Common Features of Timeseries and Regime Shift Testing

Detailing the Regime Shifts in Maine Coastal Current Behavior

{
  library(tidyverse)
  library(gmRi)
  library(patchwork)
  library(showtext)
  library(legendry)
}

# namespace conflicts
conflicted::conflict_prefer("select", "dplyr")
conflicted::conflict_prefer("filter", "dplyr")


# Set the theme
theme_set(
  theme_gmri() +
    theme(strip.text.y = element_text(angle = 0),
          legend.position = "bottom", 
          legend.title.position = "top", 
          legend.title = element_text(hjust = 0.5), 
          strip.text = element_text(size = 8),
          axis.text = element_text(size = 8)))

# Use GMRI style
use_gmri_style_rmd()

Reviewing STARS Regime Changes in Space/Time

Stationary Mean with Variation

The most basic timeseries is one where there is no change in the mean over time. Just a sequence of data that has some measurable variance. Timeseries of this form would not be expected to show any breakpoints when evaluated using breakpoint testing methods.

# Set seed for reproducibility
set.seed(123)

# Time settings
n_years <- 20
n <- n_years * 12  # monthly data
time <- seq(from = 1, to = n)
dates <- seq(from = as.Date("2000-01-01"), by = "1 month", length.out = n)

# 4. Periodicity (e.g., annual cycle + noise)
period <- 12  # one cycle per year

# Determine change point: 2/3 of the way through for changepoint example
change_point <- floor(n * 2 / 3)

# Means 1 & 2
mean1 <- 0
mean2 <- 3
sd1 <- 0.8

# 1. Stationary mean with some variance (white noise)
ts_types <- tibble(
  "date" = dates,
  "Stationary Mean+Variance" = rnorm(n, mean = mean1, sd = sd1),
  "Trends" = time * 0.025 + rnorm(n, mean = mean1, sd = sd1),
  "Seasonal Periods" = sin(2 * pi * time / 12) + rnorm(n, mean = mean1, sd = 0.3),
  "White-noise: phi = 0" = arima.sim(model = list(ar = 0), n = n),
  "Positive autocorrelation (red-noise): phi = 0 to 1" = arima.sim(model = list(ar = 0.7), n = n),
  #"random walk: phi = 1" = arima.sim(model = list(ar = 1), n = n),
  #"Explosive Process: phi > 1" = arima.sim(model = list(ar = 2), n = n),
  "Negative autocorrelation: phi  0 to -1" = arima.sim(model = list(ar = -.7), n = n),
  #"Perfect negative autocorrelation: phi= -1" = arima.sim(model = list(ar = -1), n = n),
  "Mean (Regime) Shifts" = c(
    rnorm(change_point, mean = mean1, sd = 1),
    rnorm(n - change_point, mean = mean2, sd = 1))) %>% 
  pivot_longer(cols = -date, names_to = "ts_type", values_to = "vals")

ts_types %>% 
  filter(str_detect(ts_type, "phi") == FALSE) %>% 
ggplot(aes(date, vals)) +
  geom_line(color = "gray20") +
  facet_wrap(~ts_type, ncol = 2, scales = "free") +
  labs(x = "Date", y = "Value")

ts_types %>% 
  filter(str_detect(ts_type, "phi") == FALSE,
         str_detect(ts_type, "Stationary") == FALSE) %>% 
ggplot(aes(date, vals)) +
  geom_line(color = "gray20") +
  facet_wrap(~ts_type, ncol = 1, scales = "free") +
  labs(x = "Date", y = "Value")

ts_types %>% 
  filter(str_detect(ts_type, "phi") == TRUE) %>% 
  mutate(ts_type = factor(ts_type, levels = c(
    "Positive autocorrelation (red-noise): phi = 0 to 1",
    "White-noise: phi = 0",
    "Negative autocorrelation: phi  0 to -1"))) %>% 
  ggplot(aes(date, vals)) +
  geom_line(color = "gray20") +
  facet_wrap(~ts_type, ncol = 1, scales = "free") +
  labs(x = "Date", y = "Value")