mlear1 {HKprocess}

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)

Arguments

data

time series data

interval

φ

interval estimation

tol

estimation error tolerance

Value

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

Note

The function likelihoodfunction.c is called from the C library of the package. Ideas for creating this function came from McLeod et al. (2007).

Author(s)

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. 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. 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. doi:10.1007/s00382-013-1804-y.

Examples

# Estimate the parameters for the Nile time series.

mlear1(Nile)