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).
Warning
ARMA_MEAN() function is deprecated as of version 1.63: use ARMA_FIT function instead.
Remarks
- The underlying model 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 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.
- $\hat x_t$ is the fitted model value (i.e. conditional mean) at time t.
- 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:
|
|
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: 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
Comments
Article is closed for comments.