estimate {aTSA} R Documentation

## Estimate an ARIMA Model

### Description

Estimates an ARIMA model for a univariate time series, including a sparse ARIMA model.

### Usage

estimate(x, p = 0, d = 0, q = 0, PDQ = c(0, 0, 0), S = NA,
method = c("CSS-ML", "ML", "CSS"), intercept = TRUE, output = TRUE, ...)


### Arguments

 x a univariate time series. p the AR order, can be a positive integer or a vector with several positive integers. The default is 0. d the degree of differencing. The default is 0. q the MA order, can be a positive integer or a vector with several positive integers. The default is 0. PDQ a vector with three non-negative integers for specification of the seasonal part of the ARIMA model. The default is c(0,0,0). S the period of seasonal ARIMA model. The default is NA. method fitting method. The default is CSS-ML. intercept a logical value indicating to include the intercept in ARIMA model. The default is TRUE. output a logical value indicating to print the results in R console. The default is TRUE. ... optional arguments to arima function.

### Details

This function is similar to the ESTIMATE statement in ARIMA procedure of SAS, except that it does not fit a transfer function model for a univariate time series. The fitting method is inherited from arima in stats package. To be specific, the pure ARIMA(p,q) is defined as

X[t] = \mu + \phi*X[t-1] + ... + \phi[p]*X[p] + e[t] - \theta*e[t-1] - ... - \theta[q]*e[t-q].

The p and q can be a vector for fitting a sparse ARIMA model. For example, p = c(1,3),q = c(1,3) means the ARMA((1,3),(1,3)) model defined as

X[t] = \mu + \phi*X[t-1] + \phi*X[t-3] + e[t] - \theta*e[t-1] - \theta*e[t-3].

The PDQ controls the order of seasonal ARIMA model, i.e., ARIMA(p,d,q)x(P,D,Q)(S), where S is the seasonal period. Note that the difference operators d and D = PDQ are different. The d is equivalent to diff(x,differences = d) and D is diff(x,lag = D,differences = S), where the default seasonal period is S = frequency(x).

The residual diagnostics plots will be drawn.

### Value

A list with class "estimate" and the same results as arima. See arima for more details.

### Note

Missing values are removed before the estimate. Sparse seasonal ARIMA(p,d,q)x(P,D,Q)(S) model is not allowed.

Debin Qiu

### References

Brockwell, P. J. and Davis, R. A. (1996). Introduction to Time Series and Forecasting. Springer, New York. Sections 3.3 and 8.3.

arima, identify, forecast

### Examples

estimate(lh, p = 1) # AR(1) process
estimate(lh, p = 1, q = 1) # ARMA(1,1) process
estimate(lh, p = c(1,3)) # sparse AR((1,3)) process

# seasonal ARIMA(0,1,1)x(0,1,1)(12) model
estimate(USAccDeaths, p = 1, d = 1, PDQ = c(0,1,1))


[Package aTSA version 3.1.2 Index]