# sarimaSS¶

## Purpose¶

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

## Format¶

vOut = sarimaSS(y, p, d, q, P_s, D_s, Q_s, s, trend, const)
Parameters:
• y (Nx1 vector) – data.

• p (Scalar) – the autoregressive order.

• d (Scalar) – the order of differencing.

• q (Scalar) – the moving average order.

• P_s (Scalar) – the seasonal autoregressive order.

• D_S (Scalar) – the seasonal order of differencing.

• Q_s (Scalar) – the seasonal moving average order.

• s (Scalar) – the seasonal frequency term.

• 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:

amo (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;
cls;
library tsmt;

airline = loadd( getGAUSSHome() \$+ "pkgs/tsmt/examples/airline.dat");

// Transform data
y = ln(airline);

p = 0;
d = 1;
q = 1;

P_s = 0;
D_s = 1;
Q_s = 1;
s=12;

trend = 0;
const = 0;

struct arimamtOut amo;
amo = sarimaSS( y, p, d, q, P_s, D_s, Q_s, s, trend, const );


tsmt

sarima_ss.src