NAG Library Function Document

nag_tsa_cp_binary_user (g13nec)

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:    $\mathbf{mdepth}$ – IntegerInput

On entry: $K$, the maximum depth for the iterative process, which in turn puts an upper limit on the number of change points with $m\le 2^K$.

If $K\le 0$ then no limit is put on the depth of the iterative process and no upper limit is put on the number of change points, other than that inherent in the length of the series and the value of minss.

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

chgpfn must calculate a proposed change point, and the associated costs, within a specified segment.

The specification of chgpfn is:

void  chgpfn (Nag_TS_SegSide side, Integer u, Integer w, Integer minss, Integer *v, double cost[], Nag_Comm *comm, Integer *info)

1:    $\mathbf{side}$ – Nag_TS_SegSideInput

On entry: flag indicating what chgpfn must calculate and at which point of the Binary Segmentation it has been called.

$\mathbf{side}=\mathrm{Nag\_FirstSegCall}$

only $C\left(y_{u:w}\right)$ need be calculated and returned in $\mathbf{cost}\left[0\right]$, neither v nor the other elements of cost need be set. In this case, $u=1$ and $w=\mathrm{n}$.

$\mathbf{side}=\mathrm{Nag\_SecondSegCall}$

all elements of cost and v must be set. In this case, $u=1$ and $w=\mathrm{n}$.

$\mathbf{side}=\mathrm{Nag\_LeftSubSeg}$

the segment, $y_{u:w}$, is a left hand side subsegment from a previous iteration of the Binary Segmentation algorithm. All elements of cost and v must be set.

$\mathbf{side}=\mathrm{Nag\_RightSubSeg}$

the segment, $y_{u:w}$, is a right hand side subsegment from a previous iteration of the Binary Segmentation algorithm. All elements of cost and v must be set.

The distinction between $\mathbf{side}=\mathrm{Nag\_LeftSubSeg}$ and $\mathrm{Nag\_RightSubSeg}$ may allow for chgpfn to be implemented in a more efficient manner. See section Section 10 for one such example.

The first call to chgpfn will always have $\mathbf{side}=\mathrm{Nag\_FirstSegCall}$ and the second call will always have $\mathbf{side}=\mathrm{Nag\_SecondSegCall}$. All subsequent calls will be made with $\mathbf{side}=\mathrm{Nag\_LeftSubSeg}$ or $\mathrm{Nag\_RightSubSeg}$.

2:    $\mathbf{u}$ – IntegerInput

On entry: $u$, the start of the segment of interest.

3:    $\mathbf{w}$ – IntegerInput

On entry: $w$, the end of the segment of interest.

4:    $\mathbf{minss}$ – IntegerInput

On entry: the minimum distance between two change points, as passed to nag_tsa_cp_binary_user (g13nec).

5:    $\mathbf{v}$ – Integer *Output

On exit: if $\mathbf{side}=\mathrm{Nag\_FirstSegCall}$ then v need not be set.

if $\mathbf{side}\ne \mathrm{Nag\_FirstSegCall}$ then $v$, the proposed change point. That is, the value which minimizes

$$\underset{v}{\mathrm{minimize}}C\left(y_{u:v}\right)+C\left(y_{v+1:w}\right)$$

for $v=u+\mathbf{minss}-1$ to $w-\mathbf{minss}$.

6:    $\mathbf{cost}\left[3\right]$ – doubleOutput

On exit: costs associated with the proposed change point, $v$.

If $\mathbf{side}=\mathrm{Nag\_FirstSegCall}$ then $\mathbf{cost}\left[0\right]=C\left(y_{u:w}\right)$ and the remaining two elements of cost need not be set.

If $\mathbf{side}\ne \mathrm{Nag\_FirstSegCall}$ then

• $\mathbf{cost}\left[0\right]=C\left(y_{u:v}\right)+C\left(y_{v+1:w}\right)$.
• $\mathbf{cost}\left[1\right]=C\left(y_{u:v}\right)$.
• $\mathbf{cost}\left[2\right]=C\left(y_{v+1:w}\right)$.

7:    $\mathbf{comm}$ – Nag_Comm *

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

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_tsa_cp_binary_user (g13nec) you may allocate memory and initialize these pointers with various quantities for use by chgpfn when called from nag_tsa_cp_binary_user (g13nec) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

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

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

On exit: in most circumstances info should remain unchanged.

If info is set to a strictly positive value then nag_tsa_cp_binary_user (g13nec) terminates with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

If info is set to a strictly negative value the current segment is skipped (i.e., no change points are considered in this segment) and nag_tsa_cp_binary_user (g13nec) continues as normal. If info was set to a strictly negative value at any point and no other errors occur then nag_tsa_cp_binary_user (g13nec) will terminate with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NW_POTENTIAL_PROBLEM.

Note: chgpfn should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_tsa_cp_binary_user (g13nec). If your code inadvertently does return any NaNs or infinities, nag_tsa_cp_binary_user (g13nec) 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

Note: the dimension, dim, of the array tau must be at least

• $\min \left(\lceil \frac{\mathbf{n}}{\mathbf{minss}}\rceil ,2^{\mathbf{mdepth}}\right)$ when $\mathbf{mdepth}>0$;
• $\lceil \frac{\mathbf{n}}{\mathbf{minss}}\rceil$ otherwise.

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 by setting $\mathbf{info}=〈\mathit{\text{value}}〉$.

NW_POTENTIAL_PROBLEM

User requested a segment to be skipped by setting $\mathbf{info}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13nece.c)

10.2

Program Data

Program Data (g13nece.d)

10.3

Program Results

Program Results (g13nece.r)