NAG CL Interface
g13bbc (multi_​filter_​transf)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{y}\left[\mathbf{ny}\right]$ – const double Input

On entry: the $Q_y^{\prime }$ backforecasts starting with backforecast at time $1-Q_y^{\prime }$ to backforecast at time $0$ followed by the time series starting at time $1$, where $Q_y^{\prime }=\mathbf{arimas}\mathbf{.}\mathbf{q}+\mathbf{arimas}\mathbf{.}\mathbf{bigq}\times \mathbf{arimas}\mathbf{.}\mathbf{s}$. If there are no backforecasts either because the ARIMA model for the time series is not known or because it is known but has no moving average terms, then the time series starts at the beginning of y.

2: $\mathbf{ny}$ – Integer Input

On entry: the total number of backforecasts and time series data points in array y.

Constraint: $\mathbf{ny}\ge \max (1+Q_y^{\prime },\mathbf{npar})$.

3: $\mathbf{transfv}$ – Nag_TransfOrder * Input

On entry: the orders of the transfer function model where the triplet (transfv. nag_b, transfv. nag_q, transfv. nag_p) corresponds to the triplet $(b,q,p)$ as described in Section 2.3.1 in the G13 Chapter Introduction.

Constraints:

• $\mathbf{transfv}\mathbf{.}\mathbf{nag\_b}\ge 0$;
• $\mathbf{transfv}\mathbf{.}\mathbf{nag\_q}\ge 0$;
• $\mathbf{transfv}\mathbf{.}\mathbf{nag\_p}\ge 0$.

4: $\mathbf{arimas}$ – Nag_ArimaOrder * Input

On entry: if available, the orders for the filtering ARIMA model for the time series as a pointer to structure of type Nag_ArimaOrder with the following members:

p – Integer

d – IntegerInput

q – IntegerInput

bigp – IntegerInput

bigd – IntegerInput

bigq – IntegerInput

s – IntegerInput

On entry: these seven members of arimas must specify the orders vector $(p,d,q,P,D,Q,s)$, respectively, of the ARIMA model for the output noise component.

$p$, $q$, $P$ and $Q$ refer, respectively, to the number of autoregressive ($\varphi$), moving average ($\theta$), seasonal autoregressive ($\Phi$) and seasonal moving average ($\Theta$) parameters.

$d$, $D$ and $s$ refer, respectively, to the order of non-seasonal differencing, the order of seasonal differencing and the seasonal period.

If no ARIMA model for the series is to be supplied arimas should be set to a NULL pointer.

Constraints:

• $\mathbf{arimas}\mathbf{.}\mathbf{p}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{d}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{q}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{bigp}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{bigd}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{bigq}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{s}\ge 0$;
• $\mathbf{arimas}\mathbf{.}\mathbf{s}\ne 1$;
• if $\mathbf{arimas}\mathbf{.}\mathbf{s}=0$, $\mathbf{arimas}\mathbf{.}\mathbf{bigp}+\mathbf{arimas}\mathbf{.}\mathbf{bigd}+\mathbf{arimas}\mathbf{.}\mathbf{bigq}=0$;
• if $\mathbf{arimas}\mathbf{.}\mathbf{s}\ne 0$, $\mathbf{arimas}\mathbf{.}\mathbf{bigp}+\mathbf{arimas}\mathbf{.}\mathbf{bigd}+\mathbf{arimas}\mathbf{.}\mathbf{bigq}\ne 0$.

5: $\mathbf{par}\left[\mathbf{npar}\right]$ – const double Input

On entry: the parameters of the filtering transfer function model followed by the parameters of the ARIMA model for the time series. In the transfer function model the parameters are in the standard order of MA-like followed by AR-like operator parameters. In the ARIMA model the parameters are in the standard order of non-seasonal AR and MA followed by seasonal AR and MA.

6: $\mathbf{npar}$ – Integer Input

On entry: the total number of parameters held in array par.

