# R function for Dynamic Ordinary Least Squares regression

SHORT VERSION: Made a workflow function, want a better output with methods.

General Background

I have been working on a package for some time to eliminate the tedium of preliminary time series econometrics (unit root testing, cointegration, model building and lag/lead selection). I am aware of many alternatives out there but I am still happy with the direction I am going for now. Based off of Stock & Watson.

Function Workflow (simple version)

1. Takes a user-specified cointegrating relationship (written as a formula): $$Y_t = \alpha_t + X_t$$ in R: Y ~ 1 + X where the dependent and independent variables are all nonstationary and alpha is the (optional) constant.

2. Creates the formula $$Y_t = \alpha_t + X_t + \sum_{i = -k}^k \Delta X_{t-i}$$ in R: Y ~ 1 + X + L(diff(X),-k:k) using dynlm's handy L() capabilities (although I do not use D() for diff(). Where k is the maximum lag/lead value.

3. The rest of the function runs different k values and selects the best model using the BIC function (but any model selection function can be put in as an argument). It also computes HAC estimated errors using Newey West.

Code Here is the function. I am very open to criticism/critiques/comments.

Requires packages:

library(dynlm)
library(lmtest)
library(sandwich)

buildDOLS <- function (coint_formula, data, fixedk = NULL, robusterrors = TRUE, selection = BIC){
# checks
stopifnot(is.ts(data)) # time series data
stopifnot(is.null(fixedk)|is.numeric(fixedk)) # fixed k either is null or is numeric
stopifnot(is.function(selection)) # selection method is a function (should work on a function)
#  Formula creation
ff <- coint_formula
all_names <- dimnames(attr(terms(ff), "factors")) # X and Y variables
y_names <- all_names[[1]][!(all_names[[1]] %in% all_names[[2]])]
x_names <- all_names[[2]][all_names[[2]] %in% colnames(data)]
# Dynamic Ordinary Least Squares formulation
ff_LHS <- y_names
ff_RHS <- paste(c(ifelse(attr(terms(ff), "intercept") == 1, "1", "-1"), # constant
x_names, # input variables
paste0("L(diff(", x_names, "),-k:k)")), # sum of lead/lagged differences of x variables
collapse=" + ")
ff_k <- paste(ff_LHS, "~", ff_RHS)
# if k (the maximum number of lags/leads) was not fixed, use a default value
k <- ifelse(is.null(fixedk), floor(dim(data)[1]^(1/3)/2), fixedk)
# run the model. If k was fixed, this is the final model:
DOLS_k <- dynlm(formula(ff_k), data = data)
# If k was not fixed, DOLS_k will be used to keep constant the start and end dates during model selection
if(is.null(fixedk)){
# Use any selection function that is indicated in the selection argument
k_select <- sapply(1:k, function(k) match.fun(FUN = selection)(dynlm(formula(ff_k),
data = data,
start = start(DOLS_k),
end = end(DOLS_k))))
# only re-estimate the model if k_select differs from k to be efficient
if(k != which.min(k_select)){
k <- which.min(k_select)
DOLS_k <- dynlm(formula(ff_k), data = data)
}
# save the selection matrix results inside the model
DOLS_k$selection <- cbind(1:k, k_select, DOLS_k$df + length(DOLS_k$coeff), start(DOLS_k)[1], end(DOLS_k)[1]) colnames(DOLS_k$selection) <- c("# of lags/leads (k)", deparse(substitute(selection)),"#Obs",
"StartDate", "EndDate")
}
DOLS_k$k <- k # save the lag used inside the model # save the HAC estimated errors inside the model if(robusterrors) DOLS_k$HAC <- lmtest::coeftest(DOLS_k, vcov = sandwich::NeweyWest(DOLS_k, lag = k))
# rewriting the call function to be a run on its own
DOLS_k$call <- as.call(c(quote(dynlm), formula = formula(gsub("-k:k", paste0("-",k,":",k), ff_k)), data = substitute(data))) class(DOLS_k) <- append(class(DOLS_k), "workflow") DOLS_k }  Example Case Say we have the cointegrating relationship: MB ~ RTPS from lmtest::valueofstocks. (The interpretation is not important here). dols <- buildDOLS(coint_formula = MB ~ RTPS, data = valueofstocks, fixedk = NULL, robusterrors = T, selection = BIC) dols summary(dols) # the Non-HAC, biased standard errors but model fit results dols$selection # shows the model selection process
dols$k # the result of that process dols$call # a stand-alone call function to replicate results with dynlm
dols$HAC # the HAC estimated standard errors/significance values  Output The output is not ideal as it is hidden within the model. I have written a few methods but would like some feedback. Does it clearly show what is interesting to the user? Is it too long? etc. Print Method Shows model selection and a cleaner eval print.workflow <- function(x) { if(!is.null(x$selection)){
cat("\n    Selecting k for Model\n")
cat("______________________________\n")
print(x$selection) } cat("\n Model with k =",x$k,"\n")
cat("______________________________")
print(eval(x$call)) } dols #** Is it too long? Does it give the important information?  Summary Method Shows HAC estimated errors automatically summary.workflow <- function(x, ...){ if("HAC" %in% names(x)){ # if the function has a robusterrors arg addHAC <- NextMethod(x) # alter the summary coeffs addHAC$coefficients <- x$HAC cat("*Summary table depicts HAC estimated errors found by:\n") cat(paste0("lmtest::coeftest(model, vcov = sandwich::NeweyWest(model, lag = ",x$k,"))\n"))
} else {
warning("\tSummary table does not depict HAC estimated errors\n\tPlease indicate the buildDOLS robusterrors argument to be TRUE")
print(NextMethod(x))
}
}
summary(dols)


Please let me know what you think!

The choice of k, half the cube root, is not obvious. Please cite http://www.ssc.wisc.edu/~kwest/publications/1990/ Automatic Lag Selection eqn. 2.1 (though I still found \gamma hat & parameter a bit mysterious).