************************************************************************* ** PROGRAM: NETLE ** ** PURPOSE: Feedforward Neural Networks and Lyapunov Exponents ** ** Estimation ** ** COPYRIGHT: Chung-Ming Kuan, Tung Liu, and Ramazan Gencay ** ** VERSION: 3.01, January 1997 ** ************************************************************************* UPDATE: (1/2/1997) NETLE 3.01 is a Windows 95/NT program to estimate feedforward neural network models and compute Lyapunov exponents (LE). The maximum number of data values is 7000. The maximum inputs and hiddens are 20. Current version runs under the DOS prompt. The future version will be run under Windows. Changes: 1/2/1997 Compute LE for inputs up to 20. CONTENTS: Section 1. INTRODUCTION What is NETLE? Installation and run the program. Section 2. SYSTEM REQUIREMENTS Section 3. PROGRAM RESTRICTIONS: The data and neural network restrictions for this program. Section 4. DATA FILE: The structure of the data file. Section 5. CONTROL FILE: A file with the information and options for running this program. Section 6. PROGRAM OUTPUT: How to read the program output. Section 7. CORRESPONDENCE: The address, phone number, and email address for the authors. ======================================================================== 1. INTRODUCTION This program, NETLE.EXE, estimates feedforward neural network models and computes Lyapunov exponents (LE). Neural networks 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)). Note that a positive Lyapunov exponent indicates that the underlying series is chaotic. This disk (or 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 NETLE3.ZIP to a directory. Put the main program, your data file, and the control file in one directory. And run the program from the DOS prompt by typing: C:> NETLE control_file_name The structure of your data file must follow the format described in the later section. The detail of the control file is also explained in this document. You may test NETLE with the supplied sample control file and data file by typing: C:> NETLE HENON.IN This disk is distributed for academic purposes only; proper citation of this program is gratefully appreciated. REFERENCES: Kuan, Chung-Ming and Tung Liu (1995). "Forecasting exchange rates using feedforward and recurrent networks," Journal of Applied Econometrics, Vol. 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. ======================================================================== 2. SYSTEM REQUIREMENTS NETLE.EXE requires an IBM or IBM compatible PC. Since the NLS estimation requires a lot of CPU time, a high speed 486 or Pentium PC is recommended. The program is for 32 bits OS. This requires a Windows 95 or NT system. ======================================================================== 3. PROGRAM RESTRICTIONS Current version of NETLE.EXE has the following restrictions: (a) Data: The maximum number of observations is 7000. (b) Network: The maximum number of inputs is 20; The maximum number of hidden units is 20; You may run NETLE with the above maximum feature only if your PC has enough RAM. ======================================================================== 4. 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. ======================================================================== 5. 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 SAMPLE.IN is included in the disk. The simplest way to create your own control file is to revise the content of SAMPLE.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 test the program using SAMPLE.IN, type C:> NETLE SAMPLE.IN 5.1 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 2.1 (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. 5.2. 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 3.0 (neural NETwork for LE) by Kuan, Liu, & Gencay. *] Henon Map [* Data File Name: *] henon.dat [* Output File Name: *] henon.out [* Number of Observations: *] 200 [* Number of Inputs: *] 2 [* Minimum and Maximum Number of Hidden Units: *] 1 2 [* 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 ======================================================================== 6. 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 SAMPLE.IN is as follows. Hiddens 1: MSE = .226113 SIC = -1.35426 Lyapunov Exponents: lambda( 1) = -1.451576 lambda( 2) = -4.839406 Hiddens 2: MSE = .744204E-08 SIC = -18.4777 Lyapunov Exponents: lambda( 1) = .4331328 lambda( 2) = -1.636965 The values of lambda's are the estimated Lyapunov exponents. If the calculation of Lyapunov exponents is set to "0" in SAMPLE.IN, the values of lambda will not be given, and the result reads: Hiddens 1: MSE = .226113 SIC = -1.35426 Hiddens 2: MSE = .744204E-08 SIC = -18.4777 6.1 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, 6.2. 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). ======================================================================== 7. CORRESPONDENCES Questions of this program should be addressed to: Prof. Tung Liu Department of Economics Ball State University Muncie, IN 47306 U.S.A. (765) 285-3724 E-Mail: tliu@bsu-cs.bsu.edu Other authors can be reached at: Prof. Chung-Ming Kuan Department of Economics National Taiwan University Taipei 10020 TAIWAN (886-2) 351-9641 ext. 522 E-mail: ckuan@ccms.ntu.edu.tw Prof. Ramazan Gencay Department of Economics University of Windsor Windsor Ontario Canada, N9B3P4 (519) 253-4232 ext. 2382 E-mail: gencay@uwindsor.ca