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