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PROGRAM: NETLE
PURPOSE: Feedforward Neural Networks and Lyapunov Exponents
Estimation
COPYRIGHT: Chung-Ming Kuan, Tung Liu, and Ramazan Gencay
VERSION: 4.1. July 2007
Revision History:
7/20/2007: Distributed as Version 4.1.
2/12/2006: V4.01 Compute the standard errors for LE estimate.
1/2/1997: V3.01. Compute LE for inputs up to 20.
2/1995: V2.1
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CONTENTS:
Section 1. INTRODUCTION
Section 2. HOW TO RUN NETLE PROGRAM
Section 3. DATA FILE
Section 4. CONTROL FILE
Section 5. PROGRAM OUTPUT
Section 6. CORRESPONDENCE
1. INTRODUCTION
NETLE 4.1 is a Windows program to estimate feedforward neural
network models and compute Lyapunov exponents (LE). The selected
neural network models are estimated by the method of nonlinear least
squares (NLS) (Kuan and Liu (1995)). Lyapunov exponents are calculated
from the derivative matrices of estimated network models (Gencay and
Dechert (1992)). A positive Lyapunov exponent estimate indicates
that the underlying series is chaotic. The standard error of the LE
estimate is derived by Shintani and Linton (2004).
The running of the current program is under DOS prompt. The future version will run under Windows. Since the NLS estimation requires a lot of CPU time, a high speed PC is recommended. The maximum number of data values is 7000. The maximum inputs and hiddens are 20.
This disk is distributed for academic purposes only; proper citation of this program is gratefully appreciated. Please contact Tung Liu at tliu@bsu.edu for any questions on this program.
REFERENCES:
Kuan, Chung-Ming and Tung Liu (1995).
"Forecasting exchange rates using feedforward and recurrent networks,"
Journal of Applied Econometrics, 10:347-364.
Gencay, Ramazan and W. D. Dechert (1992).
"An algorithm for the n Lyapunov exponents of an n-dimensional unknown
dynamical system," Physica D, 59:142-157.
Shintani, M. and Linton, O. (2004).
Nonparametric Neural Network Estimation of Lyapunov Exponents and a
Direct Test for Chaos. Journal of Econometrics. 120(1):133.
2. HOW TO RUN NETLE PROGRAM
The current version can only run under DOS prompt in Windows
Operation System. This zip file contains the main program,
a sample data, and a control file:
README.TXT This file.
NETLE.EXE The main program.
HENON.IN A sample control file for NETLE.EXE.
HENON.DAT An example data set with 600 observations and 4 inputs.
To run NETLE, unzip the file NETLE41.ZIP to a directory. Before you
run the program, you will need to have a data file and a control file.
The structure of your data file must follow the format described in
Section 4 below. The detail of the control file is explained in
Section 5. Put the main program, data file, and the control file
in one directory. And run the program from the DOS prompt by typing:
C:> NETLE control_file_name
You may test NETLE program using the sample control file and data file
in this zip file by typing
C:> NETLE HENON.IN
3. DATA FILE
The first column of the data file must be a series of ID numbers (e.g.
1,2,3,....,n); the second column should contain the target (dependent)
variable; the other columns should be input (explanatory) variables.
4. CONTROL FILE
NETLE is not an interactive program. The execution of this program
is controlled by a control file which contains information of the
data file name, network structure, and other options for computation.
A sample of this control file HENON.IN is included in the disk. The
simplest way to create your own control file is to revise the content
of HENON.IN and rename it with a new file name. After you create your
own control file, you can run NETLE from the DOS prompt by typing
C:> NETLE control_file_name
For example, to run the program with HENON.IN, type
C:> NETLE HENON.IN
4.1 Contents of a Control File:
This file contains 16 instruction lines. Each line is followed by
a single information line. The user must supply all the information
in these information lines. If no information is needed, a blank line
must exist between two instruction lines. The program will not function
properly if wrong information or more than one information line is supplied.
