Variations on two-parameter families of forecasting functions: seasonal/nonseasonal Models, comparison to the exponential smoothing and ARIMA models, and applications to stock market data
双参数预测函数族:季节性模型、平滑与 ARIMA 比较及股市应用AI 解读 ↓
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双参数预测函数族:季节性模型、平滑与 ARIMA 比较及股市应用AI 解读 ↓
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We introduce twenty four two-parameter families of advanced time series forecasting functions using a new and nonparametric approach. We also introduce the concept of powering and derive nonseasonal and seasonal models with examples in education, sales, finance and economy. We compare the performance of our twenty four models to both Holt--Winters and ARIMA models for both nonseasonal and seasonal times series. We show in particular that our models not only do not require a decomposition of a seasonal time series into trend, seasonal and random components, but leads also to substantially lower sum of absolute error and a higher number of closer forecasts than both Holt--Winters and ARIMA models. Finally, we apply and compare the performance of our twenty four models using five-year stock market data of 467 companies of the S&P500.
具有分组边效应的降秩网络自回归
We propose the Edge-Grouped Reduced-Rank Network Autoregressive model (Edge-Grouped RRNAR) for multivariate time series observed over a network. The model allows transmission effects to vary across prespecified and economically interpretable groups of edges, while using a low-rank structure to capture cross-variable dynamics. This structure separates where network transmission occurs from which variables transmit and respond. We develop a topology-aware and block-specific…
含未知趋势与周期成分的球面嵌入时间序列
Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity driven by latent trend and periodic components. Traditional Euclidean time series methods fail to account for the intrinsic non-Euclidean geometry of the sphere, leaving a critical gap in rigorous methodologies for modelling and forecasting…
半参数高维时间序列关系图的贝叶斯学习
Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several independent univariate time series, which are then orthogonally rotated and sparsely linearly transformed. With this approach, any specified intrinsic relations among component time series given by a graphical structure can be maintained at all…
基于条件状态与轨迹类比的多变量概率预测
We propose Conditional Regime Analog Forecasting with Trajectories (CRAFT), a nonparametric framework for multivariate probabilistic time-series prediction. The method constructs paired backward and forward trajectory profiles from cumulative multi-horizon returns, learns recurrent low-dimensional regime labels in both spaces using singular value decomposition, change-point segmentation, and segment clustering, and estimates a backward-to-forward conditional regime…
用 BAND 缓解维度灾难:高维非参数分布估计
Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality. We propose a sparse Bayesian network approach in which each conditional probability is estimated using sparsity-aware conditional mean methods. The resulting estimator, \textit{BAyesian Network Distribution regression} (BAND), handles mixed data types in high-dimensional time series and achieves polynomial total variation convergence rates while allowing the…
高维时间序列数据的局部交互自回归模型
High-dimensional matrix and tensor time series often exhibit local dependency, where each entry interacts mainly with a small neighborhood. Accounting for local interactions in a prediction model can greatly reduce the dimensionality of the parameter space, leading to more efficient inference and more accurate predictions. We propose a Local Interaction Autoregressive (LIAR) framework and study Separable LIAR, a variant with shared row and column components, for…