Abstract:

Maximum Likelihood Estimates of Non-Gaussian ARMA Models


Authors: Keh-Shin Lii and Mark Lehr

Copyright (c) 1998. Keh-Shin Lii and Mark Lehr. All Rights Reserved.

Keywords: autoregressive moving average, maximum likelihood estimate, non-causal, non-invertible, non-Gaussian, stationary, white noise, genetic algorithm, simulated annealing.

Reference: Mark Lehr and Keh-Shin Lii, "Maximum Likelihood Estimates of Non-Gaussian ARMA Models," working paper, 1998. [Postscript] or [PDF]

Description: We consider an approximate maximum likelihood algorithm for estimating parameters of possibly non-causal and non-invertible autoregressive moving average processes driven by independent identically distributed non-Gaussian noise. The normalized approximate maximum likehoood estimate has a global maximum which is consistent and efficient. The estimates and their associated asymptotic covariance matrix are calculated with a subroutine implemented in Fortran 77.

Platforms: Any machine having a Fortran 77 compiler.

Support: Limited. Please contact the authors with questions or suggestions at mlehr@pacbell.net.

Documentation: The source code is annotated, and there are "readme" files in each subdirectory.

Archive file: nsf98aa.zip

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Manifest:

drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 10 16:47 Library
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 10 16:59 PostScript
-rw-r--r--   1 nsf98aa  nsf98       1257 Jul 10 16:46 Read.Me
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:58 Test1a
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:58 Test1b
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:58 Test1c
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:59 Test2a
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:59 Test2b
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:59 Test2c
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 12 10:59 Test3a
drwxr-xr-x   2 nsf98aa  nsf98        512 Jul 15 21:08 Test3c

Library:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:46 covar.f
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:46 popfnc.f
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:47 public.f
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:47 search.f

Postscript:
-rw-r--r--   1 nsf98aa  nsf98     867244 Jul 10 17:01 publish.ps

Test1a:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:33 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        642 Jul 17 18:28 MLE.X11A
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:33 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:34 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1588 Jul 10 16:34 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:34 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98      11316 Jul 10 16:34 X11.DAT
-rw-r--r--   1 nsf98aa  nsf98      10416 Jul 17 18:28 Z.X11A
-rw-r--r--   1 nsf98aa  nsf98        690 Jul 10 16:34 dnsity1.for
-rw-r--r--   1 nsf98aa  nsf98       7918 Jul 10 16:34 driver1a.for
-rwxr-xr-x   1 nsf98aa  nsf98     217072 Jul 10 16:38 x11a.out

Test1b:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:47 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        642 Jul 12 12:32 MLE.X11B
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:47 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:48 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1611 Jul 10 16:48 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:48 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98      11316 Jul 10 16:48 X11.DAT
-rw-r--r--   1 nsf98aa  nsf98      10416 Jul 12 12:32 Z.X11B
-rw-r--r--   1 nsf98aa  nsf98        690 Jul 10 16:49 dnsity1.for
-rw-r--r--   1 nsf98aa  nsf98       7897 Jul 10 16:49 driver1b.for
-rwxr-xr-x   1 nsf98aa  nsf98     217064 Jul 10 21:55 x11b.out

Test1c:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:49 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        677 Jul 12 21:43 MLE.X11C
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:49 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:50 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1627 Jul 10 16:50 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:50 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98      11316 Jul 10 16:50 X11.DAT
-rw-r--r--   1 nsf98aa  nsf98      10416 Jul 12 21:43 Z.X11C
-rw-r--r--   1 nsf98aa  nsf98        690 Jul 10 16:50 dnsity1.for
-rw-r--r--   1 nsf98aa  nsf98       7897 Jul 10 16:50 driver1c.for
-rwxr-xr-x   1 nsf98aa  nsf98     217064 Jul 10 21:56 x11c.out

