Functions to specify the measurement equations
Functions required to specify the measurement equations: observables can be linked to specific elements of a block of states. The measurement equation can include lagged of the latent states, conditional expectations for those states, and linear combinations of them.
jd3_ssf_equation
output
Creates a JD+ object of the class JD3_SsfEquation
usage
jd3_ssf_equation(name,variance, fixed )
Argument | Definition | Default | Remarks |
---|---|---|---|
name | string refering to the name the user wants to give to the equation | ex. "equation1", do not forget the commmas | |
variance | double representing the value of $\sigma^2_{\epsilon}$, which is associated to the variance of the I.I.D. measurement error $ \epsilon_{t}$ | 0 | Note that $ var(\epsilon_{t}) =\sigma^2 \sigma^2_{\epsilon}$, so setting variance=2 implies that $ var(\epsilon_{t}) =\sigma^2 \times 2 $, where $ \sigma^2 $ is common to the variance of all shocks (including noise terms in the remaining measurement equations and transtion equation shocs) |
fixed | logical that triggers estimation of the variance $\sigma^2_{\epsilon}$ (FALSE) or fixes it (TRUE) to the value pre-specified by the input variance (zero by defaut) | TRUE |
Examples of use
eq1 <-jd3_ssf_equation("variableName")
eq1 <-jd3_ssf_equation("variableName",variance=1, fixed = TRUE)
jd3_ssf_loadings
output
Creates a JD+ object of the class JD3_SsfLoading
usage
jd3_ssf_loadings(pos, weights )
Argument | Definition | Default | Remarks |
---|---|---|---|
pos | double array defining the position of each one of the elements of the block of states defined | Empty or Null indicates by default the first state included in the block (pos=0) | For instance, the block of states generated with the jd3_ssf_ar2(...) function follows the following pattern: x(t-nlags), x(t-nlags+1),..., x(t),x(t+1|t),...,x(t+h|t), where p represents the number of lags selected and h stands for the forecast horizon selected. This means that in order to select x(t-nlags), one must specify pos=0. Alternatively, the contemporaneous and future values of the state (i.e. x(t),x(t+1|t),...,x(t+h|t)) are selected by specifying pos=c(nlags,nlags+1,...,nlags+h) |
weights | double array defining the weights associated to each one of the state variables included in the block | Empty or Null | By default, all the weights associated to the other argument, pos, will be equal to one. Otherwise, one can esily specify the weights as weights=c(w0,w1,...,wh), where wi are doubles. Make sure length(pos) is equal to length(weights) |
Examples of use
jd3_ssf_loadings(0) // this is called by default when the function is not applied
jd3_ssf_loadings(c(4,3,2,1,0),c(1,0,0,-1)) //
add
This function adds selected latent variables from the JD+ class JD3_SsfItem
into
the measurement equation of the model, which belongs to the JD+ class JD3_SsfEquation
.
output
Modifies a JD+ object of the class JD3_SsfEquation
usage
add(object, item , coeff, fixed, loading)
Argument | Definition | Default | Remarks |
---|---|---|---|
object | JD3_SsfEquation object | generated with the jd3_ssf_equation(name,variance,fixed) function | |
item | JD3_SsfItem object representing a block of latent variables with dynamics given by a specific time-series model | ||
coeff | double setting the value of the coefficient associated to the block of latent variables defined by item | 1 | this coefficient defines the loadings specified in the last argument of the function |
fixed | logical that triggers estimation of coeff (FALSE) or fixes it (TRUE) to a pre-specified value | TRUE | |
loading | object of the class JD3_SsfLoading. Given that the JD3_SsfItem item contains a block of latent states, the loadings argument specifies the elements of the block are loaded in the equation and their weights | Null | defined by the jd3_ssf_loading(pos, weights) |
Examples of use
add(eq1, "trend")
add(eq1, "cycle")
add(eq2, "trend2", 1.5, FALSE)
add(eq2, "cycle2", 0.5, FALSE, jd3_ssf_loadings(4))
add(eq3, "cycle2", 0.5, FALSE, jd3_ssf_loadings(c(4,3,2,1,0),c(1,0,0,-1))