aTSA (version 3.1.2)

estimate: 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, ...)

Value

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

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.

Author

Debin Qiu

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 $$X[t]=\mu +\varphi [1]\ast X[t-1]+...+\varphi [p]\ast X[p]+e[t]-\theta [1]\ast e[t-1]-...-\theta [q]\ast e[t-q].$$ 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 $$X[t]=\mu +\varphi [1]\ast X[t-1]+\varphi [3]\ast X[t-3]+e[t]-\theta [1]\ast e[t-1]-\theta [3]\ast e[t-3].$$ 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.

References

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

See Also

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))