On the Predictive Information of Futures' Prices: A Wavelet‐Based Assessment

Abstract

While in speculative markets forward prices could be regarded as natural predictors for future spot rates, empirically, forward prices often fail to indicate ex ante the direction of price movements. In terms of forecasting, the random walk approximation of speculative prices has been established to provide ‘naive’ predictors that are most difficult to outperform by both purely backward‐looking time series models and more structural approaches processing information from forward markets. We empirically assess the implicit predictive content of forward prices by means of wavelet‐based prediction of two foreign exchange (FX) rates and the price of Brent oil quoted either in US dollars or euros. Essentially, wavelet‐based predictors are smoothed auxiliary (padded) time series quotes that are added to the sample information beyond the forecast origin. We compare wavelet predictors obtained from padding with constant prices (i.e. random walk predictors) and forward prices. For the case of FX markets, padding with forward prices is more effective than padding with constant prices, and, moreover, respective wavelet‐based predictors outperform purely backward‐looking time series approaches (ARIMA). For the case of Brent oil quoted in US dollars, wavelet‐based predictors do not signal predictive content of forward prices for future spot prices. Copyright © 2016 John Wiley & Sons, Ltd.

The usefulness of oil price forecasts—Evidence from survey predictions

“…Furthermore, using a quadratic error measure leads to a penalization of comparatively large forecast errors. The RMSE given in Formula below is one very commonly applied error measure (see, e.g., Andres & Spiwoks, ; Espinoza, Fornari, & Lombardi, ; Hyndman & Koehler, ; Kisinbay, ; Leitch & Tanner, ; and more recently Herwartz & Schlüter, ; Ryan & Whiting, ; as well as Wegener, Spreckelsen, Basse, & Mettenheim, ). …”

Predicting exchange rates in Asia: New insights on the accuracy of survey forecasts

“…Additionally, the Diebold Mariano (DM) test to check for equal predictive ability of the survey forecast and the naïve prediction is applied (see also Diebold & Mariano, 1995). 8 The RMSE itself is an often applied measure of forecast accuracy (see also Leitch & Tanner, 1991;Hyndman & Koehler, 2006;Herwartz & Schlüter, 2017;Ryan & Whiting, 2017.) 9 The naïve prediction is used as competing forecast for the survey prediction.…”

“…The RMSE itself is an often applied measure of forecast accuracy (see alsoLeitch and Tanner, 1991;Hyndman and Koehler, 2006;Herwartz and Schlüter, 2017;Ryan and Whiting, 2017).8 The naïve prediction is used as competing forecast for the survey prediction. Throughout this paper the naïve prediction is defined as the no change forecast, (i.e.Ŝ t+h = S t ) whereas S t is the FX spot rate at t andŜ t+h is the forecast of the FX spot rate for t + h. Alternatively, instead of the no change forecast the naïve prediction could have also been defined as trend following.…”

The wavelet scaling approach to forecasting: Verification on a large set of Noisy data

“…There exist numerous forecasting procedures utilizing the wavelet transform, encompassing such diversified approaches as wavelet denoising of deterministic signals based on various thresholding rules followed by ARIMA model building (Alrumaih & Al-Fawzan, 2002;Ferbar, Čreslovnik, Mojškerc, & Rajgelj, 2009;Herwartz & Schlüter, 2017), wavelet multiresolution decomposition combined with principal component analysis and/or a separate modeling of the signal's smooths and details (Fernandez, 2008;Rua, 2011;Rua, 2017;Wong, Ip, Xie, & Lui, 2003;Zhang, Coggins, Jabri, Dersch, & Flower, 2001), linear and nonlinear multiscale models based on the Haar wavelet coefficients (Berger, 2016;Murtagh, Starck, & Renaud, 2004;Renaud, Starck, & Murtagh, 2003), forecasting coefficients of the wavelet expansion (called wavelet and scaling coefficients) followed by applying the inverse wavelet transform to the results (Chen, Nicolis, & Vidakovic, 2010;Kaboudan, 2005;Rostan & Rostan, 2018), artificial neural networks combined with the wavelet methodology either in the form of wavelet neural networks using wavelets as activation functions in radial basis function networks (Alexandridis & Zapranis, 2013;Sermpinis, Verousis, & Theofilatos, 2016) or through the use of wavelet coefficients as inputs to a neural network model (Murtagh et al, 2004;Minu et al, 2010;Ortega & Khashanah, 2014;Renaud et al, 2003), and, finally, modeling locally stationary wavelet processes (Fryźlewicz, Van Bellegem, & von Sachs, 2003). For a detailed discussion of these concepts, see, for example, Bruzda (2013) and Schlüter and Deuschle (2014).…”