# estimate

0th

Percentile

##### Estimate an ARIMA Model

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 $$X[t] = \mu + \phi[1]*X[t-1] + ... + \phi[p]*X[p] + e[t] - \theta[1]*e[t-1] - ... - \theta[q]*e[t-q].$$ 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 $$X[t] = \mu + \phi[1]*X[t-1] + \phi[3]*X[t-3] + e[t] - \theta[1]*e[t-1] - \theta[3]*e[t-3].$$ 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[2] 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.

##### 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

• estimate
##### 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))
Documentation reproduced from package aTSA, version 3.1.2, License: GPL-2 | GPL-3

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