Exact predictive parameters for multi-step MixAR prediction
predict_coef.RdExact predictive parameters for multi-step MixAR prediction.
Details
predict_coef() implements the method of
Boshnakov (2009)
for the h-step prediction
of MixAR processes. The h-step predictive distribution has a MixAR
distribution with \(g^h\) components and this function computes its
parameters.
predict_coef() implements the results by
Boshnakov (2009)
to compute the parameters
of the predictive distributions. predict_coef() is mostly a
helper function, use multiStep_dist for
prediction/forecasting (the exact method for multiStep_dist
uses predict_coef() to do the main work).
predict_coef() returns a list of lists containing the
quantities needed for each horizon \(h\), see section Value.
Alternatiely, the parameters can be obtained as MixAR models
by calling the function generated by the exact method of
multiStep_dist with argument what = "MixAR".
Value
a list with components:
- arcoefs
a list,
arcoefs[[h]]gives the ar coefficients for the h-step predictive distribution.- sigmas
a list,
sigmas[[h]]sigmas[[h]] is a matrix, in which the \(k\)th column contains the theta coefficients needed to compute \(sigma_k\) in the formula for sigma in Equation (16) (see Boshnakov 2009) . In the paper the index is a tuple \((k_1,…,k_h)\) for clarity. In the code each tuple \((k_1,…,k_h)\) is mapped to a linear index in \(1,\ldots,g^h\) (there are \(g^h\) tuples for horizon \(h\), since the mixture has \(g^h\) components).- probs
a list,
probs[[h]]gives the mixture weights for the h-step predictive distribution.- sStable
a list,
sigmas[[h]]gives the scale parameters for the h-step predictive distribution.
References
Boshnakov GN (2009). “Analytic expressions for predictive distributions in mixture autoregressive models.” Stat. Probab. Lett. , 79(15), 1704-1709. doi:10.1016/j.spl.2009.04.009 .