Constraints:

• if $\mathbf{arimas}\text{is not}\mathbf{NULL}$, $\mathbf{npar}=\mathbf{transfv}\mathbf{.}\mathbf{nag\_q}+\mathbf{transfv}\mathbf{.}\mathbf{nag\_p}+1$;
• if $\mathbf{arimas}\text{is}\mathbf{NULL}$, $$\begin{gathered} \mathbf{npar}=\mathbf{transfv}\mathbf{.}\mathbf{nag\_q}+\mathbf{transfv}\mathbf{.}\mathbf{nag\_p}+1+\mathbf{arimas}\mathbf{.}\mathbf{p}+ \\ \mathbf{arimas}\mathbf{.}\mathbf{q}+\mathbf{arimas}\mathbf{.}\mathbf{bigp}+\mathbf{arimas}\mathbf{.}\mathbf{bigq} \end{gathered}$$.

7: $\mathbf{cy}$ – double Input

On entry: if the ARIMA model is known (i.e., $\mathbf{arimas}\text{is}\mathbf{NULL}$), cy must specify the constant term of the ARIMA model for the time series. If this model is not known (i.e., $\mathbf{arimas}\text{is not}\mathbf{NULL}$) then cy is not used.

8: $\mathbf{b}\left[\mathbf{nb}\right]$ – double Output

On exit: the filtered output series. If the ARIMA model for the time series was known, and hence $Q_y^{\prime }$ backforecasts were supplied in y, then b contains $Q_y^{\prime }$ ‘filtered’ backforecasts followed by the filtered series. Otherwise, the filtered series begins at the start of b just as the original series began at the start of y. In either case, if the value of the series at time $t$ is held in $\mathbf{y}\left[t-1\right]$, then the filtered value at time $t$ is held in $\mathbf{b}\left[t-1\right]$.

9: $\mathbf{nb}$ – Integer Input

On entry: the dimension of the array b.

In addition to holding the returned filtered series, b is also used as an intermediate work array if the ARIMA model for the time series is known.

Constraints:

• if $\mathbf{arimas}\text{is not}\mathbf{NULL}$, $\mathbf{nb}\ge \mathbf{ny}$;
• if $\mathbf{arimas}\text{is}\mathbf{NULL}$, $\mathbf{nb}\ge \mathbf{ny}+\max (\mathbf{transfv}\mathbf{.}\mathbf{nag\_b}+\mathbf{transfv}\mathbf{.}\mathbf{nag\_q},\mathbf{transfv}\mathbf{.}\mathbf{nag\_p})$.

10: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_ARRAY_SIZE

On entry, $\mathbf{nb}=⟨\mathit{\text{value}}⟩$ and the minimum size $\text{required}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{arimas}\text{is}\mathbf{NULL}$arimas is not NULL then $\mathbf{nb}\ge \max (b,p,q)$, otherwise $\mathbf{nb}\ge \mathbf{ny}$.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_CONSTRAINT

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{bigd}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{bigp}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{bigq}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{d}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{p}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{q}\ge 0$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{s}\ne 1$.

Constraint: $\mathbf{arimas}\mathbf{.}\mathbf{s}\ge 0$.

Constraint: if $\mathbf{arimas}\mathbf{.}\mathbf{s}=0$, $\mathbf{arimas}\mathbf{.}\mathbf{bigp}+\mathbf{arimas}\mathbf{.}\mathbf{bigd}+\mathbf{arimas}\mathbf{.}\mathbf{bigq}=0$.

Constraint: if $\mathbf{arimas}\mathbf{.}\mathbf{s}\ne 0$, $\mathbf{arimas}\mathbf{.}\mathbf{bigp}+\mathbf{arimas}\mathbf{.}\mathbf{bigd}+\mathbf{arimas}\mathbf{.}\mathbf{bigq}\ne 0$.

Constraint: $\mathbf{transfv}\mathbf{.}\mathbf{nag\_b}\ge 0$.

Constraint: $\mathbf{transfv}\mathbf{.}\mathbf{nag\_p}\ge 0$.

Constraint: $\mathbf{transfv}\mathbf{.}\mathbf{nag\_q}\ge 0$.

NE_INT

On entry, npar is inconsistent with transfv and arimas: $\mathbf{npar}=⟨\mathit{\text{value}}⟩$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_MODEL_PARAMS

A supplied model has invalid parameters.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_SINGULAR

The matrix used to solve for starting values for MA is singular.

NE_TIME_SERIES

The supplied time series is too short.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results