NAG CL Interface
g13aac (uni_​diff)

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1 Purpose

g13aac carries out non-seasonal and seasonal differencing on a time series. Information which allows the original series to be reconstituted from the differenced series is also produced. This information is required in time series forecasting.

2 Specification

#include <nag.h>
void  g13aac (const double x[], Integer nx, Integer d, Integer ds, Integer s, double xd[], Integer *nxd, NagError *fail)
The function may be called by the names: g13aac, nag_tsa_uni_diff or nag_tsa_diff.

3 Description

Let dsDxi be the ith value of a time series xi, for i=1,2,,n after non-seasonal differencing of order d and seasonal differencing of order D (with period or seasonality s). In general,
dsDxi=d-1sDxi+1-d-1sDxi d>0
dsDxi=dsD-1xi+s-dsD-1xi D>0
Non-seasonal differencing up to the required order d is obtained using
1xi=xi+1-xi for i=1,2,,(n-1)
2xi=1xi+1-1xi for i=1,2,,(n-2)
dxi=d-1xi+1-d-1xi for i=1,2,,(n-d)
Seasonal differencing up to the required order D is then obtained using
ds1xi=dxi+s-dxi for i=1,2,,(n-d-s)
ds2xi=ds1xi+s-ds1xi for i=1,2,,(n-d-2s)
dsDxi=dsD-1xi+s-dsD-1xi for i=1,2,,(n-d-D×s)
Mathematically, the sequence in which the differencing operations are performed does not affect the final resulting series of m=n-d-D×s values.

4 References


5 Arguments

1: x[nx] const double Input
On entry: the undifferenced time series, xi, for i=1,2,,n.
2: nx Integer Input
On entry: n, the number of values in the undifferenced time series.
Constraint: nx>d+(ds×s).
3: d Integer Input
On entry: d, the order of non-seasonal differencing.
Constraint: d0.
4: ds Integer Input
On entry: D, the order of seasonal differencing.
Constraint: ds0.
5: s Integer Input
On entry: s, the seasonality.
  • if ds>0, s>0;
  • if ds=0, s0.
6: xd[nx] double Output
On exit: the differenced values in elements 0 to nxd-1, and reconstitution data in the remainder of the array.
7: nxd Integer * Output
On exit: the number of differenced values in the array xd.
8: 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

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, d=value.
Constraint: d0.
On entry, ds=value.
Constraint: ds0.
On entry, s=value.
Constraint: s0.
On entry, ds=value.
Constraint: if s=0, ds0.
On entry, nx=value, d=value, ds=value and s=value.
Constraint: nx>d+(ds×s).
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.
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.

7 Accuracy

The computations are believed to be stable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g13aac is not threaded in any implementation.

9 Further Comments

The time taken by g13aac is approximately proportional to (d+ds)×nx.

10 Example

This example reads in a set of data consisting of 20 observations from a time series. Non-seasonal differencing of order 2 and seasonal differencing of order 1 (with seasonality of 4) are applied to the input data, giving an output array holding 14 differenced values and 6 values which can be used to reconstitute the output array.

10.1 Program Text

Program Text (g13aace.c)

10.2 Program Data

Program Data (g13aace.d)

10.3 Program Results

Program Results (g13aace.r)