Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.
Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal autoregressive integrated moving average (SARIMA) models do not reflect the distinct characteristics of each period in seasonal patterns, such as the unique behavior of specific days of the week in business data. We propose a multi-dimensional hierarchical model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is then taken, resulting in a model that successfully reflects the interactions between multiple seasonal patterns. Although this process reduces the data available for each parameter, a robust estimation can be obtained through a hierarchical Bayesian model implemented in Stan. Through this model, it becomes possible to consider both the characteristics of each seasonal period and the interactions among characteristics from multiple seasonal periods. Our new model achieved considerable improvements in prediction accuracy compared to previous models, including Fourier decomposition, which Prophet uses to model seasonality patterns. A comparison was performed on a real-world dataset of pallet transport from a national-scale logistic network.
From my email today You use an illustration of a seasonal arima model: ARIMA(1,1,1)(1,1,1)4 I would like to simulate data from this process then fit a model… but I am unable to find any information as to how this can be conducted… if I set phi1, Phi1, theta1, and Theta1 it would be reassuring that for large n the parameters returned by Arima(foo,order c(1,1,1),seasonal c(1,1,1)) are in agreement… My answer: Unfortunately arima.