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ARIMA 噪声模型的重复时间序列分析AI 解读

This article develops a theory and methodology for repeated time series (RTS) measurements on autoregressive integrated moving average-noise (ARIMAN) process. The theory enables us to relax the normality assumption in the ARIMAN model and to identify models for each component series of the process. We discuss the properties, estimation, and forecasting of RTS ARIMAN models and illustrate with examples.

参数化年龄别生育率的多元时间序列预测AI 解读

Projection of individual age-specific fertility rates is a forecasting problem of high dimension. We solve this dimensionality problem by using parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. These yield forecasts of future fertility curves, which are then used to compute age-specific fertility rate forecasts. This reduces the dimensionality of the forecasting problem and also guarantees…

无模型一步向前预测区间：渐近理论与小样本模拟AI 解读

We show that the empirical quantile process from an ARMA$(1, q)$ process which is strongly mixing $\Delta_s$, and is either Gaussian or double exponential, converges to a Gaussian process. This result is used to derive model-free one-step-ahead prediction intervals for such processes. Simulations demonstrate where the asymptotic theory can and cannot be applied to small samples.

抽样未来：单变量时间序列模型预测的贝叶斯方法AI 解读

The Box–Jenkins methodology for modeling and forecasting from univariate time series models has long been considered a standard to which other forecasting techniques have been compared. To a Bayesian statistician, however, the method lacks an important facet—a provision for modeling uncertainty about parameter estimates. We present a technique called sampling the future for including this feature in both the estimation and forecasting stages. Although it is relatively easy…

管理与经济学统计AI 解读

What is Statistics? Describing Sets of Measurements Probability Random Variables and Probability Distributions Three Useful Discrete Probability Distributions The Normal and Other Continuous Probability Distributions Sampling and Sampling Distributions Large sample Estimation Large Sample Tests of Hypotheses Inferences from Small Samples The Analysis of Variance Linear Regression and Correlation Multiple Linear Regression Elements of Time Series Analysis Forecasting Models…