# Vygenerovani jedne trajektorie

X0 <- 100
dt <- 1/252
r <- 0.55
sigma <- 0.3
t <- seq (0, 4, by=dt)

X <- generuj.gBp (t, dt, X0, r, sigma)

plot (t, X, type="l", col="red", xlab="t", ylab="geometricky Brownuv pohyb")
abline (h = X0 , lty = 2)

# =============================================================================
# vynosy a jejich charakteristiky vhodne pro odhady parametru

n <- length (X)
R <- log (X[2:n] / X[1:(n-1)])

plot (t[1:(n-1)], R, type="l", col="red", xlab="t", ylab="log-returns")
abline (h = 0 , lty = 2)

hist (R, freq = FALSE)
acf (R)

mean (R)
sd (R)

library (fBasics)
skewness (R, method = "moment")
kurtosis (R, method = "moment")

# =============================================================================