Estimate an autoregressive logit model with covariates

Estimate a dynamic Autoregressive (AR) logit model with covariates ('X') by maximising the logit likelihood.

Usage

logitx(y, intercept = TRUE, ar = NULL, ewma = NULL, xreg = NULL, 
    vcov.type = c("ordinary", "robust"), lag.length = NULL, 
    initial.values = NULL, lower = -Inf, upper = Inf, control = list(), 
    eps.tol = .Machine$double.eps, solve.tol = .Machine$double.eps,
    singular.ok = TRUE, plot = NULL)

dlogitx(y, ...)

Arguments

y: a binary numeric vector, time-series or zoo object. Missing values in the beginning and at the end of the series is allowed, as they are removed with the na.trim command
intercept: logical. TRUE, the default, includes an intercept in the logit specification, whereas FALSE does not
ar: either NULL (default) or an integer vector, say, c(2,4) or 1:4. The AR-lags to include in the logit specification. If NULL, then no lags are included
ewma: either NULL (default) or a list with arguments sent to the eqwma function. In the latter case a lagged moving average of y is included as a regressor
xreg: either NULL (default) or a numeric vector or matrix, say, a zoo object, of covariates. Note that, if both y and xreg are zoo objects, then their samples are chosen to match
vcov.type: character vector of length 1, either "ordinary" (default) or "robust". Partial matching is allowed. If "ordinary", then the ordinary variance-covariance matrix is used for inference. If "robust", then a robust coefficient-covariance of the Newey and West (1987) type is used
lag.length: NULL or an integer that determines the lag-length used in the robust coefficient covariance. If lag.length is an integer, then it is ignored unless method = 3
initial.values: NULL or a numeric vector with the initial parameter values passed on to the optimisation routine, nlminb. If NULL, the default, then the values are chosen automatically
lower: numeric vector, either of length 1 or the number of parameters to be estimated, see nlminb
upper: numeric vector, either of length 1 or the number of parameters to be estimated, see nlminb
control: a list passed on to the control argument of nlminb
eps.tol: numeric, a small value that ensures the fitted zero-probabilities are not too small when the log-transformation is applied when computing the log-likelihood
solve.tol: numeric value passed on to the tol argument of solve, which is called whenever the coefficient-coariance matrix is computed. The value controls the toleranse for detecting linear dependence between columns when inverting a matrix
singular.ok: logical. If TRUE (default), then the regressors causing the singularity are dropped (using dropvar) before estimation. If FALSE, singularity returns error
plot: NULL or logical. If TRUE, then a plot is produced. If NULL (default), then the value set by options determines whether a plot is produced or not.
...: arguments passed on to logitx

Details

The function estimates a dynamic Autoregressive (AR) logit model with (optionally) covariates ('X') by maximising the logit likelihood. The estimated model is an augmented version of the model considered by Kauppi and Saikkonen (2008). Also, they considered estimation is by maximisation of the probit likelihood. Here, by contrast, estimation is by maximisation of the logit likelihood.

Value

A list of class 'logitx'.

References

Heikki Kauppi and Pentti Saikkonen (2008): 'Predicting U.S. Recessions with Dynamic Binary Response Models'. The Review of Economics and Statistics 90, pp. 777-791

Whitney K. Newey and Kenned D. West (1987): 'A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix', Econometrica 55, pp. 703-708

Author

Genaro Sucarrat, http://www.sucarrat.net/

Examples


##simulate from ar(1):
set.seed(123) #for reproducibility
y <- logitxSim(100, ar=0.3)

##estimate ar(1) and store result:
mymod <- logitx(y, ar=1)

##estimate ar(4) and store result:
mymod <- logitx(y, ar=1:4)

##create some more data, estimate new model:
x <- matrix(rnorm(5*100), 100, 5)
mymod <- logitx(y, ar=1:4, xreg=x)