Created
September 24, 2017 12:39
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require(KFAS) # 1.2.9 | |
require(dplyr) | |
require(tidyr) | |
require(ggplot2) | |
# --- ARIMA(2, 1) with linear trend --- | |
# generate a dataset | |
set.seed(42) | |
t <- 100 | |
y <- arima.sim(n = t, model = list(ar=c(.3, -0.1), ma=.2), sd=.1) + seq(from=1, to=10, length.out = t) | |
plot(y) | |
# create model | |
model <- SSModel(y~ SSMtrend(2, Q=list(0, 0)) + SSMarima(ar=c(0, 0), ma=0, Q=NA), H=0) | |
# estimate unknown parameters | |
update.fn <- function(pars, model) { | |
model <- SSModel(y ~ SSMtrend(2, Q=list(0, 0)) + | |
SSMarima(ar =artransform(pars[1:2]), ma=pars[3], Q = exp(pars[4])), H = 0) | |
model$T["slope", "slope", 1] <- pars[5] | |
return(model) | |
} | |
fit.model <- fitSSM(model, inits=rep(.1, 5), updatefn = update.fn, method="SANN") | |
# check the result | |
print(paste("Converged: ", fit.model$optim.out$convergence == 0)) | |
print(paste("log likelihood:", round(-fit.model$optim.out$value, 3))) | |
fit.model$model$Z | |
fit.model$model$T | |
fit.model$model$R | |
fit.model$model$Q | |
fit.model$model$H | |
filter.model <- KFS(fit.model$model, smoothing = "mean") | |
# plot prediced values | |
pred <- predict(fit.model$model, n.ahead = 20, interval = "confidence", type="response", level=.95) | |
df <- data.frame(t=1:length(y), y=as.numeric(y)) | |
df <- bind_rows(df, data.frame(pred) %>% rename(y=fit) %>% mutate(t=time(pred))) # ignore warning | |
ggplot(filter(df, t>= 10)) + geom_line(aes(x=t, y=y), lwd=1) + | |
geom_ribbon(aes(x=t, ymin=lwr, ymax=upr), fill="blue", alpha=.2) |
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