HKprocess (version 0.1-1)

inferf: Posterior distribution of the φ parameter of the AR(1) process, using an Accept-Reject algorithm

Description

The function inferf is used to create a sample from the posterior distribution of φ. The function uses the eq.10 (Tyralis and Koutsoyiannis 2014) to make inference on φ and an Accept-Reject algorithm (see Robert and Casella 2004, Algorithm A.4).

Usage

inferf(data, n, add = 0.001, minu = -0.999, maxu = 0.999)

Value

Vector with the simulated sample.

Arguments

data

time series data

n

The size of the simulated sample

add

A number added to the maximum value of the natural logarithm of eq.10, to avoid bugs of the Accept-Reject algorithm due to computation errors

minu

A lower bound to the parameter φ

maxu

An upper bound to the parameter φ

Author

Hristos Tyralis

References

Robert CP, Casella G (2004) Monte Carlo Statistical Methods. New York: Springer. tools:::Rd_expr_doi("10.1007/978-1-4757-4145-2").

Tyralis H, Koutsoyiannis D (2014) A Bayesian statistical model for deriving the predictive distribution of hydroclimatic variables. Climate Dynamics 42(11-12):2867--2883. tools:::Rd_expr_doi("10.1007/s00382-013-1804-y").

Examples

# Posterior distribution of the phi parameter of the AR(1) process for the Nile
# time series.

set.seed(12345)

samp.sim <- inferf(Nile,500)

hist(samp.sim, breaks = 20, main = expression(paste("Histogram of ",phi)),
xlab = expression(phi))