State Space Model
Fits a simple univariate state space model, x[t] = alpha + phi x[t-1] + w[t], and y[t] = A x[t] + v[t]. The parameters alpha, phi, sigma[w] and sigma[v] are estimated; parameter phi may be fixed. State predictions and smoothers and corresponding error variances are evaluated at the estimates. The sample size must be at least 20.
ssm(y, A, phi, alpha, sigw, sigv, fixphi = FALSE)
y |
data |
A |
measurement value (fixed constant) |
phi |
initial value of phi, may be fixed |
alpha |
initial value for alpha |
sigw |
initial value for sigma[w] |
sigv |
initial value for sigma[v] |
fixphi |
if TRUE, the phi parameter is fixed |
The script works for a specific univariate state space model. The initial state conditions use a default calculation and cannot be specified. The parameter estimates are printed and the script returns the state predictors and smoothers.
At the MLEs, these are returned invisibly:
Xp |
time series - state prediction, x_t^t-1 |
Pp |
corresponding MSPEs, P_t^t-1 |
Xf |
time series - state filter, x_t^t |
Pf |
corresponding MSEs, P_t^t |
Xs |
time series - state smoother, x_t^n |
Ps |
corresponding MSEs, P_t^n |
D.S. Stoffer
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