Computes the loglikelihood function (LLF) of the estimated ARMA model.
Syntax
ARMA_LLF(X, Order, mean, sigma, phi, ARRAY)
 X
 is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).
 Order
 is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).
Order Description 1 ascending (the first data point corresponds to the earliest date) (default) 0 descending (the first data point corresponds to the latest date)  mean
 is the ARMA model mean (i.e. mu).
 sigma
 is the standard deviation of the model's residuals/innovations.
 phi
 are the parameters of the AR(p) component model (starting with the lowest lag).
 ARRAY
 are the parameters of the MA(q) component model (starting with the lowest lag).
Remarks
 The underlying model is described here.
 The LogLikelihood Function (LLF) is described here.

Warning: ARMA_AIC() function is deprecated as of version 1.63: use ARMA_GOF function instead.
 The time series is homogeneous or equally spaced.
 The time series may include missing values (e.g. #N/A) at either end.
 The residuals/innovations standard deviation (i.e. $\sigma$) should be greater than zero.
 ARMA model has independent and normally distributed residuals with constant variance. The ARMA loglikelihood function becomes:
$$\ln L^* = T\left(\ln 2\pi \hat \sigma^2+1\right)/2 $$
Where:
 $\hat \sigma$ is the standard deviation of the residuals.
 The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
 The number of parameters in the input argument  phi  determines the order of the AR component.
 The number of parameters in the input argument  theta  determines the order of the MA component.
Examples
Example 1:


Formula  Description (Result) 

=ARMA_LLF($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6)  LogLikelihood Function (2660.88) 
=ARMA_CHECK($D$3,$D$4,$D$5,$D$6)  Is ARMA model stable? (1) 
Files Examples
Related Links
References
 D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
 James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
 Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0471690740
 Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
 Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568
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