ARMA_MEAN - ARMA fitted values of conditional mean

Returns an array of cells for the fitted values of the conditional mean.

 

Syntax

ARMA_MEAN(X, Order, mean, sigma, phi, theta)

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).

theta are the parameters of the MA(q) component model (starting with the lowest lag).

 

Remarks

  1. The underlying model is described here.
  2. Warning: ARMA_MEAN() function is deprecated as of version 1.63: use ARMA_FIT function instead.
  3. The time series is homogeneous or equally spaced.
  4. The time series may include missing values (e.g. #N/A) at either end.
  5. The ARMA model fitted values are defined as:

    $$\hat x_t = \mu + \sum_{i=1}^p \phi_i x_{t-i} + \sum_{j=1}^q \theta_j a_{t-j} $$

    Where:
    • $\hat x_t$ is the fitted model value (i.e. conditional mean) at time t.

      $1\leq t \leq T $
    • $T$ is the number of non-missing values in the data sample.
  6. The number of parameters in the input argument - phi - determines the order of the AR component.
  7. The number of parameters in the input argument - theta - determines the order of the MA component.

Examples

Example 1:

 
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A B C D E
Date Data ARMA_MEAN    
January 10, 2008 -0.30 -0.342 ARMA  
January 11, 2008 -1.28 -0.447 Mean -0.35
January 12, 2008 0.24 -0.597 Sigma 1.3059
January 13, 2008 1.28 0.244 Phi_1 -0.4296
January 14, 2008 1.20 -0.008 Theta_1 0.999897
January 15, 2008 1.73 0.207    
January 16, 2008 -2.18 0.060    
January 17, 2008 -0.23 -1.611    
January 18, 2008 1.10 0.921    
January 19, 2008 -1.09 -0.813    
January 20, 2008 -0.69 -0.312    
January 21, 2008 -1.69 -0.607    
January 22, 2008 -1.85 -0.853    
January 23, 2008 -0.98 -0.679    
January 24, 2008 -0.77 -0.382    
January 25, 2008 -0.30 -0.539    
January 26, 2008 -1.28 -0.168    
January 27, 2008 0.24 -1.002    
January 28, 2008 1.28 0.623    
January 29, 2008 1.20 -0.373    
January 30, 2008 1.73 0.545    
January 31, 2008 -2.18 -0.130    
February 1, 2008 -0.23 -1.545    
February 2, 2008 1.10 0.892    
February 3, 2008 -1.09 -0.774    
February 4, 2008 -0.69 -0.348    
February 5, 2008 -1.69 -0.559    
February 6, 2008 -1.85 -0.901    
February 7, 2008 -0.98 -0.644    

Files Examples

References

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