NAG Library Function Document
nag_tsa_inhom_iema_all (g13mfc)
1
Purpose
nag_tsa_inhom_iema_all (g13mfc) calculates the iterated exponential moving average for an inhomogeneous time series, returning the intermediate results.
2
Specification
#include <nag.h> |
#include <nagg13.h> |
void |
nag_tsa_inhom_iema_all (Nag_OrderType order,
Integer nb,
const double z[],
double iema[],
Integer pdiema,
const double t[],
double tau,
Integer m1,
Integer m2,
const double sinit[],
const Nag_TS_Interpolation inter[],
Nag_TS_Transform ftype,
double *p,
const double x[],
Integer *pn,
double rcomm[],
NagError *fail) |
|
3
Description
nag_tsa_inhom_iema_all (g13mfc) calculates the iterated exponential moving average for an inhomogeneous time series. The time series is represented by two vectors of length : a vector of times, ; and a vector of values, . Each element of the time series is therefore composed of the pair of scalar values , for . Time can be measured in any arbitrary units, as long as all elements of use the same units.
The exponential moving average (EMA), with parameter
, is an average operator, with the exponentially decaying kernel given by
The exponential form of this kernel gives rise to the following iterative formula (
Zumbach and Müller (2001)) for the EMA operator:
where
The value of
depends on the method of interpolation chosen and the relationship between
and the input series
depends on the transformation function chosen.
nag_tsa_inhom_iema_all (g13mfc) gives the option of three interpolation methods:
1. |
Previous point: |
; |
2. |
Linear: |
; |
3. |
Next point: |
. |
and three transformation functions:
1. |
Identity: |
; |
2. |
Absolute value: |
; |
3. |
Absolute difference: |
; |
where the notation
is used to denote the integer nearest to
. In the case of the absolute difference
is a user-supplied vector of length
and therefore each element of the time series is composed of the triplet of scalar values,
.
The
-iterated exponential moving average,
, is defined using the recursive formula:
with
For large datasets or where all the data is not available at the same time, and, where required, can be split into arbitrary sized blocks and nag_tsa_inhom_iema_all (g13mfc) called multiple times.
4
References
Dacorogna M M, Gencay R, Müller U, Olsen R B and Pictet O V (2001) An Introduction to High-frequency Finance Academic Press
Zumbach G O and Müller U A (2001) Operators on inhomogeneous time series International Journal of Theoretical and Applied Finance 4(1) 147–178
5
Arguments
- 1:
– Nag_OrderTypeInput
-
On entry: the
order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by
. See
Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint:
or .
- 2:
– IntegerInput
-
On entry:
, the number of observations in the current block of data. At each call the size of the block of data supplied in
z,
t and
x can vary; therefore
nb can change between calls to
nag_tsa_inhom_iema_all (g13mfc).
Constraint:
.
- 3:
– const doubleInput
-
On entry:
, the current block of observations, for
, where
is the number of observations processed so far, i.e., the value supplied in
pn on entry.
Constraint:
if or and , , for .
- 4:
– doubleOutput
Note: the dimension,
dim, of the array
iema
must be at least
.
Where
appears in this document, it refers to the array element
- when ;
- when .
On exit: the iterated exponential moving average.
If , .
If , .
For
,
and
is the number of observations processed so far, i.e., the value supplied in
pn on entry.
- 5:
– IntegerInput
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
iema.
Constraints:
- if , ;
- otherwise .
- 6:
– const doubleInput
-
On entry:
, the times for the current block of observations, for
, where
is the number of observations processed so far, i.e., the value supplied in
pn on entry.
If
,
NE_NOT_STRICTLY_INCREASING will be returned, but
nag_tsa_inhom_iema_all (g13mfc) will continue as if
was strictly increasing by using the absolute value.
- 7:
– doubleInput
-
On entry: , the parameter controlling the rate of decay. must be sufficiently large that , can be calculated without overflowing, for all .
Constraint:
.
- 8:
– IntegerInput
-
On entry: the minimum number of times the EMA operator is to be iterated.
Constraint:
.
- 9:
– IntegerInput
-
On entry: the maximum number of times the EMA operator is to be iterated. Therefore nag_tsa_inhom_iema_all (g13mfc) returns , for .
Constraint:
.
- 10:
– const doubleInput
-
On entry: if
, the values used to start the iterative process, with
- ,
- ,
- , .
If
then
sinit is not referenced and may be
NULL.
Constraint:
if , , for .
