Computes the log-likelihood function (LLF) of the estimated ARMA model.
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)).
|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).
- The underlying model is described here.
- The Log-Likelihood 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 log-likelihood function becomes:
$$\ln L^* = -T\left(\ln 2\pi \hat \sigma^2+1\right)/2 $$
- $\hat \sigma$ 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.
|=ARMA_LLF($B$2:$B$30,1,$D$3,$D$4,$D$5,$D$6)||Log-Likelihood Function (-2660.88)|
|=ARMA_CHECK($D$3,$D$4,$D$5,$D$6)||Is ARMA model stable? (1)|
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- 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: 0-471-690740
- 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