: (1) our in-sample forecasts show that all the slope estimates of our predictive regressions are significant, indicating that the RW model is misspecified; (2) the statistical accuracy criteria suggest that our OOS forecasts outperform the RW model; and (3) our trading strategies, that use stock and bond returns, generate high and significant Sharpe ratios which are uncorrelated with the traditional risk factors and other popular determinants of currency returns.

Common Factors and the Dynamics of Cereal Prices. A Forecasting Perspective

This article investigates what determines the price dynamics of the main cereals: barley, maize, rice and wheat. Using an extensive dataset of monthly time series covering the years 1980 - 2019, we extract four different common factors explaining the dynamics of commodity prices, exchange rates, financial and macroeconomic indicators. Next, we examine whether these factors are useful in explaining the movements of cereal prices. We show that models incorporating all four factors outperform significantly the naive random walk model in out-of-sample forecasting competition, especially for longer horizons. However, they have only marginally better performance than a simpler model based on the commodity factor alone.

Incorporating Reverse Search for Friend Recommendation with Random Walk

Recommending friends is an important mechanism for social networks to enhance their vitality and attractions to users. The huge user base as well as the sparse user relationships give great challenges to propose friends on social networks. Random walk is a classic strategy for recommendations, which provides a feasible solution for the above challenges. However, most of the existing recommendation methods based on random walk are only weighing the forward search, which ignore the significance of reverse social relationships. In this paper, we proposed a method to recommend friends by integrating reverse search into random walk. First, we introduced the FP-Growth algorithm to construct both web graphs of social networks and their corresponding transition probability matrix. Second, we defined the reverse search strategy to include the reverse social influences and to collaborate with random walk for recommending friends. The proposed model both optimized the transition probability matrix and improved the search mode to provide better recommendation performance. Experimental results on real datasets showed that the proposed method performs better than the naive random walk method which considered the forward search mode only.

Mean-reversion, non-linearities and the dynamics of industrial metal prices. A forecasting perspective

We analyse the dynamics of real prices for main non-ferrous industrial metals: aluminium, copper, nickel and zinc. The estimates based on monthly data from 1980 to 2019 show that the prices are mean reverting and the pace of mean reversion is regime dependent. The results of the out-of-sample forecasting competition provide ample evidence that mean-reverting models deliver significantly better forecasts than the naive random walk. However, allowing for non-linearity by introducing threshold structure does not lead to further improvement in the quality of forecasts.

Forecasting bulk prices of Bordeaux wines using leading indicators

Agricultural price forecasting has been being abandoned progressively by researchers ever since the development of large-scale agricultural futures markets. However, as with many other agricultural goods, there is no futures market for wine. This paper draws on the agricultural prices forecasting literature to develop a forecasting model for bulk wine prices. The price data include annual and monthly series for various wine types that are produced in the Bordeaux region. The predictors include several leading economic indicators of supply and demand shifts. The stock levels and quantities produced are found to have the highest predictive power. The preferred annual and monthly forecasting models outperform naive random walk forecasts by 27.1% and 3.4% respectively; their mean absolute percentage errors are 2.7% and 3.4% respectively. A simple trading strategy based on monthly forecasts is estimated to increase profits by 3.3% relative to a blind strategy that consists of always selling at the spot price.

A Credit-Based Theory of the Currency Risk Premium

This paper extends Kremens and Martin (2019) and uncovers a novel component for exchange rate predictability based on the price difference between sovereign credit default swaps denominated in different currencies. This new forecasting variable - the credit-implied risk premium - captures the expected currency depreciation conditional on a severe but rare credit event. Using data for 16 Eurozone countries, we find that the credit-implied risk premium positively forecasts the dollar-euro exchange rate return at various horizons. Moreover, a currency strategy that exploits the informative content of our predictor generates substantial out-of-sample economic value against the naive random walk benchmark.

Oil Strikes Back: Trend Factors and Exchange Rates

A well-known puzzle in international finance is that fluctuations in exchange rate are very difficult to predict and existing predictive models often perform worse than the naive random walk model. In this paper, we construct an oil trend factor and find that it performs better than the naive random walk in predicting exchange rates out-of-sample and delivers superior economic significance. This result holds in both developed and developing countries, with different forecasting horizons and with different specifications of trend factors. Notably, we also show that the predictive power of the oil trend factor is closely related to macroeconomic fundamentals.

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

AbstractIn 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 witht‐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.

