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Register a new userMacro-Economic Time Series Modeling and Interaction Networks
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Macro-economic models describe the dynamics of economic quantities. The estimations and forecasts produced by such models play a substantial role for financial and political decisions. In this contribution we describe an approach based on genetic programming and symbolic regression to identify variable interactions in large datasets. In the proposed approach multiple symbolic regression runs are executed for each variable of the dataset to find potentially interesting models. The result is a variable interaction network that describes which variables are most relevant for the approximation of each variable of the dataset. This approach is applied to a macro-economic dataset with monthly observations of important economic indicators in order to identify potentially interesting dependencies of these indicators. The resulting interaction network of macro-economic indicators is briefly discussed and two of the identified models are presented in detail. The two models approximate the help wanted index and the CPI inflation in the US.
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The ongoing rapid urbanization phenomena make the understanding of the evolution of urban environments of utmost importance to improve the well-being and steer societies towards better futures. Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring, for instance, the dependence of socio-economic indicators on city sizes. Though scaling laws allow for the definition of city-size independent socio-economic indicators, only a few efforts have been devoted to the modeling of the dynamical evolution of cities as mirrored through socio-economic variables and their mutual influence. In this work, we propose a Maximum Entropy (ME), non-linear, generative model of cities. We write in particular a Hamiltonian function in terms of a few macro-economic variables, whose coupling parameters we infer from real data corresponding to French towns. We first discover that non-linear dependencies among different indicators are needed for a complete statistical description of the non-Gaussian correlations among them. Furthermore, though the dynamics of individual cities are far from being stationary, we show that the coupling parameters corresponding to different years turn out to be quite robust. The quasi time-invariance of the Hamiltonian model allows proposing an analytic model for the evolution in time of the macro-economic variables, based on the Langevin equation. Despite no temporal information about the evolution of cities has been used to derive this model, its forecast accuracy of the temporal evolution of the system is compatible to that of a model inferred using explicitly such information.
Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue in ESNs is determining its hyperparameters, which are crucial in instantiating a well performing reservoir, but are often set manually or using heuristics. In this work we optimize the ESN hyperparameters using Bayesian optimization which, given a limited budget of function evaluations, outperforms a grid search strategy. In the context of large volumes of time series data, such as light curves in the field of astronomy, we can further reduce the optimization cost of ESNs. In particular, we wish to avoid tuning hyperparameters per individual time series as this is costly; instead, we want to find ESNs with hyperparameters that perform well not just on individual time series but rather on groups of similar time series without sacrificing predictive performance significantly. This naturally leads to a notion of clusters, where each cluster is represented by an ESN tuned to model a group of time series of similar temporal behavior. We demonstrate this approach both on synthetic datasets and real world light curves from the MACHO survey. We show that our approach results in a significant reduction in the number of ESN models required to model a whole dataset, while retaining predictive performance for the series in each cluster.
The minute-by-minute move of the Hang Seng Index (HSI) data over a four-year period is analysed and shown to possess similar statistical features as those of other markets. Based on a mathematical theorem [S. B. Pope and E. S. C. Ching, Phys. Fluids A {bf 5}, 1529 (1993)], we derive an analytic form for the probability distribution function (PDF) of index moves from fitted functional forms of certain conditional averages of the time series. Furthermore, following a recent work by Stolovitzky and Ching, we show that the observed PDF can be reproduced by a Langevin process with a move-dependent noise amplitude. The form of the Langevin equation can be determined directly from the market data.
Statistical methods such as the Box-Jenkins method for time-series forecasting have been prominent since their development in 1970. Many researchers rely on such models as they can be efficiently estimated and also provide interpretability. However, advances in machine learning research indicate that neural networks can be powerful data modeling techniques, as they can give higher accuracy for a plethora of learning problems and datasets. In the past, they have been tried on time-series forecasting as well, but their overall results have not been significantly better than the statistical models especially for intermediate length times series data. Their modeling capacities are limited in cases where enough data may not be available to estimate the large number of parameters that these non-linear models require. This paper presents an easy to implement data augmentation method to significantly improve the performance of such networks. Our method, Augmented-Neural-Network, which involves using forecasts from statistical models, can help unlock the power of neural networks on intermediate length time-series and produces competitive results. It shows that data augmentation, when paired with Automated Machine Learning techniques such as Neural Architecture Search, can help to find the best neural architecture for a given time-series. Using the combination of these, demonstrates significant enhancement in the forecasting accuracy of three neural network-based models for a COVID-19 dataset, with a maximum improvement in forecasting accuracy by 21.41%, 24.29%, and 16.42%, respectively, over the neural networks that do not use augmented data.
We consider a bivariate time series $(X_t,Y_t)$ that is given by a simple linear autoregressive model. Assuming that the equations describing each variable as a linear combination of past values are considered structural equations, there is a clear meaning of how intervening on one particular $X_t$ influences $Y_{t}$ at later times $t>t$. In the present work, we describe conditions under which one can define a causal model between variables that are coarse-grained in time, thus admitting statements like `setting $X$ to $x$ changes $Y$ in a certain way without referring to specific time instances. We show that particularly simple statements follow in the frequency domain, thus providing meaning to interventions on frequencies.
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