Illustrative Example of ARMA Software: Stock Rate Prediction

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Illustrative Example of ARMA Software: Stock Rate Prediction

Figures 1.21 and 1.22 show the part of the file 'fitimeb.h' defining the control parameters and data files.

**Figure 1.21:** Example of the file 'fitimeb.h', part 1
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}...$

**Figure 1.22:** Example of the file 'fitimeb.h', part 2
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}...$

The control parameters and the optimization results (in the case INP 0) are shown in Figure 1.23.

**Figure 1.23:** Example of the file 'results.out'
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}Number of Factors M 2 Mu... ...4141e+01 Finish progn_err 2.438730e+01\end{verbatim} \end{codebox} \end{figure}$

The comments in Figures 1.21 and 1.21 are short thus additional explanations are added.

```
#define RAND()	drand48(),
```
defines the random number generator

#define S 0 /* number of rows of matrix c */ 
#define S 0 /* number of rows of matrix c */

defines the bilinear component (see expression 1.35)

```
#define K 5 /*number of "multi-step" repetitions*/,
```
K 5 means that the multi-step predictions is repeated 5 times (see section 1.9 and Figure 1.24)

Figure 1.24: A fragment of the file 'progn.out' predicting for the first ten days
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}progn t ymin[M*t] yav[M*t... ... 1.647438e+02 2.618776e+02 3.345000e+02\end{verbatim} \end{codebox} \end{figure}$
```
#define W 0 /*W 0 means the one-step structural optimization, 
W 1 defines the multi-step one*/,
```
one-step structural optimization minimizes the average error of the "next day" predictions (see section 1.10.3), multi-step one minimizes the average error of predictions for longer periods of time
```
#define V 1 /*V 1 means with the multi-step prognoses, 
V 0 means without*/
```
the zero value of the indicator V switches off the multi-step prediction (see section 1.9) and switches on the next day prediction (see section 1.3.3 and Figure 1.24)
```
#define F  1 /*indicator of variance, F 1 involves variance*/,
```
the unit value of the indicator F means that the variance of the errors is estimated and included into the multi-step prediction process

**Figure 1.24:** A fragment of the file 'progn.out' predicting for the first ten days
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}progn t ymin[Mt] yav[Mt... ... 1.647438e+02 2.618776e+02 3.345000e+02\end{verbatim} \end{codebox} \end{figure}$

#define EPS 0/*indicator of residual printing*/,

not used in this version

```
#define INP  0 /*indicator of input display*/,
```
if INP 1 then the input values of the predicted factor are printed with their numbers (see Figure 1.25)

Figure 1.25: A fragment of input data the file 'bank.out' when INP is set to unit
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}0 165.00 1 110.00 2 16... ...7 110.00 8 200.00 9 110.00 10 200.00\end{verbatim} \end{codebox} \end{figure}$
```
#define SA  0 /*indicator of simulated annealing */
```
if SA 1 then optimization of the parameters p and q are performed using the simulated annealing method, otherwise the exhaustive search is used
```
#define PL  0/*plotting dimension*/,
```
if PL 1 then the values of objective function depending on the parameter b[PLOT1] will be written in the file 'plot.out', if PL 2 then the values of objective function depending on two parameters b[PLOT1] and b[PLOT2] will be written in the file 'plot.out' (see Figure 1.26) and plotted as Figures 1.18 using the "Gnuplot" system,, if PL 0 there will be no file 'plot.out'

Figure 1.26: A fragment of the ten entries the 'bank.plot.out' file
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim} -1.000000e+00 0.000000e... ...0e+00 0.000000e+00 3.323284e+00\end{verbatim} \end{codebox}\protect \end{figure}$

**Figure 1.25:** A fragment of input data the file 'bank.out' when INP is set to unit
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}0 165.00 1 110.00 2 16... ...7 110.00 8 200.00 9 110.00 10 200.00\end{verbatim} \end{codebox} \end{figure}$

**Figure 1.26:** A fragment of the ten entries the 'bank.plot.out' file
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim} -1.000000e+00 0.000000e... ...0e+00 0.000000e+00 3.323284e+00\end{verbatim} \end{codebox}\protect \end{figure}$

