###########################
## Dynamic Linear Quantile Regression Models ##
###########################
## multiplicative median SARIMA(1,0,0)(1,0,0)_12 model fitted to UK seatbelt data
data("UKDriverDeaths", package = "datasets")
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
data("AirPassengers", package = "datasets")
ap <- log(AirPassengers)
ap_fm <- dynrq(ap ~ trend(ap) + season(ap))
summary(ap_fm)
## Alternative time trend specifications:
## time(ap) 1949 + (0, 1, ..., 143)/12
## trend(ap) (1, 2, ..., 144)/12
## trend(ap, scale = FALSE) (1, 2, ..., 144)
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