g13bg accepts a series of new observations of an output time series and any associated input time series, for which a multi-input model is already fully specified, and updates the ‘state set’ information for use in constructing further forecasts.
- Type: array<System..::..Double>()An array of size [nsttf]On entry: the nsttf values in the state set before updating as returned by g13be or g13bj, or a previous call to g13bg.On exit: the state set values after updating.
- Type: System..::..Int32
- Type: array<System..::..Int32>()An array of size On entry: the orders vector of the ARIMA model for the output noise component., , and refer respectively to the number of autoregressive , moving average , seasonal autoregressive and seasonal moving average parameters., and refer respectively to the order of non-seasonal differencing, the order of seasonal differencing, and the seasonal period.Constraints:
- , , , , , , ;
- if , ;
- if , .
- Type: System..::..Int32On entry: the total number of input and output series. There may be any number of input series (including none), but only one output series.
- Type: array<System..::..Int32,2>[,](,)[,][,]An array of size [, nser]On entry: the transfer function model orders , and of each of the input series. The data for input series are held in column . Row 1 holds the value , row 2 holds the value and row 3 holds the value . For a simple input, .Row 4 holds the value , where for a simple input and for a transfer function input. When any nonzero contents of rows 1, 2 and 3 of column are ignored. The choice of or is an option for use in model estimation and does not affect the operation of g13bg.Constraint: , or , for .
- Type: array<System..::..Double>()An array of size [npara]On entry: estimates of the multi-input model parameters as returned by g13be. These are in order, firstly the ARIMA model parameters: values of parameters, values of parameters, values of parameters and values of parameters. These are followed by the transfer function model parameter values , for the first of any input series and similarly for each subsequent input series. The final component of para is the value of the constant .
- Type: System..::..Int32On entry: the exact number of , , , , , and parameters. ( must be included whether its value was previously estimated or was set fixed.)
- Type: System..::..Int32On entry: the number of new observation sets being used to update the state set, each observation set consisting of a value of the output series and the associated values of each of the input series at a particular time point.
- Type: array<System..::..Double,2>[,](,)[,][,]An array of size [dim1, nser]Note: dim1 must satisfy the constraint:On entry: the nnv new observation sets being used to update the state set. Column contains the values of input series , for . Column contains the values of the output series. Consecutive rows correspond to increasing time sequence.
- Type: System..::..Int32
- Type: array<System..::..Double>()An array of size [nnv]On exit: the values of the residual series corresponding to the new observations of the output series.
The multi-input model is specified in [Description] in g13be. The form of these equations required to update the state set is as follows:
the transfer models which generate input component values from one or more inputs ,
which generates the output noise component from the output and the input components, and
the ARIMA model for the output noise which generates the residuals .
The state set (as also given in [Description] in g13be) is the collection of terms
for up to the maximum lag associated with each of these series respectively, in the above model equations. is the latest time point of the series from which the state set has been generated.
The method accepts further values of the series , , for , and applies the above model equations over this time range, to generate new values of the various model components, noise series and residuals. The state set is reconstructed, corresponding to the latest time point , the earlier values being discarded.
The set of residuals corresponding to the new observations may be of use in checking that the new observations conform to the previously fitted model. The components of the new observations of the output series which are due to the various inputs, and the noise component, are also optionally returned.
The parameters of the model are not changed in this method.
Box G E P and Jenkins G M (1976) Time Series Analysis: Forecasting and Control (Revised Edition) Holden–Day
Errors or warnings detected by the method:
Some error messages may refer to parameters that are dropped from this interface (LDXXYN) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.
On entry, iwa is too small.
- On entry, one of the , stored in , for does not equal , or .
The computations are believed to be stable.
The time taken by g13bg is approximately proportional to .
The following are computed and printed out: the updated state set, the residuals and the values of the components and the output noise component corresponding to the new observations.