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, ...)

_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.

_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.

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

     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?

_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:

     'summary.arma' for summarizing ARMA model fits; 'arma-methods' for
     further methods; '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)