- 11:
– const Nag_TS_InterpolationInput
-
On entry: the type of interpolation used with
indicating the interpolation method to use when calculating
and
the interpolation method to use when calculating
,
.
Three types of interpolation are possible:
- Previous point, with .
- Linear, with .
- Next point, .
Zumbach and Müller (2001) recommend that linear interpolation is used in second and subsequent iterations, i.e.,
, irrespective of the interpolation method used at the first iteration, i.e., the value of
.
Constraint:
, or , for .
- 12:
– Nag_TS_TransformInput
-
On entry: the function type used to define the relationship between
and
when calculating
. Three functions are provided:
- The identity function, with .
- The absolute value, with .
- The absolute difference, with , where the vector is supplied in x.
Constraint:
, or .
- 13:
– double *Input/Output
-
On entry: , the power used in the transformation function.
On exit: if
, then
, the actual power used in the transformation function is returned, otherwise
p is unchanged.
Constraint:
.
- 14:
– const doubleInput
-
On entry: if
,
, the vector used to shift the current block of observations, for
, where
is the number of observations processed so far, i.e., the value supplied in
pn on entry.
If
then
x is not referenced and may be
NULL.
Constraint:
if and , , for .
- 15:
– Integer *Input/Output
-
On entry:
, the number of observations processed so far. On the first call to
nag_tsa_inhom_iema_all (g13mfc), or when starting to summarise a new dataset,
pn must be set to
. On subsequent calls it must be the same value as returned by the last call to
nag_tsa_inhom_iema_all (g13mfc).
On exit: , the updated number of observations processed so far.
Constraint:
.
- 16:
– doubleCommunication Array
-
On entry: communication array, used to store information between calls to
nag_tsa_inhom_iema_all (g13mfc).
If
then
pn must be set to zero
and all the data must be supplied in one go.
- 17:
– 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_ARRAY_SIZE
-
On entry, , and .
Constraint: .
On entry, , and .
Constraint: .
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_ILLEGAL_COMM
-
rcomm has been corrupted between calls.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INT_2
-
On entry, and .
Constraint: .
- 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_NOT_STRICTLY_INCREASING
-
On entry,
,
and
.
Constraint:
t should be strictly increasing.
- NE_PREV_CALL
-
If
then
ftype must be unchanged since previous call.
If
then
inter must be unchanged since previous call.
On entry,
.
On entry at previous call,
.
Constraint: if
then
m1 must be unchanged since previous call.
On entry,
.
On entry at previous call,
.
Constraint: if
then
m2 must be unchanged since previous call.
On entry,
.
On exit from previous call,
.
Constraint: if
then
p must be unchanged since previous call.
On entry,
.
On exit from previous call,
.
Constraint: if
then
pn must be unchanged since previous call.
On entry,
.
On entry at previous call,
.
Constraint: if
then
tau must be unchanged since previous call.
- NE_REAL
-
On entry, , and .
Constraint: if or and for any then .
On entry, , , and .
Constraint: if and for any then .
On entry,
.
Constraint: absolute value of
p must be representable as an integer.
On entry, .
Constraint: if , . If , the nearest integer to must not be .
On entry, .
Constraint: .
- NE_REAL_ARRAY
-
On entry, , and .
Constraint: if , , for .
On entry, , and .
Constraint: if linear interpolation is being used.
- NW_OVERFLOW_WARN
-
Truncation occurred to avoid overflow, check for extreme values in
t,
z,
x or for
tau. Results are returned using the truncated values.
7
Accuracy
Not applicable.
8
Parallelism and Performance
nag_tsa_inhom_iema_all (g13mfc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_tsa_inhom_iema_all (g13mfc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
Approximately real elements are internally allocated by nag_tsa_inhom_iema_all (g13mfc).
The more data you supply to
nag_tsa_inhom_iema_all (g13mfc) in one call, i.e., the larger
nb is, the more efficient the routine will be.
Checks are made during the calculation of
and
to avoid overflow. If a potential overflow is detected the offending value is replaced with a large positive or negative value, as appropriate, and the calculations performed based on the replacement values. In such cases
NW_OVERFLOW_WARN is returned. This should not occur in standard usage and will only occur if extreme values of
z,
t,
x or
tau are supplied.
10
Example
This example reads in three blocks of simulated data from an inhomogeneous time series, then calculates and prints the iterated EMA for between and .
10.1
Program Text
Program Text (g13mfce.c)
10.2
Program Data
Program Data (g13mfce.d)
10.3
Program Results
Program Results (g13mfce.r)