dynlm {dynlm}R Documentation

Dynamic Linear Models and Time-Series Regression


Interface to lm.wfit for fitting dynamic linear models and time-series regression relationships.


dynlm(formula, data, subset, weights, na.action, method = "qr",
  model = TRUE, x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE,
  contrasts = NULL, offset, start = NULL, end = NULL, ...)


formula a "formula" describing the linear model to be fit. For details see below and lm.
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 lm 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, currently only method = "qr" is supported; method = "model.frame" returns the model frame (the same as with model = TRUE, see below).
model, x, y, qr logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response, the QR decomposition) are returned.
singular.ok logical. If FALSE (the default in S but not in R) a singular fit is an error.
contrasts an optional list. See the contrasts.arg of model.matrix.default.
offset this can be used to specify an a priori known component to be included in the linear predictor during fitting. An offset term can be included in the formula instead or as well, and if both are specified their sum is used.
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.


The interface and internals of dynlm are very similar to lm, but currently dynlm offers two advantages over the direct use of lm: 1. extended formula processing, 2. preservation of time-series attributes.

For specifying the formula of the model to be fitted, there are additional functions available which facilitate the specification of 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.

The specification of dynamic relationships only makes sense if there is an underlying ordering of the observations. Currently, lm offers only limited support for such data, hence a major aim of dynlm 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 not internal NAs were created by the na.action).

See Also

zoo, merge.zoo


## multiplicative SARIMA(1,0,0)(1,0,0)_12 model fitted
## to UK seatbelt data
uk <- log10(UKDriverDeaths)
dfm <- dynlm(uk ~ L(uk, 1) + L(uk, 12))
## explicitely set start and end
dfm <- dynlm(uk ~ L(uk, 1) + L(uk, 12), start = c(1975, 1), end = c(1982, 12))

## remove lag 12
dfm0 <- update(dfm, . ~ . - L(uk, 12))
anova(dfm0, dfm)

## add season term
dfm1 <- dynlm(uk ~ 1, start = c(1975, 1), end = c(1982, 12))
dfm2 <- dynlm(uk ~ season(uk), start = c(1975, 1), end = c(1982, 12))
anova(dfm1, dfm2)

lines(fitted(dfm0), col = 2)
lines(fitted(dfm2), col = 4)

## Examples 7.11/7.12 from Greene (1993)
if(require(lmtest)) {
dfm1 <- dynlm(consumption ~ gnp + L(consumption), data = USDistLag)
dfm2 <- dynlm(consumption ~ gnp + L(gnp), data = USDistLag)
plot(USDistLag[, "consumption"])
lines(fitted(dfm1), col = 2)
lines(fitted(dfm2), col = 4)
encomptest(dfm1, dfm2)

[Package dynlm version 0.1-1 Index]