If two numbers are required in an information line, these numbers must be
separated by space(s). DO NOT erase the instruction lines in your control
file as the program will read them as NULL lines.
The following are the instruction lines and explanation.
(1) [* NETLE Version 4.1 (neural NETwork for LE) by Kuan, Liu, & Gencay. *]
The TITLE you would like to have in your output file.
(2) [* Data File Name: *]
The name of the data file to be read by the program.
(3) [* Output File Name: *]
The name of the output file.
(4) [* Number of Observations: *]
Total number of observations in the data file specified in (2).
(5) [* Number of Inputs: *]
The number of inputs (explanatory variables).
(6) [* Minimum and Maximum Number of Hidden Units: *]
Two integer values. The first value, q, is a number specifying the
minimum number of hidden units; the second value, Q, is a number
specifying the maximum number of hidden units. The program will
estimate total (Q-q+1) networks.
(7) [* Calculating the Lyapunov Exponent: 0/No, 1/Yes *]
Enter 0 or 1. The Lyapunov exponents will be computed if 1 is entered.
(8) [* Method of Scaling Inputs: *]
Enter one of the following 4 choices:
0: no scaling is made;
1: each input is standardized by subtracting its mean and divided
by its standard deviation;
2: each input is standardized between 0 and 1 using a logistic
transformation: x*=1/(1+exp(-x));
3: each input is standardized between -1 and 1 using a logistic
transformation: x*=2/(1+exp(-x)) - 1;
Notice that this value will be set to 0 by the program if the
calculation of Lyapunov exponents is requested.
(9) [* Seeds (Positive Number); NTRY: *]
The first number specifies the seed of the (standard normal)
random number generator; the second gives the number of
sets of initial parameters to be generated. The program will
select the set of initial parameters which results in the lowest
MSE as the starting values for NLS estimation.
(10) [* Number of Iterations; Tolerance in NLS: *]
The first number specifies the maximum number of iterations in
NLS estimation; the second specifies the tolerance level
for NLS convergence.
(11) [* Creating the Parameters File: 0/No, 1/Yes *]
Enter 0 or 1. A file for parameter estimates will be created under
the name specified in (12) if 1 is entered.
(12) [* Parameters File Name: (The Option Above Must Be "1") *]
The file name for parameter estimates. If 0 is specified in
(11), you may leave this line blank, or the program will ignore the
content of this line.
(13) [* Creating the Fitted Values File: 0/No, 1/Yes *]
Enter 0 or 1. A file for fitted values will be created under the
name specified in (14) if 1 is entered.
(14) [* Fitted Values File Name: *]
The file name for fitted values. If 0 is specified in (13),
you may leave this line blank, or the program will ignore the content
of this line.
(15) [* Creating the Derivatives: 0/No, 1/Yes *]
Enter 0 or 1. A file for derivatives will be created under the
name specified in (16) if 1 is entered.
(16) [* Derivatives File Name: *]
The file name for derivatives which is used to compute Lyapunov
exponents. If 0 is specified in (15), you may leave this line blank,
or the program will ignore the content of this line.
4.2. A Sample Control File
Below is a sample control file HENON.IN. The user may create a new
control file by suitably modifying this sample file.
[* NETLE Version 4.1 (neural NETwork for LE) by Kuan, Liu, & Gencay. *]
Henon Map
[* Data File Name: *]
henon.dat
[* Output File Name: *]
henon.out
[* Number of Observations: *]
600
[* Number of Inputs: *]
4
[* Minimum and Maximum Number of Hidden Units: *]
2 6
[* Calculating the Lyapunov Exponent: 0/No, 1/Yes *]
1
[* Method of Scaling Inputs: *]
0
[* Seeds (Positive Number); NTRY: *]
56666459 500
[* Number of Iterations; Tolerance in NLS: *]
900 1.0d-9
[* Creating the Parameters File: 0/No, 1/Yes *]
1
[* Parameters File Name: (The Option Above Must Be "1") *]
henon.par
[* Creating the Fitted Values File: 0/No, 1/Yes *]
1
[* Fitted Values File Name: *]
henon.fit
[* Creating the Derivatives: 0/No, 1/Yes *]
1
[* Derivatives File Name: *]
henon.der
5. PROGRAM OUTPUT
The results of the program will be displayed on the screen and
written to an output file as specified in the control file.
