arimaSS¶

Purpose¶

Estimates ARIMA models using a state space representation, the Kalman filter, and maximum likelihood.

Format¶

vOut = arimaSS(y, p, d, q, trend, const)¶

Parameters:

y (Nx1 vector) – data.
p (Scalar) – the autoregressive order.
d (Scalar) – the order of differencing.
q (Scalar) – the moving average order.
trend (Scalar) – an indicator variable to include a trend in the model. Set to 1 to include trend, 0 otherwise.
const (Scalar) – an indicator variable to include a constant in the model. Set to 1 to include trend, 0 otherwise.

Returns:

vOut (struct) –

An instance of an arimamtOut structure containing the following members:

amo.aic	Scalar, value of the Akaike information criterion.
amo.b	Kx1 vector, estimated model coefficients.
amo.e	Nx1 vector, residual from fitted model.
amo.ll	Scalar, the value of the log likelihood function.
amo.sbc	Scalar, value of the Schwartz Bayesian criterion.
amo.lrs	Lx1 vector, the Likelihood Ratio Statistic.
amo.vcb	KxK matrix, the covariance matrix of estimated model coefficients.
amo.mse	Scalar, mean sum of squares for errors.
amo.sse	Scalar, the sum of squares for errors.
amo.ssy	Scalar, the sum of squares for Y data.
amo.rstl	an instance of the kalmanResult structure.

Example¶

new;
library tsmt;

// Create file name with full path
fname = getGAUSSHome() $+ "pkgs/tsmt/examples/wpi1.dat";

// Load variable 'wpi' from 'wpi1.dat'
y = loadd(fname, "wpi");

// Model settings
p = 1;
d = 1;
q = 1;
trend = 0;
const = 1;

// Declare 'amo' to be an arimamtOut structure
// to hold the estimation results and then
// estimate the model
struct arimamtOut amo;
amo = arimaSS(y, p, d, q, trend, const);

The example above prints the following results

ARIMA(1,1,1) Results
                     2022-07-14 16:08:37


Number of Observations:                 123.0000
Degrees of Freedom:                          119
Mean of Y:                               62.7742
Standard Deviation of Y :                30.2436
Sum of Squares of Y:                    112504.7755


                         COEFFICIENTS

Coefficient Estimates
------------------------------------------------------------------------------------------

     Variables      Coefficient               se            tstat             pval
  phi : y[t-1]            0.868           0.0639             13.6          4.8e-42
theta : e[t-1]           -0.406            0.123            -3.29         0.000985
        Sigma2            0.524           0.0462             11.3         7.69e-30
      Constant              0.8            0.296             2.71          0.00682
------------------------------------------------------------------------------------------
*p-val<0.1 **p-val<0.05 ***p-val<0.001

Library¶

tsmt

Source¶

sarima_ss.src