#define PLOT1 0 /*first plotting coordinate is b[PLOT1}*/
#define PLOT2 1/*second plotting coordinate is b[PLOT2}*/,

defines which components of vector-parameter b are considered

#define A1 -1.5 /*lower bound of  b[PLOT1}*/
#define B1 1.5/*upper bound of  b[PLOT2}*/
#define A2 -1.5 /*lower bound of  b[PLOT2}*/
#define B2 1.5/*upper bound of  b[PLOT2}*/
#define DN 50 /*number of plotting steps*/

defines the range and the density of the plotting points

#define ST 10000. /*temperature of simulated annealing */
#define SI 100 /*number of simulated annealing iterations*/

defines the parameters of simulated annealing method (if SA is applied)

#define Ps M  /*starting number of AR parameters*/
#define Qs 0  /*starting number of MA parameters*/
#define Pmin M /*minimal number of AR parameters*/
#define Qmin 0  /*minimal number of MA parameters*/
#define Pmax 2*M  /*maximal number of AR parameters*/
#define Qmax 2  /*maximal number of MA parameters*/

defines the initial, the minimal and the maximal number of parameters p and q in the structural optimization

#define T 120*M /* number of data entries in DATAFILE
(divisible by M)*/,

defines the total number of entries in DATAFILE

```
#define T0 T/3 /*T0<T number of  entries 
for a and b optimization (divisible by M)*/
#define T1 2*T0 /*T1>=T0, number of  entries 
for P and Q optimization(divisible by M)*/,
```
divides the DATAFILE (see Figures 1.27 and 1.17) into three parts: the first part for a,b optimization, the second part for p,q optimization, and the third part for testing the results

Figure 1.27: A fragment of the ten recent days of the DATAFILE 'bank.data' inckuding the date code and data of seven main Lithuanian commercial banks
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim} 5786.09 180.00 224.00 2... ... 230.00 221.00 36.00 20.00 85.00 15.50\end{verbatim} \end{codebox} \end{figure}$
```
#define TR -1*M /*TR <= T, TR/M is the  number of 
the first line in DATAFILE used for simple regression 
(negative TR prints no regression)*/
#define TE 25*M/*TE>TR, TE/M is the number of 
the last line for regression*/,
```
is used only in the case when the ARMA model of time series prediction is reduced to the linear regression model of diagnosis.
```
#define INIFILE "bank2.ini",
```
defines the input control file INIFILE (see Figure 1.28)

Figure 1.28: Example of the INIFILE 'bank2.ini'
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}INP bank.data COL 3 COL 4\end{verbatim} \end{codebox} \end{figure}$
```
#define M 2 /*number of factors*/,
```
defines the number of factors, including the predicted and the external ones
```
#define LOCAL_METH EXKOR,
```
means that the EXKOR method is used for local optimization
```
#define GLOBAL_METH BAYES1
```
means that the BAYES1 method is used for global optimization

**Figure 1.27:** A fragment of the ten recent days of the DATAFILE 'bank.data' inckuding the date code and data of seven main Lithuanian commercial banks
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim} 5786.09 180.00 224.00 2... ... 230.00 221.00 36.00 20.00 85.00 15.50\end{verbatim} \end{codebox} \end{figure}$

**Figure 1.28:** Example of the INIFILE 'bank2.ini'
$\begin{figure}\begin{codebox}{4.7in} \begin{verbatim}INP bank.data COL 3 COL 4\end{verbatim} \end{codebox} \end{figure}$

#define BAYES1_MAX_IT  	5*M	/* bayes1 IT */
#define BAYES1_LT	 5	/* bayes1 LT */

means that 5*M iterations and 5 initial iterations of the BAYES1 method are used

#define EXKOR_MAX_IT	 6*M 	/* exkor IT */
#define EXKOR_INIT_POINTS 6	/* exkor LT */

means that 6*M iterations and 6 initial iterations of the EXKOR method are used

Next: Illustrative Example of ARMA Up: Multi-Factor ARMA Software Previous: Multi-Factor ARMA Software

mockus 2008-06-21