NAG Toolbox: nag_tsa_uni_arima_update (g13ag)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{st}\left(\mathbf{nst}\right)$ – double array

The state set derived from nag_tsa_uni_arima_estim (g13ae) or nag_tsa_uni_arima_estim_easy (g13af), or as modified using earlier calls of nag_tsa_uni_arima_update (g13ag).

2:     $\mathrm{mr}\left(7\right)$ – int64int32nag_int array

The orders vector $\left(p,d,q,P,D,Q,s\right)$ of the ARIMA model, in the usual notation.

Constraints:

• $p,d,q,P,D,Q,s\ge 0$;
• $p+q+P+Q>0$;
• $s\ne 1$;
• if $s=0$, $P+D+Q=0$;
• if $s>1$, $P+D+Q>0$.

3:     $\mathrm{par}\left(\mathbf{npar}\right)$ – double array

The estimates of the $p$ values of the $\varphi$ parameters, the $q$ values of the $\theta$ parameters, the $P$ values of the $\Phi$ parameters and the $Q$ values of the $\Theta$ parameters in the model – in that order, using the usual notation.

4:     $\mathrm{c}$ – double scalar

The constant to be subtracted from the differenced data.

5:     $\mathrm{anx}\left(\mathbf{nuv}\right)$ – double array

The new undifferenced observations which are to be used to update st.

Optional Input Parameters

1:     $\mathrm{nst}$ – int64int32nag_int scalar

Default: the dimension of the array st.

The number of values in the state set array st.

Constraint: $\mathbf{nst}=P\times s+D\times s+d+q+\max \left(p,Q\times s\right)$. (As returned by nag_tsa_uni_arima_estim (g13ae) or nag_tsa_uni_arima_estim_easy (g13af)).

2:     $\mathrm{npar}$ – int64int32nag_int scalar

Default: the dimension of the array par.

The number of $\varphi$, $\theta$, $\Phi$ and $\Theta$ parameters in the model.

Constraint: $\mathbf{npar}=p+q+P+Q$.

3:     $\mathrm{nuv}$ – int64int32nag_int scalar

Default: the dimension of the array anx.

$k$, the number of new observations in anx.

Output Parameters

1:     $\mathrm{st}\left(\mathbf{nst}\right)$ – double array

The updated values of the state set.

2:     $\mathrm{anexr}\left(\mathbf{nuv}\right)$ – double array

The residuals corresponding to the new observations in anx.

3:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{npar}\ne p+q+P+Q$,
or	the orders vector mr is invalid (check the constraints in Arguments).

   $\mathbf{ifail}=2$

On entry,

$\mathbf{nst}\ne P\times s+D\times s+d+q+\max \left(Q\times s,p\right)$.

   $\mathbf{ifail}=3$

On entry,

$\mathbf{nuv}\le 0$.

   $\mathbf{ifail}=4$

On entry,

$\mathit{nwa}<4\times \mathbf{npar}+3\times \mathbf{nst}$.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g13ag_example

function g13ag_example


fprintf('g13ag example results\n\n');

% Previously calculated state set (g13ae, g13af or prior g13ag)
st = [0.0118;  -0.0669;   0.1296;  -0.0394;   0.0422;   0.1809;   0.1211;
      0.0281;  -0.2231;  -0.1181;  -0.1468;   0.0835;   5.8201;  -0.0157;
     -0.0361;  -0.0266;  -0.0199;   0.0298;   0.0290;   0.0147;   0.0373;
     -0.0931;   0.0223;  -0.0172;  -0.0353;  -0.0413];

% Orders
mr = [int64(0);1;1;0;1;1;12];
par = [0.327;    0.627];
c = 0;

% New update observations
anx = [5.8861;  5.8348;   6.0064;   5.9814;   6.0403;   6.1570;
       6.3063;  6.3261;   6.1377;   6.0088;   5.8916;   6.0039];
nux = numel(anx);

% Update state set
[st, anexr, ifail] = g13ag( ...
                            st, mr, par, c, anx);

%  Display results
nst = numel(st);
fprintf('The updated state set array now holds the values\n');
for j = 1:8:nst
  fprintf('%8.4f', st(j:min(j+7,nst)));
  fprintf('\n');
end
fprintf('\nThe residuals corresponding to the %4d values used to\n', nux);
fprintf('update the system are\n');
for j = 1:8:nux
  fprintf('%8.4f', anexr(j:min(j+7,nux)));
  fprintf('\n');
end

g13ag example results

The updated state set array now holds the values
  0.0660 -0.0513  0.1716 -0.0250  0.0589  0.1167  0.1493  0.0198
 -0.1884 -0.1289 -0.1172  0.1123  6.0039  0.0444 -0.0070  0.0253
  0.0019  0.0354 -0.0460  0.0374  0.0151 -0.0237  0.0032  0.0188
  0.0067  0.0126

The residuals corresponding to the   12 values used to
update the system are
  0.0309  0.0031  0.0263  0.0105  0.0388 -0.0333  0.0265  0.0238
 -0.0159 -0.0020  0.0182  0.0126