avg_coverage_struct
(Package: tsPI) :
Compute the average coverage of the prediction intervals computed by code{link{struct_pi
Computes expected coverage probabilities of the prediction intervals of structural time series model. Note that for the plug-in method only standard deviations are assumed to be identical to their estimates, but the initial values for the states are still treated as diffuse. Because of this, plug-in method often performs relatively well in case of structural time series models compared to similar type of ARIMA models (local level and local linear trend models are closely related to ARIMA(0,1,1) and ARIMA(0,2,2) models), and in some cases even outperforms the importance sampling approach with uniform prior (see examples). This is not suprising, as local level and local linear trend models are closely related to ARIMA(0,1,1) and ARIMA(0,2,2) models, and the effect of uncertainty in MA components is not as significant as the uncertainty of AR components
arima_pi
(Package: tsPI) :
Prediction Intervals for ARIMA Processes with Exogenous Variables Using Importance Sampling
Function arima_pi computes prediction intervals for ARIMA processes with exogenous variables using importance sampling. For regression coefficients, diffuse (uninformative) prior is used, whereas multiple options for prior distributions for ARMA coefficients are supported.
information_arma
(Package: tsPI) :
Large Sample Approximation of Information Matrix for ARMA process
Fortran implementation of InformationMatrixARMA function of FitARMA package, except that the function uses the same ARMA model definition as arima, where both the AR and MA parts of the model are on the right side of the equation, i.e. MA coefficients differ in sign compared to InformationMatrixARMA.
tsPI
(Package: tsPI) :
Improved Prediction Intervals for ARIMA Processes and Structural Time Series
Package tsPI computes prediction intervals for ARIMA and structural time series models by 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.
providing 
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