Part of the result from the control file HENON.IN is as follows.
The Henon1.out contains the main results. For the model with 2 hiddens,
Hiddens 2: MSE = 0.125331E-07 SIC = -18.0563
Lyapunov Exponents:
lambda( 1) = 0.4249725
HAC Std Error (Newey/West) 0.0136785
HAC Std Error (Parzen) 0.0136320
HAC Std Error (Quad. Spect.) 0.0135662
lambda( 2) = -1.6241288
HAC Std Error (Newey/West) 0.0202770
HAC Std Error (Parzen) 0.0227045
HAC Std Error (Quad. Spect.) 0.0249118
lambda( 3) = -4.4671052
HAC Std Error (Newey/West) 0.3413844
HAC Std Error (Parzen) 0.1545655
HAC Std Error (Quad. Spect.) 0.1425157
lambda( 4) = -4.5935032
HAC Std Error (Newey/West) 0.3800361
HAC Std Error (Parzen) 0.1592727
HAC Std Error (Quad. Spect.) 0.1465124
The values of lambda's are the estimated Lyapunov exponents. The three
different standard errors of the estimate can be used for confidence
interval or the hypothesis testing. If the calculation of Lyapunov
exponents is set to "0" in HENON.IN, the values of lambda will not
be given.
5.1 The file for Parameter Estimates
If the parameter file is requested, both the initial values from the
random number generator and the final estimates from NLS will be written
to the parameter file. There are two lines above each set of parameters:
Initial Est.: ntobs nv nq nw
xxx x x xx
NLS Est.: ntobs nv nq nw
xxx x x xx
Here, "ntobs" is the total number of observations in the data file,
"nv" is the number of inputs, "nq" is the number of hidden units, and
"nw" is the total number of parameters of the estimated network. The
parameters of each network in the parameter file are arranged according
to the following order:
Output bias (constant term),
Parameters connecting hidden and output units,
The first hidden bias,
The parameter connecting the first input and first hidden units,
The parameter connecting the second input and first hidden units,
...
The parameter connecting the v-th input and first hidden units,
...
The q-th hidden bias,
The parameter connecting the first input and q-th hidden units,
The parameter connecting the second input and q-th hidden units,
...
The parameter connecting the v-th input and q-th hidden units,
5.2. The file for Fitted Values
The file for fitted values has 3 columns: the first contains
original target values, the second contains network fitted values,
and the third contains network errors (target - fitted values).
6. CORRESPONDENCES
Questions of this program should be addressed to:
Tung Liu, Ph. D.
Department of Economics
Ball State University
Muncie, Indiana 47306
U.S.A.
(765) 285-5360
E-Mail: tliu@bsu.edu
http://tliu.iweb.bsu.edu
Other coauthors of this program can be reached at:
Chung-Ming Kuan, Ph.D.
Institute of Economics
Academia Sinica
128 Academia Road, Sec. 2
Taipei 115, TAIWAN
886 2 2782–2791 ext. 646
886 2 2651–0647 (Direct)
886 2 2782–2019 (Fax)
E-Mail: ckuan@econ.sinica.edu.tw
URL: www.sinica.edu.tw/~ckuan
Ramazan Gencay, Ph.D.
Department of Economics
Simon Fraser University
8888 University Drive
Burnaby, British Columbia, V5A 1S6, Canada
Phone: (604) 291-3934
Email: gencay@sfu.ca
http://www.sfu.ca/~rgencay