nag_tsa_diff (g13aac) (PDF version)
g13 Chapter Contents
g13 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_tsa_diff (g13aac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_tsa_diff (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>
#include <nagg13.h>
void  nag_tsa_diff (const double x[], Integer nx, Integer d, Integer ds, Integer s, double xd[], Integer *nxd, NagError *fail)

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 doubleInput
On entry: the undifferenced time series, xi, for i=1,2,,n.
2:     nxIntegerInput
On entry: n, the number of values in the undifferenced time series.
Constraint: nx>d+ds×s.
3:     dIntegerInput
On entry: d, the order of non-seasonal differencing.
Constraint: d0.
4:     dsIntegerInput
On entry: D, the order of seasonal differencing.
Constraint: ds0.
5:     sIntegerInput
On entry: s, the seasonality.
  • if ds>0, s>0;
  • if ds=0, s0.
6:     xd[nx]doubleOutput
On exit: the differenced values in elements 0 to nxd-1, and reconstitution data in the remainder of the array.
7:     nxdInteger *Output
On exit: the number of differenced values in the array xd.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

7  Accuracy

The computations are believed to be stable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

The time taken by nag_tsa_diff (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)

nag_tsa_diff (g13aac) (PDF version)
g13 Chapter Contents
g13 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014