KalmanLike {stats} | R Documentation |

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

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

`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. |

`fast` |
If `TRUE` the `mod` object may be modified. |

These functions work with a general univariate state-space model
with state vector `a`

, transitions `a <- T a + R e`

,
*e ~ N(0, kappa Q)* and observation
equation `y = Z'a + 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
`Pn`

- 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.

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 `var`

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.

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

In particular, `KalmanLike`

alters the objects passed as
the elements `a`

, `P`

and `Pn`

of `mod`

, so these
should not be shared. Use `fast=FALSE`

to prevent this.

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

[Package *stats* version 2.2.1 Index]