baogorek

library(splines)

exp_decay <- function(t, tau) {
  exp(-t / tau)
}

get_true_phi <- function(t) {
  0.07 * exp_decay(t, 60) - 0.27 * exp_decay(t, 13)
}
days_grid <- 1:259

baogorek

library(splines)
my_spline <- ns(1:259, Boundary.knots = c(1, 259), knots = c(14, 40, 100))

z_vars <- list()
for (n in 1:nrow(train_df)) {
  spline_pred  <- predict(my_spline, newx = (n - 1):1)
  spline_vars  <- colSums(spline_pred * train_df$w[1:(n - 1)]) # convolution
  spline_const <- sum(train_df$w[1:(n - 1)])
  z_vars[[n]]  <- c(spline_const, spline_vars)
}

baogorek

get_eta_hat <- function(t_seq) {
  spline_vars_grid <- predict(my_spline, newx = t_seq)
  spline_vars_grid <- cbind(1, spline_vars_grid)
  eta_hat <- spline_vars_grid %*% coef(spline_reg)[-1]
  as.numeric(eta_hat)
}

convolve_with_fn <- function(training, n, impulse_fn) {
  sum(training[1:(n - 1)] * impulse_fn((n - 1):1))
}

baogorek

library(ggplot2)

# Figure 1
plot_df <- rbind(
  data.frame(day = days_grid, level = phi, type = "true \u03D5(t)"),
  data.frame(day = days_grid, level = eta_star, type = "best fit \u03B7*(t)")
)

ggplot(plot_df, aes(x = day, y = level, color = type, linetype = type)) +
  geom_line(size = 2) +

baogorek

get_perf_params <- function(world_record_perf, able_bodied_perf, limit,
                             type = "running") {
  # sum of squares around fixed point
  rss <- function(a, b, world_record_perf, able_bodied_perf, limit) {
    (1000 - b * log(a / (world_record_perf - limit))) ** 2 +
    (0    - b * log(a / (able_bodied_perf - limit))) ** 2
  }

  stopifnot(type %in% c("running", "jumping"))
  a_starting <- ifelse(type == "running", 5, -5)

baogorek

library(ggplot2)

# Files are at ...
folder_path <- "c:/devl/swimming" # Update accordingly

perf_params <- get_perf_params(world_record_perf = 1.8,
                               able_bodied_perf = 0.5, limit = 2.0,
                               type = "jumping")

get_perf_in_cp <- function(perf, a, b, limit) {

baogorek

library(dplyr)
library(gridExtra)
library(ggplot2)

exp_decay <- function(t, tau) {
    exp(-t / tau)
}

convolve_training<- function(training, n, tau) {
   sum(training[1:(n - 1)] * exp_decay((n - 1):1, tau))

baogorek

library(dplyr)
library(ggplot2)
library(splines)

days_grid <- 0:180
interior_knots <- c(2, 6, 25)
#interior_knots <- c(6, 25, 80)

my_spline <- ns(days_grid, knots = interior_knots)

baogorek

baogorek

N <- 10000
theta <- 1.4

e <- rnorm(N)

e_lag <- c(NA, e[1:(N-1)])

y <- e - theta * e_lag

acf(y[2:N])