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This study investigates the relationships between agricultural spot markets and external uncertainties via the multifractal detrending moving-average cross-correlation analysis (MF-X-DMA). The dataset contains the Grains \& Oilseeds Index (GOI) and its five sub-indices of wheat, maize, soyabeans, rice, and barley. Moreover, we use three uncertainty proxies, namely, economic policy uncertainty (EPU), geopolitical risk (GPR), and volatility Index (VIX). We observe the presence of multifractal cross-correlations between agricultural markets and uncertainties. Further, statistical tests show that maize has intrinsic joint multifractality with all the uncertainty proxies, exhibiting a high degree of sensitivity. Additionally, intrinsic multifractality among GOI-GPR, wheat-GPR and soyabeans-VIX is illustrated. However, other series have apparent multifractal cross-correlations with high possibilities. Moreover, our analysis suggests that among the three kinds of external uncertainties, geopolitical risk has a relatively stronger association with grain prices., Comment: 30 pages, 21 figures

Grains account for more than 50% of the calories consumed by people worldwide, and military conflicts, pandemics, climate change, and soaring grain prices all have vital impacts on food security. However, the complex price behavior of the global grain spot markets has not been well understood. A recent study performed multifractal moving average analysis (MF-DMA) of the Grains & Oilseeds Index (GOI) and its sub-indices of wheat, maize, soyabeans, rice, and barley and found that only the maize and barley sub-indices exhibit an intrinsic multifractal nature with convincing evidence. Here, we utilize multifractal fluctuation analysis (MF-DFA) to investigate the same problem. Extensive statistical tests confirm the presence of intrinsic multifractality in the maize and barley sub-indices and the absence of intrinsic multifractality in the wheat and rice sub-indices. Different from the MF-DMA results, the MF-DFA results suggest that there is also intrinsic multifractality in the GOI and soyabeans sub-indices. Our comparative analysis does not provide conclusive information about the GOI and soyabeans and highlights the high complexity of the global grain spot markets., Comment: 23 pages including 14 figures

By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock Exchange Composite Index (SZCI). The characteristics of the corresponding multifractal spectra are defined as a measurement of market volatility. It is found that there is a statistically significant relationship between the stock index returns and the spectral characteristics, which can be applied to forecast the future market return. The in-sample and out-of-sample tests on the return predictability of multifractal characteristics indicate the spectral width $\Delta {\alpha}$ is a significant and positive excess return predictor. Our results shed new lights on the application of multifractal nature in asset pricing., Comment: 2 figures, 5 tables, and 12 pages

Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross correlations based on wavelet analysis, termed multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, the empirical joint multifractality of MFXWT is found to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indexes and uncover intriguing joint multifractal nature in pairs of index returns and volatilities.