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, ...)
statspackage. 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
qcan 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
PDQcontrols 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
dand D =
PDQ are different. The
dis 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.
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))