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TSdata
TSmodel
TSestModel

There are also functions for forecasting with the models and for evaluating the performance of forecasting models. Finally, there are functions for evaluating model estimation techniques.

In addition to this help facility there is a document called a "Brief User's Guide" which explains, with examples, the use of the main functions in the library. This is available in a postscript or as a pdf file. The functions described in the guide should work fairly reliably, however, many of the functions described in this help facility are still under development and may not work. In addition, there may be functions described in the help facility for which the code has not yet been included with the software. This is a compromise which allows me to make the software available with minimum effort. This software is not a commercial product. It is the by-product of an ongoing research effort. Constructive suggestions and comments are welcomed. I can be reached at pgilbert@bank-banque-canada.ca or by phone at (613) 782-7346.

Description

Class "TSdata" of time series data objects for use with TSmodels.

Generation

This class of objects is returned by the function TSdata or can be built according to the description below. Functions in this library which use data pass it through the function TSdata (which may not do much other than check that the data has class TSdata).

Methods

The TSdata class of objects has methods for the generic functions print, plot, periods, start, end, ..., test.equal, series.names, input.series.names, output.series.names Also, the function is.TSdata is supported.

Inheritance

Other data classes inherit from the class TSdata.

Structure

Objects are a list with class the most general class "TSdata". The native form for this library has elements input and output. Any other elements are ignored. input and output are matrices (or tframe or time series matrices) of the input and output data, with each series in a column. TSPADIdata objects inherit from this class but have a somewhat different structure. TSPADIdata makes it possible to retrieve data from an external database when it is needed. These subclass objects do not contain the actual data, but only the names of the series and the data base where they are located. The function set.data can be used to set up an object of class c("TSPADIdata", TSdata").

See Also

TSmodel.object, TSestModel.object, tframe.object, TSPADI.object

Description

Class "TSmodel" of time series model objects.

Generation

This class of objects is returned by estimation methods or can be built according to the description for specific sub-class (eg "ARMA", "SS", "troll").

Methods

The TSmodel class of objects has methods for the generic functions print, test.equal, series.names, input.series.names, output.series.names, l, roots, stability, forecast, feather.forecasts, horizon.forecasts, simulate, monte.carlo.simulations Also, the function is.TSmodel and the functions to.SS, to.ARMA, to.troll are supported.

Inheritance

Other model classes inherit from the class TSmodel.

Structure and Details

This class of objects contains a time series model. It is the class of objects expected by many of the functions in this library. A TSmodel is a list. The two sub-class ARMA and SS are described below. See troll.object for the sub-class "troll". ARMA. and SS indicate linear, time-invariant ARMA and state space models. State space models have a further sub-class: innov or non-innov, indicating an innovations form or a non-innovations form. Many of the functions in this library are designed for estimating and converting among various representations of these types of models.

The ARMA model is defined by: A(L)y(t) = B(L)w(t) + C(L)u(t)

A(L)

(axpxp) is the auto-regressive polynomial array.

B(L)

(bxpxp) is the moving-average polynomial array.

C(L)

(cxpxm) is the input polynomial array.

y

is the p dimensional output data.

u

is the m dimensional control (input) data.


The state space (SS) model is defined by:

z(t) = Fz(t-1) + Gu(t) + Qe(t)
y(t) = Hz(t) + Rw(t)

or the innovations model:

z(t) = Fz(t-1) + Gu(t) + Kw(t-1)
y(t) = Hz(t) + w(t)

FF

(nxn) is the state transition matrix F.

H

(pxn)is the output matrix H.

Q

(nxn) is the input matrix of the system noise and the noise is assumed to be white. Some authors (eg. Harvey) modify this as rt*qt*rt' where rt is the matrix for the system noise and qt is the noise cov, but that is redundant.

R

(pxp) is the input matrix of the output (measurement) noise, which is assumed white. probably need R if p>n ??

G

(nxp)is the control (input) matrix.

K

(nxp)is the Kalman gain.

y

is the p dimensional output data.

u

is the m dimensional exogenous (input) data.

z

is the n dimensional (estimated) state at time t, E[z(t)|y(t-1), u(t)] denoted E[z(t)|t-1]. An initial value for z can be specified as z0 and an initial one step ahead state tracking error (for non-innovations models) as P0.

In order to specify a model the usual method would be to specify the model arrays and us the function set.parameters (see the Brief Users' Guide for examples) to set the internal structure detailed below.
A list of class TSmodel has the elements

$description

An arbitrary description.

$parms

a vector of the parameters

$location

a character vector indicating the array in which parameters are located.

$i

a vector of the corresponding i location

$j

a vector of the corresponding j location

$const

a vector of the non zero constants

$const.location

a character vector indicating the array in which constants are located.

$const.i

a vector of the corresponding i location of constants

$const.j

a vector of the corresponding j location of constants

optionally $input.names

a vector of character strings indicating input variable names

optionally $output.names

a vector of character strings indicating output variable names


then in the case of sub-class SS

$F,$G, $H, $K $z0 $P0

for sub-sub-class innov (the Kalman gain K is specified but not Q and R ).

or $F,$G, $H, $Q, $R $z0 $P0

for sub-sub-class non-innov (Q and R are specified but not the Kalman gain K).

The integers m,n,p are implicitly defined by the array dimensions. $G should be NULL if there is no input.

and in the case of sub-class ARMA

$l

a vector of the corresponding l (lag+1) location of parameters

$const.l

a vector of the corresponding l (lag+1) location of constants

$A,$B,$C

the polynomial arrays A, B, C $C should be NULL if there is no input.

See Also

TSdata.object, TSestModel.object, TSestModel.object

Description

Class of object containing a time series model, data, and estimation information.

Details

This class of objects contains a time series model (TSmodel), data (TSdata), and information obtained by evaluating the model with the data. It is a list with three elements (and optionally more) which are also lists:

$data

is a list of data as described in TSdata.

$model

list of class TSmodel as described in TSmodel.

$estimates

is a list of:

$like

The negative log likelihood function value ( a vector of the total, constant, the det part, and the cov part)

$cov

The estimated residual covariance.

$pred

The one step ahead predictions (see predictT below). These are aligned with $data$output so that residuals = estimates$pred[1:sampleT,]-$data$output[1:sampleT,]

$sampleT

The end of the period (starting from 1) for which $data$output is used for calculating one step ahead predictions.

$predictT

The end of the period for which the model is simulated. sampleT must be less than or equal predictT. If predictT is greater than sampleT then each step ahead beyond sampleT is based on the prediction of the previous step and not corrected by the prediction error.

$filter (optional)

is a list of

$state (optional)

The one step ahead (filter) estimate of the state E[z(t)|y(t-1), u(t)]. Note: In the case where there is no input u this corresponds to what would usually be called the predicted state - not the filtered state.

$track (optional)

The estimated state tracking error P(t|t-1). Again note, this corresponds to the predicted tracking eror not the filtered tracking error. This is NULL for innovations models.

$smooth (optional)

is a list of

$state (optional)

The smoother (two sided filter) estimate of the state E[z(t)| sampleT].

$track (optional)

The smoothed estimate of the state tracking error P(t|sampleT). This is NULL for innovations models.

See Also

TSmodel, TSdata DSE