R: Estimation of a 'NAWRUmodel'

fit.NAWRUmodel {RGAP}

R Documentation

Estimation of a `NAWRUmodel`

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the NAWRU using either maximum likelihood estimation or bayesian methods.

Usage

## S3 method for class 'NAWRUmodel'
fit(
  model,
  parRestr = initializeRestr(model = model),
  signalToNoise = NULL,
  method = "MLE",
  control = NULL,
  prior = initializePrior(model),
  R = 10000,
  burnin = ceiling(R/10),
  thin = 1,
  HPDIprob = 0.85,
  pointEstimate = "mean",
  MLEfit = NULL,
  ...
)

Arguments

`model`	An object of class NAWRUmodel.
`parRestr`	A list of matrices containing the parameter restrictions for the cycle, trend, and the Phillip's curve. Each matrix contains the lower and upper bound of the involved parameters. `NA` implies that no restriction is present. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. By default, `parRestr` is initialized by the function `initializeRestr(model)`. Only used if `method = "MLE"`.
`signalToNoise`	(Optional) signal to noise ratio. Only used if `method = "MLE"`.
`method`	The estimation method. Options are maximum likelihood estimation `"MLE"` and bayesian estimation `"bayesian"`. The default is `method = "MLE"`.
`control`	(Optional) A list of control arguments to be passed on to `optim`.
`prior`	A list of matrices with parameters for the prior distribution and box constraints. By default, `prior` is initialized by `initializePrior(model)`. See details. Only used if `method = "bayesian"`.
`R`	An integer specifying the number of MCMC draws. The default is `R = 10000`. Only used if `method = "bayesian"`.
`burnin`	An integer specifying the burn-in phase of the MCMC chain. The default is `burnin = ceiling(R / 10)`. Only used if `method = "bayesian"`.
`thin`	An integer specifying the thinning interval between consecutive draws. The default is `thin = 1`, implying that no draws are dopped. For `thin = 2`, every second draw is dropped and so on. Only used if `method = "bayesian"`.
`HPDIprob`	A numeric in the interval `(0,1)` specifying the target probability of the highest posterior density intervals. The default is `HPDIprob = 0.9`. Only used if `method = "bayesian"`.
`pointEstimate`	Posterior distribution's statistic of central tendency. Possible options are `"mean"` and `"median"`. The default is `pointEstimate = "mean"`. Only used if `method = "bayesian"`.
`MLEfit`	(Optional) An object of class `NAWRUfit` which is used for initialization. Only used if `method = "bayesian"`.
`...`	additional arguments to be passed to the methods functions.

Details

The list object prior contains three list elements cycle, trend, and pcInd. Each list element is a 4 x n matrix where n denotes the number of parameters involved in the respective equation. The upper two elements specify the distribution, the lower two parameters specify box constraints. NA denotes no constraints. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. For instance, prior$cycle[, 1] contains the mean, standard deviation, lower and upper bound for the first variable, in that respective order.

The respective prior distributions are defined through their mean and standard deviation.

The Gibbs sampling procedure is as follows. For each r = 1, ..., R

The states are sampled by running the Kalman filter and smoother conditional on the parameters of the previous step, \theta_{r-1}
Trend equation parameters \theta_{trend}: Conditional on the states \alpha_r, a draw \theta_{trend,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the trend model specification.
Cycle equation parameters \theta_{cycle}: Conditional on the states \alpha_r, a draw \theta_{cycle,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the cycle model specification.
Phillip's curve equation parameters \theta_{pcInd}: Conditional on the states \alpha_r, a draw \theta_{pcInd,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, a combination thereof, or by conjugacy, depending on the Phillip's curve equation specification.

Value

For maximum likelihood estimation, an object of class NAWRUfit containing the following components:

`model`	The input object of class `NAWRUmodel`.
`SSMfit`	The estimation output from the function `fitSSM` from `KFAS`.
`SSMout`	The filtering and smoothing output from the function `KFS` from `KFAS`.
`parameters`	A data frame containing the estimated parameters, including standard errors, t-statistics, and p-values.
`parRestr`	A list of matrices containing the enforced parameter constraints.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`loglik`	Log-likelihood function values.
`AIC`	Akaike information criterion.
`BIC`	Bayesian information criterion.
`AIC`	Hannan-Quinn information criterion.
`RMSE`	root mean squared error of the Phillip's curve equation.
`R2`	R squared of the Phillip's curve equation.
`LjungBox`	Ljung-Box test output of the Phillip's curve equation.
`signal-to-noise`	Signal-to-noise ratio.

For bayesian estimation, an object of class NAWRUfit containing the following components:

`model`	The input object of class `NAWRUmodel`.
`tsl`	A list of time series containing the estimated states.
`parameters`	A data frame containing the estimated parameters, including standard errors, highest posterior density credible sets.
`prior`	A list of matrices containing the used prior distributions.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`R2`	R squared of the phillips curve equation,
`signal-to-noise`	Signal-to-noise ratio.

Examples

# define nawru model for France
data("gap")
country <- "France"
tsList <- amecoData2input(gap[[country]])
model <- NAWRUmodel(tsl = tsList)
# estimate nawru model via MLE
parRestr <- initializeRestr(model = model, type = "hp")

f <- fit(model = model, parRestr = parRestr)

# initialize priors and estimate model via Bayesian methods
prior <- initializePrior(model = model)

f <- fit(model = model, method = "bayesian", prior = prior, R = 5000, thin = 2)

[Package RGAP version 0.1.1 Index]

Estimation of a NAWRUmodel