autoregFit#
Purpose#
Estimates coefficients of a regression model with autoregressive errors of any specified order.
Format#
- aro = autoregFit(y, x, lagvars, order[, arc])#
- aro = autoregFit(dataset, formula, lagvars, order[, arc])
- Parameters:
y (Nx1 vector) – data.
x (Nxk vector) – independent data.
dataset (string) – name of data set or null string.
formula (string) – formula string of the model. E.g.
"y ~ X1 + X2"‘y’ is the name of dependent variable, ‘X1’ and ‘X2’ are names of independent variables; E.g."y ~ .",.means including all variables except dependent variable ‘y’;lagvars (Kx1 vector) – the number of periods to lag the variables inindvars. If there are no lagged variables, set to scalar 0. The variables in indvars will be lagged the number of periods indicated in the corresponding entries inlagvars. The dependent variable in depvar can be included in indvars can be repeated if each corresponding entry in lagvars is a different value.
order (scalar) – order of the autoregressive process; must be greater than 0 and less than the number of observations.
arc (struct) –
Optional input. Instance of an
automtControlstructure. The following members of arc are referenced within this routine:arc.const
scalar. If 1, constant will be used in model; else not. Default = 1.
arc.header
string, specifies the format for the output header. arc.header can contain zero or more of the following characters:
t
title is to be printed.
l
lines are to bracket the title.
d
a date and time is to be printed.
v
version number of program is to be printed.
f
file name of program is to be printed
Example:
arc.header = "tld";
If
arc.header = "", no header is printed. Default ="tldvf".arc.init
scalar. If 1, only initial estimates will be computed. Default = 0.
arc.iter
scalar. If 0, iteration information will not be printed. If 1, iteration information will be printed (arc.outputmust be nonzero). Default = 0.
arc.maxvec
scalar, the maximum number of elements allowed in any one matrix. Default = 20000.
arc.output
scalar, if nonzero, results are printed to screen. Default = 1.
arc.title
string, a title to be printed at the top of the output header (see arc.header). By default, no title is printed (
arc.title="").arc.tol
scalar, convergence tolerance. Default = 1e-5.
- Returns:
aro (struct) –
An instance of an
automtOutstructure containing the following members:aro.acor
(L+1)x1 vector, autocorrelations.
aro.acov
(L+1)x1 vector, autocovariances.
aro.chisq
scalar, -2* log-likelihood.
aro.coefs
Kx1 vector, estimated regression coefficients.
aro.phi
Lx1 vector, lag coefficients.
aro.rsq
scalar, explained variance.
aro.sigsq
scalar, variance of white noise error.
aro.tobs
scalar, number of observations.
aro.vcb
KxK matrix, covariance matrix of estimated regression coefficients.
aro.vcphi
LxL matrix, covariance matrix of phi.
aro.vsig
scalar, variance of aro.sigsq (variance of the variance of white noise error).
Examples#
Data matrices#
new;
cls;
library tsmt;
//Load data
data = loadd(getGAUSSHome() $+ "pkgs/tsmt/examples/autoregmt.dat");
y = data[., 1];
x = data[., 2 3];
//Lag of independent variables
lag_vars = 0;
//Autoregressive order
order = 3;
//Initialized automtOut structure
struct automtOut aro;
//Call autoregFit function
aro = autoregFit(y, x, lag_vars, order);
The final results are:
DEPENDENT VARIABLE: Y
Number of Observations: 200
R-squared: 0.710
Standard Error of Estimate: 1.524
Variance of White Noise Error (sigsq): 0.913
Variance of sigsq: 0.008
-2*log(likelihood): 548.000
COEFFICIENTS OF INDEPENDENT VARIABLES (beta)
Variable Coef Std. Error t-Ratio P-Value
-------------------------------------------------------------------
CONSTANT -0.266678 0.516473 -0.516344 0.606
X1 0.503195 0.060327 8.341081 0.000
X2 0.592405 0.059390 9.974846 0.000
AUTOREGRESSIVE PARAMETERS (Phi)
Lag Phi Std. Error T-Ratio P-Value
----------------------------------------------------------------
1 0.246131 0.065740 3.744029 0.000
2 0.263760 0.065397 4.033229 0.000
3 0.368323 0.065740 5.602763 0.000
AUTOCORRELATIONS AND AUTOCOVARIANCES
Lag Autocovariances Autocorrelations
----------------------------------------------------
0 2.322667 1.000000
1 1.563621 0.673201
2 1.573401 0.677411
3 1.655176 0.712619
Dataset and formula string#
new;
cls;
library tsmt;
// Lag of independent variables
lag_vars = 0;
// Autoregressive order
order = 3;
// Initialized automtOut structure
struct automtOut aro;
// Call autoregFit function
aro = autoregFit(getGAUSSHome() $+ "pkgs/tsmt/examples/autoregmt.dat", "Y ~ X1 + X2", lag_vars, order);
The results printed to screen are:
DEPENDENT VARIABLE: Y
Number of Observations: 200
R-squared: 0.710
Standard Error of Estimate: 1.524
Variance of White Noise Error (sigsq): 0.913
Variance of sigsq: 0.008
-2*log(likelihood): 548.000
COEFFICIENTS OF INDEPENDENT VARIABLES (beta)
Variable Coef Std. Error t-Ratio P-Value
-------------------------------------------------------------------
CONSTANT -0.266678 0.516473 -0.516344 0.606
X1 0.503195 0.060327 8.341081 0.000
X2 0.592405 0.059390 9.974846 0.000
AUTOREGRESSIVE PARAMETERS (Phi)
Lag Phi Std. Error T-Ratio P-Value
----------------------------------------------------------------
1 0.246131 0.065740 3.744029 0.000
2 0.263760 0.065397 4.033229 0.000
3 0.368323 0.065740 5.602763 0.000
AUTOCORRELATIONS AND AUTOCOVARIANCES
Lag Autocovariances Autocorrelations
----------------------------------------------------
0 2.322667 1.000000
1 1.563621 0.673201
2 1.573401 0.677411
3 1.655176 0.712619
Remarks#
This program will handle only datasets that fit in memory.
All autoregressive parameters are estimated up to the specified lag. You cannot estimate only the first and fourth lags, for instance.
The algorithm will fail if the model is not stationary at the estimated parameters. Thus, in that sense it automatically tests for stationarity.
Library#
tsmt
Source#
autoregmt.src
See also
Functions arimaFit(), arimaSS(), arimaControlCreate()