| Title: | Weather Analysis and Markov Regime Switching Jump Diffusion Models |
| Version: | 0.1.1 |
| Description: | Provides statistical tools for analyzing weather patterns, temperature anomalies, and climate risk. Implements Markov regime-switching jump diffusion (MRJD) models to capture abrupt shifts, extreme weather events, and structural breaks in environmental time series data. Estimates model parameters using maximum likelihood estimation and offers utility functions for simulating regime-dependent stochastic processes. The regime-switching methodology is based on Hamilton (1989) "Analysis of Time Series Subject to Changes in Regime" <doi:10.2307/1912559>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| Imports: | stats |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| VignetteBuilder: | knitr |
| Config/roxygen2/version: | 8.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2026-08-19 16:35:46 UTC; Dr. O. J. Obulezi |
| Author: | Okechukwu J. Obulezi
 [aut, cre] |
| Maintainer: | Okechukwu J. Obulezi <oj.obulezi@unizik.edu.ng> |
| Repository: | CRAN |
| Date/Publication: | 2026-08-20 15:20:02 UTC |
Calibrate Dynamic SDE and Jump Parameters
Description
Estimates mean-reversion speed, unconditional volatility, and jump characteristics.
Usage
calibrate_mrjd(residuals, n_years, threshold_sigma = 2.5)
Arguments
residuals |
Numeric vector of detrended temperature residuals X(t). |
n_years |
Numeric scalar representing total observation period in years. |
threshold_sigma |
Threshold multiplier for jump identification (default: 2.5). |
Value
A named list of calibrated stochastic differential parameters.
Examples
set.seed(123)
res <- stats::rnorm(730, sd = 2)
calib <- calibrate_mrjd(res, n_years = 2)
print(calib$kappa)
Fit Fourier Seasonal Baseline Trend
Description
Fits a truncated Fourier series to daily atmospheric temperature observations.
Usage
fit_seasonal_trend(temp, day_of_year)
Arguments
temp |
Numeric vector of observed daily average temperatures. |
day_of_year |
Numeric vector of day-of-year indices (1 to 365/366). |
Value
A list containing the fitted OLS model, fitted values, and isolated residuals.
Examples
doy <- rep(1:365, times = 2)
temp <- 15 + 10 * sin(2 * pi * doy / 365) + stats::rnorm(730, sd = 2)
fit <- fit_seasonal_trend(temp, doy)
print(fit$rmse)
Price HDD and CDD Weather Derivatives
Description
Evaluates fair values and Monte Carlo standard errors for HDD and CDD Call Options.
Usage
price_weather_option(
temp_paths,
strike,
type = c("HDD", "CDD"),
r = 0.04,
base_temp = 18
)
Arguments
temp_paths |
Matrix of simulated temperature paths from simulate_weather_paths. |
strike |
Strike index level K. |
type |
Option contract type: "HDD" or "CDD". |
r |
Risk-free discount rate (default 0.04). |
base_temp |
Threshold index baseline (default 18.0 deg C). |
Value
A list containing estimated price, standard error, and index distribution metrics.
Examples
paths <- simulate_weather_paths(n_paths = 100, days = 90)
hdd_opt <- price_weather_option(paths, strike = 500, type = "HDD")
print(hdd_opt$price)
Simulate Temperature Paths via Non-Homogeneous Jump-Diffusion
Description
Generates discretized Monte Carlo sample trajectories of daily average temperatures.
Usage
simulate_weather_paths(
n_paths = 5000,
days = 365,
kappa = 0.08,
sigma_0 = 2.5,
lambda_0 = 0.05,
lambda_1 = 0.03,
mu_jump = -3,
sigma_jump = 1.5,
baseline_temp = 14.5,
amplitude_temp = 11.2
)
Arguments
n_paths |
Integer count of simulation paths. |
days |
Horizon length in days (default 365). |
kappa |
Mean-reversion speed. |
sigma_0 |
Baseline volatility. |
lambda_0 |
Baseline jump intensity. |
lambda_1 |
Amplitude of dynamic seasonal jump intensity. |
mu_jump |
Mean jump magnitude. |
sigma_jump |
Volatility of jump magnitude. |
baseline_temp |
Baseline temperature parameter A. |
amplitude_temp |
Seasonal temperature amplitude. |
Value
An (n_paths x days) matrix of simulated daily temperatures.
Examples
paths <- simulate_weather_paths(n_paths = 50, days = 30)
dim(paths)