An Artificial Neural Network-Based Approach to the Monetary Model of Exchange Rate

This paper aims to investigate the predictive accuracy of the flexible price monetary model of the exchange rate, estimated by an approach based on combining the vector autoregressive model and multilayer feedforward neural networks. The forecasting performance of this nonlinear, nonparametric model is analyzed comparatively with a monetary model estimated in a linear static framework; the monetary model estimated in a linear dynamic vector autoregressive framework; the monetary model estimated in a parametric nonlinear dynamic threshold vector autoregressive framework; and the naive random walk model applied to six different exchange rates over three forecasting periods. The models are compared in terms of both the magnitude of their forecast errors and the economic value of their forecasts. The proposed model yielded promising outcomes by performing better than the random walk model in 16 out of 18 instances in terms of the root mean square error and 15 out of 18 instances in terms of mean return and Sharpe ratio. The model also performed better than linear models in 17 out of 18 instances for root mean square error and 14 out of 18 instances for mean returns and Sharpe ratio. The distinguishing feature of the proposed model versus the present models in the literature is its robustness to outperform the random walk model, regardless of whether the magnitude of forecast errors or the economic value of the forecasts is chosen as a performance measure.

Using the hybrid Phillips curve with memory to forecast US inflation

AbstractThis paper adopts the Caputo fractional derivative to re-specify the hybrid Phillips curve as a dynamic process of inflation with memory. The Caputo fractional derivative contains a non-integer differencing order, providing the same insight for persistence as emphasized in the Autoregressive Fractionally Integrated Moving Average (ARFIMA) time series models. We utilize the hybrid Phillips curve with memory to forecast US inflation during 1967–2014. The results indicate that our model performs well against a traditional hybrid Phillips curve, an integrated moving average model and a naive random walk model in quasi-in-sample forecasts. In out-of-sample forecasts based on Consumer Price Index (CPI) and Personal Consumption Expenditure (PCE) data, we find that the forecasting performance of Phillips curve models depends on the sample period. Our model with CPI data can outperform others in out-of-sample forecasts during and after the most recent financial crisis (2006–2014).

A Lagrangian model for soil water dynamics during rainfall-driven conditions

Abstract. Within this study we propose a stochastic approach to simulate soil water dynamics in the unsaturated zone by using a non-linear, space domain random walk of water particles. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker–Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. A naive random walk, which assumes all water particles to move at the same drift velocity and diffusivity, overestimated depletion of soil moisture gradients compared to a Richards solver. This is because soil water and hence the corresponding water particles in smaller pore size fractions are, due to the non-linear decrease in soil hydraulic conductivity with decreasing soil moisture, much less mobile. After accounting for this subscale variability in particle mobility, the particle model and a Richards solver performed highly similarly during simulated wetting and drying circles in three distinctly different soils. Both models were in very good accordance during rainfall-driven conditions, regardless of the intensity and type of the rainfall forcing and the shape of the initial state. Within subsequent drying cycles the particle model was typically slightly slower in depleting soil moisture gradients than the Richards model. Within a real-world benchmark, the particle model and the Richards solver showed the same deficiencies in matching observed reactions of topsoil moisture to a natural rainfall event. The particle model performance, however, clearly improved after a straightforward implementation of rapid non-equilibrium infiltration, which treats event water as different types of particles, which travel initially in the largest pore fraction at maximum velocity and experience a slow diffusive mixing with the pre-event water particles. The proposed Lagrangian approach is hence a promising, easy-to-implement alternative to the Richards equation for simulating rainfall-driven soil moisture dynamics, which offers straightforward opportunities to account for preferential, non-equilibrium flow.

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

Abstract The seminal study of Meese et al. (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. 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.

A Reconsideration of the Meese-Rogoff Puzzle: An Alternative Approach to Model Estimation and Forecast Evaluation

This study revisits the Meese-Rogoff puzzle by estimating the traditional monetary models of exchange rate determination in state-space form and comparing the accuracy of these forecasts against the naive random walk model using a wide range of conventional and alternative measures of forecasting accuracy. The results demonstrate that incorporating stochastic movements in the parameters of exchange rate models does not enable the Meese-Rogoff puzzle to be overturned. However, estimating these models in state-space form substantially improves forecasting accuracy to the extent that the model and random walk produce an equivalent magnitude of error. Furthermore, the results prove that the Meese-Rogoff puzzle can be overturned if the forecasts are evaluated by alternative criteria. These criteria include direction accuracy, profitability, and measures that jointly take into account both magnitude and direction accuracy.

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.