Description Usage Arguments Details See Also
Function arimaSSM
creates a state space
representation of ARIMA model.
1 2 3 4 5 |
arima |
A list or a list of lists with components
|
H |
A p*p covariance matrix (or p*p*n array in of time-varying case) of the disturbance terms ε[t] of the observation equation. Default gives p*p zero matrix ie. ordinary ARIMA model without additional noise. Omitted in case of non-Gaussian distributions. Augment the state vector if you to add want additional noise. |
Q |
A p*p covariance matrix of the disturbance terms η[t] of the system equation. Default is p*p identity matrix ie. ordinary ARIMA model with disturbance terms having unit variance. |
y |
A time series object of class |
u |
Only used with non-Gaussian distribution. See details. |
distribution |
Specify the distribution of the observations. Default is "Gaussian". |
transform |
The functions of |
tolF |
Tolerance parameter for Finf. Smallest value not counted for zero. |
tol0 |
Tolerance parameter for LDL decomposition, determines which diagonal values are counted as zero. |
The linear Gaussian state space model is given by
y[t] = Z[t]α[t] + ε[t], (observation equation)
α[t+1] = T[t]α[t] + R[t]η[t], (transition equation)
where ε[t] ~ N(0,H[t]), η[t] ~ N(0,Q[t]) and α[1] ~ N(a[1],P[1]) independently of each other. In case of non-Gaussian observations, the observation equation is of form p(y[t]|θ[t]) = p(y[t]|Z[t]α[t]), with p(y[t]|θ[t]) being one of the following:
If observations are Poisson distributed, parameter of Poisson distribution is u[t]λ[t] and θ[t]=log(λ[t]).
If observations are from binomial distribution, u is a vector specifying number the of trials at times 1,…,n, and θ[t] = log(π[t]/(1-π[t])), where π[t] is the probability of success at time t.
For non-Gaussian models u[t]=1 as a default. For Gaussian models, parameter is omitted.
Only univariate observations are supported when observation equation is non-Gaussian.
regSSM
for state space representation of a
regression model, structSSM
for structural
time series model, and SSModel
for custom
SSModel
object.
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