NAG Library Function Document
nag_tsa_inhom_iema (g13mec)
1
Purpose
nag_tsa_inhom_iema (g13mec) calculates the iterated exponential moving average for an inhomogeneous time series.
2
Specification
#include <nag.h> |
#include <nagg13.h> |
void |
nag_tsa_inhom_iema (Integer nb,
double iema[],
const double t[],
double tau,
Integer m,
const double sinit[],
const Nag_TS_Interpolation inter[],
Integer *pn,
double rcomm[],
NagError *fail) |
|
3
Description
nag_tsa_inhom_iema (g13mec) 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 for the EMA operator (see
Zumbach and Müller (2001)):
where
The value of
depends on the method of interpolation chosen.
nag_tsa_inhom_iema (g13mec) gives the option of three interpolation methods:
1. |
Previous point: |
; |
2. |
Linear: |
; |
3. |
Next point: |
. |
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 can be split into arbitrary sized blocks and nag_tsa_inhom_iema (g13mec) 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:
– IntegerInput
-
On entry:
, the number of observations in the current block of data. The size of the block of data supplied in
iema and
t can vary; therefore
nb can change between calls to
nag_tsa_inhom_iema (g13mec).
Constraint:
.
- 2:
– doubleInput/Output
-
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.
On exit: the iterated EMA, with .
- 3:
– 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 (g13mec) will continue as if
was strictly increasing by using the absolute value.
- 4:
– doubleInput
-
On entry: , the argument controlling the rate of decay, which must be sufficiently large that , can be calculated without overflowing, for all .
Constraint:
.
- 5:
– IntegerInput
-
On entry: , the number of times the EMA operator is to be iterated.
Constraint:
.
- 6:
– const doubleInput
-
On entry: if
, the values used to start the iterative process, with
- ,
- ,
- , for .
If
,
sinit is not referenced and may be
NULL.
- 7:
– 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 .
- 8:
– Integer *Input/Output
-
On entry:
, the number of observations processed so far. On the first call to
nag_tsa_inhom_iema (g13mec), 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 (g13mec).
On exit: , the updated number of observations processed so far.
Constraint:
.
- 9:
– doubleCommunication Array
-
On entry: communication array, used to store information between calls to
nag_tsa_inhom_iema (g13mec).
If
then
pn must be set to zero
and all the data must be supplied in one go.
- 10:
– 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 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_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
inter must be unchanged since previous call.
On entry,
.
On entry at previous call,
.
Constraint: if
then
m 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, .
Constraint: .
- NE_REAL_ARRAY
-
On entry, , and .
Constraint: if linear interpolation is being used.
- NW_OVERFLOW_WARN
-
Truncation occurred to avoid overflow, check for extreme values in
t,
iema or for
tau. Results are returned using the truncated values.
7
Accuracy
Not applicable.
8
Parallelism and Performance
nag_tsa_inhom_iema (g13mec) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_tsa_inhom_iema (g13mec) 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 (g13mec).
The more data you supply to
nag_tsa_inhom_iema (g13mec) in one call, i.e., the larger
nb is, the more efficient the function will be.
Checks are made during the calculation of
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
iema,
t or
tau are supplied.
10
Example
The example reads in a simulated time series, and calculates the iterated exponential moving average.
10.1
Program Text
Program Text (g13mece.c)
10.2
Program Data
Program Data (g13mece.d)
10.3
Program Results
Program Results (g13mece.r)
This example plot shows the exponential moving average for the same data using three different values of and illustrates the effect on the EMA of altering this argument.