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- Investigating theaccuracy of autoregressive recurrent networks using hierarchical aggregation structure-based data partitioningPublication . Oliveira, José Manuel; Ramos, PatríciaGlobal models have been developed to tackle the challenge of forecasting sets of series that are related or share similarities, but they have not been developed for heterogeneous datasets. Various methods of partitioning by relatedness have been introduced to enhance the similarities of sets, resulting in improved forecasting accuracy but often at the cost of a reduced sample size, which could be harmful. To shed light on how the relatedness between series impacts the effectiveness of global models in real-world demand-forecasting problems, we perform an extensive empirical study using the M5 competition dataset. We examine cross-learning scenarios driven by the product hierarchy commonly employed in retail planning to allow global models to capture interdependencies across products and regions more effectively. Our findings show that global models outperform state-of-the-art local benchmarks by a considerable margin, indicating that they are not inherently more limited than local models and can handle unrelated time-series data effectively. The accuracy of data-partitioning approaches increases as the sizes of the data pools and the models’ complexity decrease. However, there is a trade-off between data availability and data relatedness. Smaller data pools lead to increased similarity among time series, making it easier to capture cross-product and cross-region dependencies, but this comes at the cost of a reduced sample, which may not be beneficial. Finally, it is worth noting that the successful implementation of global models for heterogeneous datasets can significantly impact forecasting practice.
- Financial Contagion from the Subprime Crisis: A Copula ApproachPublication . Mendes, Rita I.L.; Gomes, Luís; Ramos, PatríciaThe magnitude of the subprime crisis effects caused recessions in several economies, giving rise to the global financial crisis. The scale of this major shock and the different recovery profiles of European economies motivated this paper. The main objective is to look for evidence of contagion between the North American financial market (S&P500) and the financial markets of Portugal (PSI20), Spain (IBEX35), Greece (ATHEX) and Italy (FTSEMIB), in the South of Europe, and the financial markets of Sweden (OMXS30), Denmark (OMX2C0), Finland (OMXH25) and Norway (OsloOBX), in the North of Europe. Considering the period from January 1, 2003 to December 31, 2013, the ARMAGARCH models were estimated to remove the autoregressive and conditional heteroscedastic effects from the time series of the daily returns. Then, the copula models were used to estimate the dependence relationships between the European stock indexes and the North American stock index, from the precrisis subperiod to the crisis subperiod. The results indicate financial contagion of the subprime crisis for all analyzed European countries. The North European markets intensified the relations of financial integration (both in negative and positive shocks) with the North American market, apart from the Danish against the Portuguese. In addition to the contribution made by the joint application of the ARMA-GARCH models, the findings are useful to identify channels of financial contagion between markets and to warn about the effects of possible new crisis, which will require different levels of adaptation by the companies’ financial managers and intervention by the authorities.
- Asymmetric wealth effect between US stock markets and US housing market and european stock markets: evidences from TAR and MTARPublication . Coelho, Pedro; Gomes, Luís; Ramos, PatríciaEvidence of the asymmetric wealth effect has important implications for investors and continues to merit research attention, not least because much of the evidence based on linear models has been refuted. Indeed, stock and house prices are influenced by economic activity and react nonlinearly to positive/negative shocks. This problem justifies our research. The objective of this study is to examine evidence of cointegrations between the US housing and stock markets and between the US and European stock markets, given the international relevance of these exchanges. Using data from 1989:Q1 to 2020:Q2, the Threshold Autoregression model as well as the Momentum Threshold Autoregression model were calculated by combining the US Freddie, DJIA, and SPX indices and the European STOXX and FTSE indices. The results suggest a long-term equilibrium relationship with asymmetric adjustments between the housing market and the US stock markets, as well as between the DJIA, SPX, and FTSE indices. Moreover, the wealth effect is stronger when stock prices outperform house prices above an estimated threshold. This empirical evidence is useful to portfolio managers in their search for non-perfectly related markets that allow investment diversification and control risk exposure across different assets.
- Forecasting Seasonal Sales with Many Drivers: Shrinkage or Dimensionality Reduction?Publication . Ramos, Patricia; Oliveira, José Manuel; Kourentzes, Nikolaos; Fildes, RobertRetailers depend on accurate forecasts of product sales at the Store SKU level to efficiently manage their inventory. Consequently, there has been increasing interest in identifying more advanced statistical techniques that lead to accuracy improvements. However, the inclusion of multiple drivers affecting demand into commonly used ARIMA and ETS models is not straightforward, particularly when many explanatory variables are available. Moreover, regularization regression models that shrink the model’s parameters allow for the inclusion of a lot of relevant information but do not intrinsically handle the dynamics of the demand. These problems have not been addressed by previous studies. Nevertheless, multiple simultaneous effects interacting are common in retailing. To be successful, any approach needs to be automatic, robust and efficiently scaleable. In this study, we design novel approaches to forecast retailer product sales taking into account the main drivers which affect SKU demand at store level. To address the variable selection challenge, the use of dimensionality reduction via principal components analysis (PCA) and shrinkage estimators was investigated. The empirical results, using a case study of supermarket sales in Portugal, show that both PCA and shrinkage are useful and result in gains in forecast accuracy in the order of 10% over benchmarks while offering insights on the impact of promotions. Focusing on the promotional periods, PCA-based models perform strongly, while shrinkage estimators over-shrink. For the non-promotional periods, shrinkage estimators significantly outperform the alternatives.
- Forecasting: theory and practicePublication . Petropoulos, Fotios; Ramos, PatriciaForecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
- Robust sales forecasting using deep learning with static and dynamic covariatesPublication . Ramos, Patrícia; Oliveira, José Manuel: Retailers must have accurate sales forecasts to efficiently and effectively operate their businesses and remain competitive in the marketplace. Global forecasting models like RNNs can be a powerful tool for forecasting in retail settings, where multiple time series are often interrelated and influenced by a variety of external factors. By including covariates in a forecasting model, we can often better capture the various factors that can influence sales in a retail setting. This can help improve the accuracy of our forecasts and enable better decision making for inventory management, purchasing, and other operational decisions. In this study, we investigate how the accuracy of global forecasting models is affected by the inclusion of different potential demand covariates. To ensure the significance of the study’s findings, we used the M5 forecasting competition’s openly accessible and well-established dataset. The results obtained from DeepAR models trained on different combinations of features indicate that the inclusion of time-, event-, and ID-related features consistently enhances the forecast accuracy. The optimal performance is attained when all these covariates are employed together, leading to a 1.8% improvement in RMSSE and a 6.5% improvement in MASE compared to the baseline model without features. It is noteworthy that all DeepAR models, both with and without covariates, exhibit a significantly superior forecasting performance in comparison to the seasonal naïve benchmark.