ArmaStatistics             package:fArma             R Documentation

_S_t_a_t_i_s_t_i_c_s _o_f _t_h_e _T_r_u_e _A_R_M_A _P_r_o_c_e_s_s

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

     A collection and description of functions  to compute statistics
     of a true ARMA time series process. 

     The functions are:

       'armaRoots'    Roots of the characteristic ARMA polynomial,
       'armaTrueacf'  True autocorrelation function of an ARMA process.

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

     armaRoots(coefficients, n.plot = 400, digits = 4, ...) 
     armaTrueacf(model, lag.max = 20, type = c("correlation", "partial", "both"), 
         doplot = TRUE) 

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

coefficients: [armaRoots] - 
           a numeric vector with the coefficients of the
          characterisitic  polynomial. 

  digits: [armaRoots] - 
           output precision, an integer value. 

  doplot: [armaRoots] - 
           a logical. Should a plot be displayed? 

 lag.max: [armaTrueacf] - 
           maximum number of lags at which to calculate the acf or 
          pacf, an integer value by default 20. 

   model: [armaTrueacf] - 
           a specification of the ARMA model with two elements:
          'model$ar' is the vector of the AR coefficients, and 
          'model$ma' is the vector of the MA coefficients. 

       n: [armaSim] - 
           an integer value setting the length of the series to be
          simulated  (optional if 'innov' is provided). The default
          value is 100. 

  n.plot: [armaRoots] - 
           the number of data points to plot the unit circle; an
          integer value. 

    type: [armaTrueacf] - 
           a character string, "correlation" to compute the true 
          autocorrelation function, "partial" to compute the true
          partial autocorrelation function, or "both" if both functions
          are desired. The start of one of the strings  will suffice. 

     ...: additional arguments to be passed. 

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

     'armaRoots'  
      returns a three column data frame with the real, the imaginary
     part  and the radius of the roots. The number of rows corresponds
     to the coefficients.

     'armaTrueacf' 
      returns a two column data frame with the lag and the correlation 
     function.

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

     M. Plummer and B.D. Ripley for 'ar' functions and code,
      B.D. Ripley for 'arima' and 'ARMAacf' functions and code, 
      C. Fraley and F. Leisch for 'fracdiff' functions and code, and 
      Diethelm Wuertz for the Rmetrics R-port.

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

     Brockwell, P.J. and Davis, R.A. (1996);  _Introduction to Time
     Series and Forecasting_,  Second Edition, Springer, New York. 

     Durbin, J. and Koopman, S.J. (2001);  _Time Series Analysis by
     State Space Methods_,   Oxford University Press.

     Gardner, G, Harvey, A.C., Phillips, G.D.A. (1980);  _Algorithm
     AS154. An algorithm for exact maximum likelihood  estimation of
     autoregressive-moving average models by means of  Kalman
     filtering_, Applied Statistics, 29, 311-322.

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

     Harvey, A.C. (1993);  _Time Series Models_, 2nd Edition, Harvester
     Wheatsheaf, Sections 3.3 and 4.4.

     Jones, R.H. (1980);  _Maximum likelihood fitting of ARMA models to
     time series with missing observations_, Technometrics, 20,
     389-395.

     Percival, D.P. and Walden, A.T. (1998);  _Spectral Analysis for
     Physical Applications._  Cambridge University Press.

     Whittle, P. (1963);  _On the fitting of multivariate
     autoregressions and the approximate canonical factorization of a
     spectral  matrix._ Biometrika 40, 129-134.

     Haslett J. and Raftery A.E. (1989); _Space-time Modelling with
     Long-memory Dependence: Assessing  Ireland's Wind Power Resource
     (with Discussion)_, Applied Statistics 38, 1-50.

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

     ## armaRoots -
        # Calculate and plot the roots of an ARMA process:
        par(mfrow = c(2, 2), cex = 0.7)
        coefficients = c(-0.5, 0.9, -0.1, -0.5)
        armaRoots(coefficients)
        
     ## armaTrueacf -
        model = list(ar = c(0.3, +0.3), ma = 0.1)
        armaTrueacf(model)
        model = list(ar = c(0.3, -0.3), ma = 0.1)
        armaTrueacf(model)

