Computes the log-likelihood function (LLF) of the estimated ARMA model.
ARMA_LLF ([x], order, µ, σ, [φ], [θ])
- Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
- Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Value Order 1 Ascending (the first data point corresponds to the earliest date) (default). 0 Descending (the first data point corresponds to the latest date).
- Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
- Required. Is the standard deviation value of the model's residuals/innovations.
- Optional. Are the parameters of the AR(p) component model: [φ1, φ2 … φp] (starting with the lowest lag).
- Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (starting with the lowest lag).
ARMA_LLF(.) function is deprecated as of version 1.63: use ARMA_GOF(.) function instead.
- The underlying model is described here.
- The Log-Likelihood Function (LLF) is described here.
- 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 (σ) must be greater than zero.
- The 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 - ([φ]) - determines the order of the AR component.
- The number of parameters in the input argument - ([θ]) - determines the order of the MA component.
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