dynlm (version 0.2-1)

dynlm: Dynamic Linear Models and Time-Series Regression

Description

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

Usage

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, ...)

Arguments

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)

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

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 b

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 dynlm are very similar to lm, but currently dynlm offers three advantages over the direct use of lm: 1. extended formula processing, 2. preservation of time-series attributes, 3. instrumental variables regression (via two-stage least squares).

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. For L(), it can also be vector-valued, e.g., y ~ L(y, 1:4). Furthermore, Furthermore, there is an additional function season(x, ref = NULL) which 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. See below for examples and M1Germany for a more elaborate application.

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 no internal NAs were created by the na.action).

To specify a set of insruments, formulas of type y ~ x1 + x2 + x3| z1 + z2 can be used where z1 and z2 represent the instruments. Again, the extended formula processing described above can be employed for all variables in the model.

See Also

zoo, merge.zoo

Examples

## 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))
dfm
## explicitely set start and end
dfm <- dynlm(uk ~ L(uk, 1) + L(uk, 12), start = c(1975, 1), end = c(1982, 12))
dfm

## 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)

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

## regression on multiple lags in a single L() call
dfm3 <- dynlm(uk ~ L(uk, c(1, 11, 12)), start = c(1975, 1), end = c(1982, 12))
anova(dfm, dfm3)

## Examples 7.11/7.12 from Greene (1993)
if(require("lmtest")) {
data("USDistLag")
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)
}