Nothing
## ----setup, include = FALSE----------------------------------------------
knitr::opts_chunk$set(
warning = F,
message = F,
collapse = TRUE,
comment = "#>"
)
## ----sim-----------------------------------------------------------------
library(kendallRandomWalks)
library(dplyr)
library(ggplot2)
set.seed(17)
walks <- simulate_kendall_rw(1000, 1000, rnorm, 0.5, T)
walks2 <- simulate_kendall_rw(1000, 1000, rcauchy, 0.5, T)
## ----ex1-----------------------------------------------------------------
plot(walks, max_id = 1)
plot(walks2, max_id = 1)
## ----unique--------------------------------------------------------------
ggplot(summarise_kendall_rw(walks, n_distinct), aes(x = aggregated), color = "black") +
theme_bw() +
geom_density() +
geom_density(data = summarise_kendall_rw(walks2, n_distinct), color = "blue") +
ylab("Estimated density") +
xlab("Number of unique values") +
scale_color_discrete(guide = "legend")
## ----jumps---------------------------------------------------------------
diffs <- mutate_kendall_rw(walks, function(x) x - lag(x), F)
plot(diffs, max_id = 1)
diffs2 <- mutate_kendall_rw(walks2, function(x) x - lag(x), F)
plot(diffs2, max_id = 1)
## ----skoki_dlugosc-------------------------------------------------------
diffs3 <- mutate_kendall_rw(diffs, function(x) as.numeric(x != 0), F)
lengths <- diffs3$simulation %>%
group_by(sim_id) %>%
mutate(id = 1:n()) %>%
filter(sim != 0) %>%
mutate(previous = ifelse(is.na(lag(id)), 0, lag(id))) %>%
mutate(length = id - previous)
diffs4 <- mutate_kendall_rw(diffs2, function(x) as.numeric(x != 0), F)
lengths2 <- diffs4$simulation %>%
group_by(sim_id) %>%
mutate(id = 1:n()) %>%
filter(sim != 0) %>%
mutate(previous = ifelse(is.na(lag(id)), 0, lag(id))) %>%
mutate(length = id - previous)
ggplot(subset(lengths, sim_id < 5),
aes(x = length, fill = as.factor(sim_id), group = as.factor(sim_id))) +
geom_density() +
theme_bw() +
ggtitle("Distribution of time with no state-change (by simulation)")
ggplot(lengths, aes(x = length)) +
geom_density() +
theme_bw() +
xlab("Jump size") +
ggtitle("Distribution of time with no state-change (aggregated)")
ggplot(lengths2, aes(x = length)) +
geom_density() +
theme_bw() +
xlab("Jump size") +
ggtitle("Distribution of time with no state-change (aggregated)")
ggplot(subset(lengths, sim_id < 10), aes(x = id, y = length, color = as.factor(sim_id))) +
geom_point() +
theme_bw() +
geom_line() +
guides(color = "none") +
xlab("Time") +
ylab("Jump size") +
ggtitle("Time with no state-change in time")
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