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[1] "^VIX"

fitvix <- StructTS(vix, "level")
fitvix

Call:
StructTS(x = vix, type = "level")

Variances:
  level  epsilon  
  2.809    1.564  

StructTS(x = vix, type = "level")

Call:
StructTS(x = vix, type = "level")

Variances:
  level  epsilon  
  2.809    1.564  

plot(vix, col = "blue")
lines(fitted(fitvix), lty ="dashed", lwd =2)

lines(tsSmooth(fitvix),lty = "dotted", lwd =2)

plot(forecast(fitvix))

# rearranged not reason for kalman est unfit ie. forecast command

#lines(kalman_est, lty = "dotted", ,lwd = 2, col = "yellow")
# the kalman est fit did not run, syntax or logic error, for reader to pursue, kalman fit below.

# an ARIMA fit
fit3 <- arima(vix, c(1, 1, 0))
predict(fit3, 12)

$pred
Time Series:
Start = 2021.36828956105 
End = 2021.39840653812 
Frequency = 365.2425 
 [1] 20.15919 19.73782 19.86942 19.82832 19.84115 19.83715 19.83840 19.83801
 [9] 19.83813 19.83809 19.83810 19.83810

$se
Time Series:
Start = 2021.36828956105 
End = 2021.39840653812 
Frequency = 365.2425 
 [1] 2.327088 2.824240 3.363826 3.794770 4.190882 4.549962 4.883490 5.195422
 [9] 5.489725 5.769014 6.035399 6.290512

## reconstruct this
pr <- KalmanForecast(12, fit3$model)
pr$pred + fit3$coef[4]

 [1] NA NA NA NA NA NA NA NA NA NA NA NA

sqrt(pr$var * fit3$sigma2)

 [1] 2.327088 2.824240 3.363826 3.794770 4.190882 4.549962 4.883490 5.195422
 [9] 5.489725 5.769014 6.035399 6.290512

## and now do it year by year
mod <- fit3$model
for(y in 1:3) {
  pr <- KalmanForecast(4, mod, TRUE)
  print(list(pred = pr$pred + fit3$coef["intercept"],
             se = sqrt(pr$var * fit3$sigma2)))
  mod <- attr(pr, "mod")
}

$pred
[1] NA NA NA NA

$se
[1] 2.327088 2.824240 3.363826 3.794770

$pred
[1] NA NA NA NA

$se
[1] 4.190882 4.549962 4.883490 5.195422

$pred
[1] NA NA NA NA

$se
[1] 5.489725 5.769014 6.035399 6.290512

fit_kalman <- KalmanLike(vix, mod, nit = 0L, update = FALSE)
out <- KalmanSmooth(vix, mod, nit = 0L)
kalman_est <- out$smooth[ ,2]
plot.ts(vix)

plot(kalman_est, lty = "dashed", lwd = 2,col = "green")

vix <-  ts_timeSeries(vix)
histPlot(vix)