Test2a:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:52 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        966 Jul 17 18:29 MLE.X212A
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:53 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:53 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1601 Jul 10 16:53 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:53 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98       6246 Jul 10 16:53 X212.DAT
-rw-r--r--   1 nsf98aa  nsf98       4354 Jul 17 18:29 Z.X212A
-rw-r--r--   1 nsf98aa  nsf98        684 Jul 10 16:53 dnsity2.for
-rw-r--r--   1 nsf98aa  nsf98       8013 Jul 10 16:53 driver2a.for
-rwxr-xr-x   1 nsf98aa  nsf98     217240 Jul 10 21:58 x212a.out

Test2b:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:54 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        966 Jul 12 12:30 MLE.X212B
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:54 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:54 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1612 Jul 10 16:54 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:54 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98       6246 Jul 10 16:54 X212.DAT
-rw-r--r--   1 nsf98aa  nsf98       4354 Jul 12 12:30 Z.X212B
-rw-r--r--   1 nsf98aa  nsf98        684 Jul 10 16:54 dnsity2.for
-rw-r--r--   1 nsf98aa  nsf98       8004 Jul 10 16:55 driver2b.for
-rwxr-xr-x   1 nsf98aa  nsf98     217232 Jul 11 20:52 x212b.out

Test2c:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:54 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98        966 Jul 12 12:30 MLE.X212B
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:54 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:54 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       1612 Jul 10 16:54 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:54 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98       6246 Jul 10 16:54 X212.DAT
-rw-r--r--   1 nsf98aa  nsf98       4354 Jul 12 12:30 Z.X212B
-rw-r--r--   1 nsf98aa  nsf98        684 Jul 10 16:54 dnsity2.for
-rw-r--r--   1 nsf98aa  nsf98       8004 Jul 10 16:55 driver2b.for
-rwxr-xr-x   1 nsf98aa  nsf98     217232 Jul 11 20:52 x212b.out

Test3a:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:56 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98       1158 Jul 17 18:30 MLE.X23A
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:56 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:57 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       2484 Jul 10 16:57 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:57 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98      28144 Jul 10 16:57 X23.DAT
-rw-r--r--   1 nsf98aa  nsf98      26768 Jul 17 18:30 Z.X23A
-rw-r--r--   1 nsf98aa  nsf98        815 Jul 10 16:57 dnsity3.for
-rw-r--r--   1 nsf98aa  nsf98       8060 Jul 10 16:57 driver3a.for
-rwxr-xr-x   1 nsf98aa  nsf98     217492 Jul 11 20:57 x23a.out

Test3c:
-rw-r--r--   1 nsf98aa  nsf98      22756 Jul 10 16:58 COVAR.for
-rw-r--r--   1 nsf98aa  nsf98       1193 Jul 16 03:05 MLE.X23C
-rw-r--r--   1 nsf98aa  nsf98      28489 Jul 10 16:58 POPFNC.for
-rw-r--r--   1 nsf98aa  nsf98     120640 Jul 10 16:58 PUBLIC.for
-rw-r--r--   1 nsf98aa  nsf98       2596 Jul 10 16:58 Read.Me
-rw-r--r--   1 nsf98aa  nsf98      42695 Jul 10 16:58 SEARCH.for
-rw-r--r--   1 nsf98aa  nsf98      28144 Jul 10 16:58 X23.DAT
-rw-r--r--   1 nsf98aa  nsf98      26768 Jul 16 03:05 Z.X23C
-rw-r--r--   1 nsf98aa  nsf98        815 Jul 10 16:59 dnsity3.for
-rw-r--r--   1 nsf98aa  nsf98       8042 Jul 10 16:59 driver3c.for
-rwxr-xr-x   1 nsf98aa  nsf98     217468 Jul 11 20:58 x23c.out


The Fortran programs in this collection were compiled on a Sun Ultrasparc running Solaris 2.5.1. The compilations were error-free.

Archived by Grace Katagiri, 22 July 1998.