quantreg (version 5.98)

dynrq: Dynamic Linear Quantile Regression

Description

Interface to rq.fit and rq.wfit for fitting dynamic linear quantile regression models. The interface is based very closely on Achim Zeileis's dynlm package. In effect, this is mainly ``syntactic sugar'' for formula processing, but one should never underestimate the value of good, natural sweeteners.

Usage

dynrq(formula, tau = 0.5, data, subset, weights, na.action, method = "br",
  contrasts = NULL, start = NULL, end = NULL, ...)

Arguments

formula

a "formula" describing the linear model to be fit. For details see below and rq.

tau

the quantile(s) to be estimated, may be vector valued, but all all values must be in (0,1).

data

an optional "data.frame" or time series object (e.g., "ts" or "zoo"), containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which rq is called.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. If specified, weighted least squares is used with weights weights (that is, minimizing sum(w*e^2)); otherwise ordinary least squares is used.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The “factory-fresh” default is na.omit. Another possible value is NULL, no action. Note, that for time series regression special methods like na.contiguous, na.locf and na.approx are available.

method

the method to be used; for fitting, by default method = "br" is used; method = "fn" employs the interior point (Frisch-Newton) algorithm. The latter is advantageous for problems with sample sizes larger than about 5,000.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

start

start of the time period which should be used for fitting the model.

end

end of the time period which should be used for fitting the model.

...

additional arguments to be passed to the low level regression fitting functions.

Details

The interface and internals of dynrq are very similar to rq, but currently dynrq offers two advantages over the direct use of rq for time series applications of quantile regression: extended formula processing, and preservation of time series attributes. Both features have been shamelessly lifted from Achim Zeileis's package dynlm.

For specifying the formula of the model to be fitted, there are several functions available which allow for convenient specification of dynamics (via d() and L()) or linear/cyclical patterns (via trend(), season(), and harmon()). These new formula functions require that their arguments are time series objects (i.e., "ts" or "zoo").

Dynamic models: An example would be d(y) ~ L(y, 2), where d(x, k) is diff(x, lag = k) and L(x, k) is lag(x, lag = -k), note the difference in sign. The default for k is in both cases 1. For L(), it can also be vector-valued, e.g., y ~ L(y, 1:4).

Trends: y ~ trend(y) specifies a linear time trend where (1:n)/freq is used by default as the covariate, n is the number of observations and freq is the frequency of the series (if any, otherwise freq = 1). Alternatively, trend(y, scale = FALSE) would employ 1:n and time(y) would employ the original time index.

Seasonal/cyclical patterns: Seasonal patterns can be specified via season(x, ref = NULL) and harmonic patterns via harmon(x, order = 1). season(x, ref = NULL) creates a factor with levels for each cycle of the season. Using the ref argument, the reference level can be changed from the default first level to any other. harmon(x, order = 1) creates a matrix of regressors corresponding to cos(2 * o * pi * time(x)) and sin(2 * o * pi * time(x)) where o is chosen from 1:order.

See below for examples.

Another aim of dynrq is to preserve time series properties of the data. Explicit support is currently available for "ts" and "zoo" series. Internally, the data is kept as a "zoo" series and coerced back to "ts" if the original dependent variable was of that class (and no internal NAs were created by the na.action).

See Also

zoo, merge.zoo

Examples

###########################
## Dynamic Linear Quantile Regression Models ##
###########################

if(require(zoo)){
## multiplicative median SARIMA(1,0,0)(1,0,0)_12 model fitted to UK seatbelt data
     uk <- log10(UKDriverDeaths)
     dfm <- dynrq(uk ~ L(uk, 1) + L(uk, 12))
     dfm

     dfm3 <- dynrq(uk ~ L(uk, 1) + L(uk, 12),tau = 1:3/4)
     summary(dfm3)
 ## explicitly set start and end
     dfm1 <- dynrq(uk ~ L(uk, 1) + L(uk, 12), start = c(1975, 1), end = c(1982, 12))
 ## remove lag 12
     dfm0 <- update(dfm1, . ~ . - L(uk, 12))
     tuk1  <- anova(dfm0, dfm1)
 ## add seasonal term
     dfm1 <- dynrq(uk ~ 1, start = c(1975, 1), end = c(1982, 12))
     dfm2 <- dynrq(uk ~ season(uk), start = c(1975, 1), end = c(1982, 12))
     tuk2 <- anova(dfm1, dfm2)
 ## regression on multiple lags in a single L() call
     dfm3 <- dynrq(uk ~ L(uk, c(1, 11, 12)), start = c(1975, 1), end = c(1982, 12))
     anova(dfm1, dfm3)
}

###############################
## Time Series Decomposition ##
###############################

## airline data
if (FALSE) {
ap <- log(AirPassengers)
fm <- dynrq(ap ~ trend(ap) + season(ap), tau = 1:4/5)
sfm <- summary(fm)
plot(sfm)
}

## Alternative time trend specifications:
##   time(ap)                  1949 + (0, 1, ..., 143)/12
##   trend(ap)                 (1, 2, ..., 144)/12
##   trend(ap, scale = FALSE)  (1, 2, ..., 144)

###############################
## An Edgeworth (1886) Problem##
###############################
# DGP
if (FALSE) {
fye <- function(n, m = 20){
    a <- rep(0,n)
    s <- sample(0:9, m, replace = TRUE)
    a[1] <- sum(s)
    for(i in 2:n){
       s[sample(1:20,1)] <- sample(0:9,1)
       a[i] <- sum(s)
    }
    zoo::zoo(a)
}
x <- fye(1000)
f <- dynrq(x ~ L(x,1))
plot(x,cex = .5, col = "red")
lines(fitted(f), col = "blue")
}