HKprocess (version 0.1-1)

mlear1: Maximum likelihood estimation for the AR(1) parameters.

Description

The function mlear1 is used to estimate the μ, σ and φ parameters of the AR(1) process as defined in Tyralis and Koutsoyiannis (2014). The method for their estimation is described in eqs.8-9 (Tyralis and Koutsoyiannis 2011).

Usage

mlear1(data, interval = c(-0.9999, 0.9999), tol = .Machine$double.eps^0.25)

Value

A vector whose values are the maximum likelihood estimates of μ, σ and φ.

Arguments

data

time series data

interval

φ interval estimation

tol

estimation error tolerance

Author

Hristos Tyralis

References

McLeod AI, Yu H, Krougly ZL (2007) Algorithms for linear time series analysis: With R package. Journal of Statistical Software 23(5):1--26. tools:::Rd_expr_doi("10.18637/jss.v023.i05").

Tyralis H, Koutsoyiannis D (2011) Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process. Stochastic Environmental Research & Risk Assessment 25(1):21--33. tools:::Rd_expr_doi("10.1007/s00477-010-0408-x").

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

# Estimate the parameters for the Nile time series.

mlear1(Nile)