KalmanLike                package:ts                R Documentation

_K_a_l_m_a_n _F_i_l_t_e_r_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     Use Kalman Filtering to find the (Gaussian) log-likelihood, or for
     forecasting or smoothing.

_U_s_a_g_e:

     KalmanLike(y, mod, nit = 0)
     KalmanRun(y, mod, nit = 0)
     KalmanSmooth(y, mod, nit = 0)
     KalmanForecast(n.ahead = 10, mod)
     makeARIMA(phi, theta, Delta, kappa = 1e6)

_A_r_g_u_m_e_n_t_s:

       y: a univariate time series.

     mod: A list describing the state-space model: see Details.

     nit: The time at which the initialization is computed. `nit = 0'
          implies that the initialization is for a one-step prediction,
          so `Pn' should not be computed at the first step.

 n.ahead: The number of steps ahead for which prediction is required.

phi, theta: numeric vectors of length >=0 giving AR and MA parameters.

   Delta: vector of differencing coefficients, so an ARMA model is
          fitted to `y[t] - Delta[1]*y[t-1] - ...'.

   kappa: the prior variance (as a multiple of the innovations
          variance) for the past observations in a differenced model.

_D_e_t_a_i_l_s:

     These functions work with a general univariate state-space model
     with state vector `a', transitions `a <- T a + e', e ~ N(0, kappa
     Q) and observation equation `y = Z'a + R eta', eta ~ N(0, kappa
     h).  The likelihood is a profile likelihood after estimation of
     kappa.

     The model is specified as a list with at least components

     `_T' the transition matrix

     `_Z' the observation coeficients

     `_h' the observation variance

     `_V' `RQR''

     `_a' the current state estimate

     `_P' the current estimate of the state uncertainty matrix

     `_P_n' the estimate at time t-1 of the state uncertainty matrix

     `KalmanSmooth' is the workhorse function for `tsSmooth'.

     `makeARIMA' constructs the state-space model for an ARIMA model.

_V_a_l_u_e:

     For `KalmanLike', a list with components `Lik' (the log-likelihood
     less some constants) and `s2', the estimate of of kappa.

     For `KalmanRun', a list with components `values', a vector of
     length 2 giving the output of `KalmanLike', `resid' (the
     residuals) and `states', the contemporaneous state estimates, a
     matrix with one row for each time.

     For `KalmanSmooth', a list with two components. Component `smooth'
     is a `n' by `p' matrix of state estimates based on all the
     observations, with one row for each time. Component `smooth' is a
     `n' by `p' by `p' array of variance matrices.

     For `KalmanForecast', a list with components `pred', the
     predictions, and `var', the unscaled variances of the prediction
     errors (to be muliplied by `s2').

     For `makeARIMA', a model list including components for its
     arguments.

_W_a_r_n_i_n_g:

     These functions are designed to be called from other functions
     which check the validity of the arguments passed, so very little
     checking is done.

_A_u_t_h_o_r(_s):

     B. D. Ripley

_R_e_f_e_r_e_n_c_e_s:

     Durbin, J. and Koopman, S. J. (2001) Time Series Analysis by State
     Space Methods.  Oxford University Press.

_S_e_e _A_l_s_o:

     `arima', `StructTS'. `tsSmooth'.

