NAG Library Function Document

nag_tsa_cp_pelt_user (g13nbc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the time series.

Constraint: $\mathbf{n}\ge 2$.

2:    $\mathbf{beta}$ – doubleInput

On entry: $\beta$, the penalty term.

There are a number of standard ways of setting $\beta$, including:

SIC or BIC

$\beta =p\times \log \left(n\right)$ 

AIC

$\beta =2p$ 

Hannan-Quinn

$\beta =2p\times \log \left(\log \left(n\right)\right)$ 

where $p$ is the number of parameters being treated as estimated in each segment. The value of $p$ will depend on the cost function being used.

If no penalty is required then set $\beta =0$. Generally, the smaller the value of $\beta$ the larger the number of suggested change points.

3:    $\mathbf{minss}$ – IntegerInput

On entry: the minimum distance between two change points, that is ${\tau }_i-{\tau }_{i-1}\ge \mathbf{minss}$.

Constraint: $\mathbf{minss}\ge 2$.

4:    $\mathbf{k}$ – doubleInput

On entry: $K$, the constant value that satisfies equation (2). If $K$ exists, it is unlikely to be unique in such cases, it is recommened that the largest value of $K$, that satisfies equation (2), is chosen. No check is made that $K$ is the correct value for the supplied cost function.

5:    $\mathbf{costfn}$ – function, supplied by the userExternal Function

The cost function, $C$. costfn must calculate a vector of costs for a number of segments.

The specification of costfn is:

void  costfn (Integer ts, Integer nr, const Integer r[], double c[], Nag_Comm *comm, Integer *info)

1:    $\mathbf{ts}$ – IntegerInput

On entry: a reference time point.

2:    $\mathbf{nr}$ – IntegerInput

On entry: number of segments being considered.

3:    $\mathbf{r}\left[\mathbf{nr}\right]$ – const IntegerInput

On entry: time points which, along with ts, define the segments being considered, $0\le \mathbf{r}\left[i-1\right]\le n$ for $i=1,2,\dots \mathbf{nr}$.

4:    $\mathbf{c}\left[\mathbf{nr}\right]$ – doubleOutput

On exit: the cost function, $C$, with

$$\mathbf{c}\left[i-1\right]=\left\{\begin{array}{ll}C\left(y_{r_i:t}\right)& \text{ if }t>r_i,\\ C\left(y_{t:r_i}\right)& \text{ otherwise.}\end{array}\right.$$

where $t=\mathbf{ts}$ and $r_i=\mathbf{r}\left[i-1\right]$.

It should be noted that if $t>r_i$ for any value of $i$ then it will be true for all values of $i$. Therefore the inequality need only be tested once per call to costfn.

5:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to costfn.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_tsa_cp_pelt_user (g13nbc) you may allocate memory and initialize these pointers with various quantities for use by costfn when called from nag_tsa_cp_pelt_user (g13nbc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

6:    $\mathbf{info}$ – Integer *Input/Output

On entry: $\mathbf{info}=0$.

On exit: set info to a nonzero value if you wish nag_tsa_cp_pelt_user (g13nbc) to terminate with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

Note: costfn should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_tsa_cp_pelt_user (g13nbc). If your code inadvertently does return any NaNs or infinities, nag_tsa_cp_pelt_user (g13nbc) is likely to produce unexpected results.

6:    $\mathbf{ntau}$ – Integer *Output

On exit: $m$, the number of change points detected.

7:    $\mathbf{tau}\left[\mathit{dim}\right]$ – IntegerOutput

On exit: the first $m$ elements of tau hold the location of the change points. The $i$th segment is defined by $y_{\left({\tau }_{i-1}+1\right)}$ to $y_{{\tau }_i}$, where ${\tau }_0=0$ and ${\tau }_i=\mathbf{tau}\left[i-1\right],1\le i\le m$.

The remainder of tau is used as workspace.

8:    $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{minss}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{minss}\ge 2$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_USER_STOP

User requested termination.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13nbce.c)

10.2

Program Data

Program Data (g13nbce.d)

10.3

Program Results

Program Results (g13nbce.r)