plot.fkf: Plotting fkf Objects
In FKF: Fast Kalman Filter

Description Usage Arguments Details Value Author(s) See Also Examples

Plotting method for objects of class fkf. This function provides tools for graphical analysis of the Kalman filter output: Visualization of the state vector, QQ-plot of the individual residuals, QQ-plot of the Mahalanobis distance, auto- as well as crosscorrelation function of the residuals.

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## S3 method for class 'fkf'
plot(x, type = c("state", "resid.qq", "qqchisq", "acf"),
     CI = 0.95, at.idx = 1:nrow(x$at), att.idx = 1:nrow(x$att), ...)

`x`	The output of `fkf`.
`type`	A string stating what shall be plotted (see Details).
`CI`	The confidence interval in case `type == "state"`. Set `CI` to `NA` if no confidence interval shall be plotted.
`at.idx`	An vector giving the indexes of the predicted state variables which shall be plotted if `type == "state"`.
`att.idx`	An vector giving the indexes of the filtered state variables which shall be plotted if `type == "state"`.
`...`	Arguments passed to either `plot`, `qqnorm`, `qqplot` or `acf`.

The argument type states what shall be plotted. type must partially match one of the following:

state: The state variables are plotted. By the arguments at.idx and att.idx, the user can specify which of the predicted (at) and filtered (att) state variables will be drawn.
resid.qq: Draws a QQ-plot for each residual-series invt.
qqchisq: A Chi-Squared QQ-plot will be drawn to graphically test for multivariate normality of the residuals based on the Mahalanobis distance.
acf: Creates a pairs plot with the autocorrelation function (acf) on the diagonal panels and the crosscorrelation function (ccf) of the residuals on the off-diagnoal panels.

Invisibly returns an list with components:

`distance`	The Mahalanobis distance of the residuals as a vector of length n.
`std.resid`	The standardized residuals as an d n-matrix. It should hold that std.resid[i,j] iid N_d(0, I)*,

where d denotes the dimension of the data and n the number of observations.

David Luethi, Philipp Erb, Simon Otziger

fkf

## Local level model for the treering width data.
## Transition equation:
## alpha[t+1] = alpha[t] + eta[t], eta[t] ~ N(0, HHt)          
## Measurement equation:
## y[t] = alpha[t] + eps[t], eps[t] ~  N(0, GGt)

y <- treering
y[c(3, 10)] <- NA  # NA values can be handled

## Set constant parameters:
dt <- ct <- matrix(0) 
Zt <- Tt <- matrix(1)
a0 <- y[1]            # Estimation of the first width
P0 <- matrix(100)     # Variance of 'a0'

## Estimate parameters:
fit.fkf <- optim(c(HHt = var(y, na.rm = TRUE) * .5,
                   GGt = var(y, na.rm = TRUE) * .5),
                 fn = function(par, ...)
                 -fkf(HHt = matrix(par[1]), GGt = matrix(par[2]), ...)$logLik,
                 yt = rbind(y), a0 = a0, P0 = P0, dt = dt, ct = ct,
                 Zt = Zt, Tt = Tt, check.input = FALSE)

## Filter Nile data with estimated parameters:
fkf.obj <- fkf(a0, P0, dt, ct, Tt, Zt, HHt = matrix(fit.fkf$par[1]),
               GGt = matrix(fit.fkf$par[2]), yt = rbind(y))

## Plot the width together with fitted local levels:
plot(y, main = "Treering data")
lines(ts(fkf.obj$att[1, ], start = start(y), frequency = frequency(y)), col = "blue")
legend("top", c("Treering data", "Local level"), col = c("black", "blue"), lty = 1)

## Check the residuals for normality:
plot(fkf.obj, type = "resid.qq")

## Test for autocorrelation:
plot(fkf.obj, type = "acf", na.action = na.pass)