Returns best SARIMAX model according to either the AIC, the AICc, the BIC or the HQC information criteria. The function conducts a (brute force) search over possible model within the order constraints provided.
This is an alternative package to the existing gretl armax package written by Yi-Nung Yang which has some limitations, e.g. it does only work for ARMA type models.
- Consideration of seasonal ARIMA models with and without exogenous regressors.
- Fine tuning the parameter space to evaluate.
- Simple API.
- GUI access through the gretl menu.
- Public convenience functions for the user for summarizing results, or retrieving the gretl ARIMA command of the 'best' model.
- Source code is tested by means of unit-tests to minimize bugs.
A detailed help file can be found here: https://raw.githubusercontent.com/atecon/auto_arima/master/src/auto_arima_help.txt
Get the package from the gretl package server and install it:
pkg install auto_arima
Once the package is installed, the user can access the GUI interface via the "Model --> Univariate time series --> Automatic ARIMA" menu. The interface will look like this:
Here is a sample script on how to use it (see also: https://raw.githubusercontent.com/atecon/auto_arima/master/src/auto_arima_sample.inp):
First, load the package and open a monthly time-series data set. In this example, we pass only the endogenous series lg (144 observations) to the main function auto_arima. However, the interested user can also pass a list of exogenous variables as the 2nd argument to auto_arima.
This function executes all the computation and estimates several seasonal ARIMA models. All relevant output is stored in the returned bundle (a kind of struct data type) named model:
clear
set verbose off
include auto_arima.gfn
# Box and Jenkins "Series G" (airline passengers)
open bjg.gdt -p -q # monthly frequency
# Find "best" ARIMA model and pass some additional option
bundle model = auto_arima(lg)
Estimating and evaluating 400 different ARIMA models takes only about 4 seconds on a 7 years old i7 laptop.
Once the computation is done, the user can print the summary results by means of the print_auto_arima_results() function. This returns for all ARIMA
print_auto_arima_results(model)
The printed table looks like this (only an extraction is shown):
***************************************************************************
Summary results of ARIMA model combinations
Three, two and one asterisk(s) below indicate the 1st, 2nd and 3rd best (that
is, minimized) values of the respective information criteria, AIC = Akaike
criterion, AICC = corrected AIC, BIC = Schwarz Bayesian criterion and
HQC = Hannan-Quinn criterion across all ARIMA model specification.
Common sample used for all models: 1877 to 1991
ARIMA-spec. aicc aic bic hqc
---------------------------------------------------------------------------
0|0|0 |0|0|0 164.084 163.996 172.821 167.582
0|0|0 |0|0|1 39.974 39.798 51.564 44.580
.
.
.
2|1|1 |0|1|1 -481.613 -482.290 -462.164 -474.112
2|1|1 |1|0|0 -463.112 -463.743 -443.152 -455.375
2|1|1 |1|0|1 -488.421* -489.269** -465.736 -479.706*
2|1|1 |1|1|0 -471.535 -472.213 -452.086 -464.034
.
.
2|1|3 |1|0|1 -488.500** -489.885*** -460.468 -477.931
2|1|3 |1|1|0 -477.911 -479.092 -453.215 -468.577
2|1|3 |1|1|1 -480.705 -482.192 -453.440 -470.509
.
.
.
***************************************************************************
Another useful public function is get_auto_arima_parameters(). It takes as arguments the model bundle, a string referring to some information criteria and a positive integer referring to the n-th best model according to this information criteria. The function prints a row vector with the ARIMA parameters of this selected model:
# Print coefficient vector of the n-th best model using the AIC
matrix arima_params = get_auto_arima_parameters(model, "aic", 1)
print arima_params
The output is:
arima_params (1 x 6)
p d q P D Q
2 1 3 1 0 1
Lastly, the user can retrieve the gretl command as a string variable for a specific model by means of the get_auto_arima_command() function. Also this function takes the same three arguments as get_auto_arima_parameters():
# Retrieve the gretl command for estimating the n-th best model according to BIC
string arima_cmd = get_auto_arima_command(model, "bic", 2)
print arima_cmd
which returns the string:
arima 2 0 0 ; 0 1 1 ; lg const L
This string can be used for estimating the selected model:
# Execute actual estimation
@arima_cmd
Calling the built-in gretl arima command returns the following estimation output:
Function evaluations: 81
Evaluations of gradient: 20
Model 1: ARMAX, using observations 1950:01-1960:12 (T = 132)
Estimated using AS 197 (exact ML)
Dependent variable: (1-Ls) lg
Standard errors based on Hessian
coefficient std. error z p-value
-------------------------------------------------------
const 0.118604 0.00904671 13.11 2.88e-39 ***
phi_1 0.590424 0.0853470 6.918 4.58e-12 ***
phi_2 0.246938 0.0853191 2.894 0.0038 ***
Theta_1 -0.558276 0.0773696 -7.216 5.37e-13 ***
foo -0.00301776 0.00239775 -1.259 0.2082
Mean dependent var 0.119822 S.D. dependent var 0.061645
Mean of innovations 0.000677 S.D. of innovations 0.035567
R-squared 0.992258 Adjusted R-squared 0.992077
Log-likelihood 250.4308 Akaike criterion -488.8616
Schwarz criterion -471.5648 Hannan-Quinn -481.8329
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root 1 1.1452 0.0000 1.1452 0.0000
Root 2 -3.5362 0.0000 3.5362 0.5000
MA (seasonal)
Root 1 1.7912 0.0000 1.7912 0.0000
-----------------------------------------------------------
See here: https://github.com/atecon/auto_arima/blob/master/src/auto_arima_help.txt