Estimate an ARIMA Model
Estimates an ARIMA model for a univariate time series, including a sparse ARIMA model.
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, ...)x |
a univariate time series. |
p |
the AR order, can be a positive integer or a vector with several positive
integers. The default is |
d |
the degree of differencing. The default is |
q |
the MA order, can be a positive integer or a vector with several positive
integers. The default is |
PDQ |
a vector with three non-negative integers for specification of the seasonal
part of the ARIMA model. The default is |
S |
the period of seasonal ARIMA model. The default is |
method |
fitting method. The default is |
intercept |
a logical value indicating to include the intercept in ARIMA model. The
default is |
output |
a logical value indicating to print the results in R console. The default is
|
... |
optional arguments to |
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] = μ + φ[1]*X[t-1] + ... + φ[p]*X[p] + e[t] - θ[1]*e[t-1] - ... - θ[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] = μ + φ[1]*X[t-1] + φ[3]*X[t-3] + e[t] - θ[1]*e[t-1] - θ[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.
Missing values are removed before the estimate. Sparse seasonal ARIMA(p,d,q)x(P,D,Q)(S) model is not allowed.
Debin Qiu
Brockwell, P. J. and Davis, R. A. (1996). Introduction to Time Series and Forecasting. Springer, New York. Sections 3.3 and 8.3.
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))
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