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.

amo.tsmtDesc

An instance of the tsmtModelDesc structure containing the following members:

tsmtDesc.depvar

Kx1 string array, names of endogenous variables.

tsmtDesc.indvars

Mx1 string array, names of exogenous variables.

tsmtDesc.timespan

2x1 string array, range of the time series. Available if date vector is passed as part of a dataframe input.

tsmtDesc.ncases

Scalar, number of observations.

tsmtDesc.df

Scalar, degrees of freedom.

tsmtDesc.model_name

String, model name.

amo.sumStats

An instance of the tsmtSummaryStats structure containing the following members:

sumStats.sse

Vector, sum of the squared errors of estimates for endogenous variables in the model.

sumStats.mse

Vector, mean squared errors of estimates for endogenous variables in the model.

sumStats.rmse

Vector, root mean squared errors of estimates for endogenous variables in the model.

sumStats.see

Vector, standard error of the estimates for endogenous variables in the model.

sumStats.rsq

Vector, r-squared of estimates for endogenous variables in the model.

sumStats.AdjRsq

Scalar, adjusted r-squared of estimates for endogenous variables in the model.

sumStats.ssy

Scalar, total sum of the squares for endogenous variables in the model.

sumStats.DW

Scalar, Durbin-Watson statistic for residuals from the estimates for endogenous variables in the model.

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 );

Library#

tsmt

Source#

sarima_ss.src

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