arma                 package:tseries                 R Documentation

_F_i_t _A_R_M_A _M_o_d_e_l_s _t_o _T_i_m_e _S_e_r_i_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Fit an ARMA model to a univariate time series by conditional least
     squares. For exact maximum likelihood estimation see `arima0'.

_U_s_a_g_e:

     arma (x, order = c(1, 1), lag = NULL, coef = NULL, include.intercept = TRUE,
           series = NULL, qr.tol = 1e-07, ...)
     coef (object)
     residuals (object)
     fitted (object)
     print (object, digits = max(3,.Options$digits-3))
     summary (object)
     plot (object, ask = interactive())
     print.summary (object, digits = max(3,.Options$digits-3),
                    signif.stars = .Options$show.signif.stars, ...)

_A_r_g_u_m_e_n_t_s:

       x: a numeric vector or time series.

   order: a two dimensional integer vector giving the orders of the
          model to fit. `order[1]' corresponds to the AR part and
          `order[2]' to the MA part.

     lag: a list with components `ar' and `ma'. Each component is an
          integer vector, specifying the AR and MA lags that are
          included in the model. If both, `order' and `lag', are given,
          only the specification from `lag' is used.

    coef: If given this numeric vector is used as the initial estimate
          of the ARMA coefficients. The preliminary estimator suggested
          in Hannan and Rissanen (1982) is used for the default
          initialization.

include.intercept: Should the model contain an intercept?

  series: name for the series. Defaults to `deparse(substitute(x))'.

  qr.tol: the `tol' argument for `qr' when computing the asymptotic
          standard errors of `coef'.

     ...: additional arguments for `optim' when fitting the model.

  object: a fit from `arma'.

digits, signif.stars: see `print.coefmat'.

     ask: Should the `plot' method work interactively? See
          `interactive'.

     ...: additional arguments for `print'.

_D_e_t_a_i_l_s:

     The following parametrization is used for the ARMA(p,q) model:


 y[t] = a[0] + a[1]y[t-1] + ... + a[p]y[t-p] + b[1]e[t-1] + ... + b[q]e[t-q] + e[t],


     where `a[0]' is set to zero if no intercept is included. By using
     the argument `lag', it is possible to fit a parsimonious submodel
     by setting arbitrary `a[i]' and `b[i]' to zero.

     `arma' uses `optim' to minimize the conditional sum-of-squared
     errors. The gradient is computed, if it is needed, by a
     finite-difference approximation. Default initialization is done by
     fitting a pure high-order AR model (see `ar.ols').  The estimated
     residuals are then used for computing a least squares estimator of
     the full ARMA model. See Hannan and Rissanen (1982) for details.

     `summary' computes the asymptotic standard errors of the
     coefficient estimates from the numerically differentiated Hessian
     matrix approximation. The AIC is computed from the conditional
     sum-of-squared errors and not from the true maximum likelihood
     function. That may be problematic.

_V_a_l_u_e:

     For `arma' and its methods `print' and `plot' a list of class
     `"arma"' with the following elements: 

     lag: the lag specification of the fitted model.

    coef: estimated ARMA coefficients for the fitted model.

     css: the conditional sum-of-squared errors.

  n.used: the number of observations of `x'.

residuals: the series of residuals.

fitted.values: the fitted series.

  series: the name of the series `x'.

frequency: the frequency of the series `x'.

    call: the call of the `arma' function.

asy.se.coef: the asymptotic-theory standard errors of the coefficient
          estimates.

convergence: The `convergence' integer code from `optim'.

include.intercept: Does the model contain an intercept?


     For `coef', a numeric vector, for `residuals' and `fitted' a
     univariate time series.

     For `summary' and `print.summary' a list of class
     `"summary.arma"'.

_A_u_t_h_o_r(_s):

     A. Trapletti

_R_e_f_e_r_e_n_c_e_s:

     E. J. Hannan and J. Rissanen (1982): Recursive Estimation of Mixed
     Autoregressive-Moving Average Order. Biometrika 69, 81-94.

_S_e_e _A_l_s_o:

     `arima0', `ar'

_E_x_a_m_p_l_e_s:

     data (tcm)  
     r <- diff(tcm10y)
     summary (r.arma <- arma (r, order = c(1, 0)))
     summary (r.arma <- arma (r, order = c(2, 0)))
     summary (r.arma <- arma (r, order = c(0, 1)))
     summary (r.arma <- arma (r, order = c(0, 2)))
     summary (r.arma <- arma (r, order = c(1, 1)))
     plot (r.arma)

     data (nino)
     s <- nino3.4
     summary (s.arma <- arma (s, order=c(20,0)))
     summary (s.arma
              <- arma (s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL)))
     acf (residuals(s.arma), na.action=na.remove)
     pacf (residuals(s.arma), na.action=na.remove)
     summary (s.arma
              <- arma (s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=12)))
     summary (s.arma
              <- arma (s, lag=list(ar=c(1,3,7,10,12,13,16,17),ma=12)))
     plot (s.arma)

