tsPI: Improved Prediction Intervals for ARIMA Processes and Structural Time Series

Prediction intervals for ARIMA and structural time series models using importance sampling approach with uninformative priors for model parameters, leading to more accurate coverage probabilities in frequentist sense. Instead of sampling the future observations and hidden states of the state space representation of the model, only model parameters are sampled, and the method is based solving the equations corresponding to the conditional coverage probability of the prediction intervals. This makes method relatively fast compared to for example MCMC methods, and standard errors of prediction limits can also be computed straightforwardly.

Estimating aggregated nutrient fluxes in four Finnish rivers via Gaussian state space models

Abstract Reliable estimates of the nutrient fluxes carried by rivers from land-based sources to the sea are needed for efficient abatement of marine eutrophication. Although nutrient concentrations in rivers generally display large temporal variation, sampling and analysis for nutrients, unlike flow measurements, are rarely performed on a daily basis. The infrequent data calls for ways to reliably estimate the nutrient concentrations of the missing days. Here, we use the Gaussian state space models with daily water flow as a predictor variable to predict missing nutrient concentrations for four agriculturally impacted Finnish rivers.