Read Topix Data 2021/1/4-2026/5/29

library(readr)
topix <- read_csv("topix.csv")
## Rows: 1320 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): date
## dbl (1): close
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
topix$price <- as.numeric(topix$close)
topix$Date  <- as.Date(topix$date)
n <- length(topix$price)

return <- 100 * diff(log(topix$price))
mydate <- topix$Date[2:n]
n <- n-1

Draw time series plot of TOPIX returns

topix.df <-data.frame(dates = mydate, value = return) 
library(ggplot2)
ggplot(topix.df, aes(x = mydate, y = return)) +
  geom_line(linewidth = 0.4) +
  geom_hline(yintercept = 0, linetype = "dashed", linewidth = 0.5) +
  geom_hline(yintercept = c(2, -2), linetype = "dotted", linewidth = 0.7) +
  labs(title = "TOPIX Daily Log Returns", 
       subtitle = "Dotted lines indicate ±2%",
       x = "Date", y = "Log return (%)") + 
  scale_x_date(date_breaks = "1 year", date_labels = "%Y")

Fit GJR-GARCH(1,1) model using rstan

library(rstan)
## Loading required package: StanHeaders
## 
## rstan version 2.32.7 (Stan version 2.32.2)
## For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores()).
## To avoid recompilation of unchanged Stan programs, we recommend calling
## rstan_options(auto_write = TRUE)
## For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,
## change `threads_per_chain` option:
## rstan_options(threads_per_chain = 1)
## Do not specify '-march=native' in 'LOCAL_CPPFLAGS' or a Makevars file
library(rstudioapi)
mydata <- list( n = n, y = return);

myinit <- function() { 
  list( omega = 0.1, alpha = 0.1, beta = 0.1, mu = 0.0, gamma = 0.1)
}
fit  <- stan(file = 'gjr-garch.stan', data = mydata, init = myinit,
             chains = 4, warmup = 1000, iter = 11000, thin=10, cores = parallel::detectCores())
## WARNING: Rtools is required to build R packages, but is not currently installed.
## 
## Please download and install the appropriate version of Rtools for 4.6.0 from
## https://cran.r-project.org/bin/windows/Rtools/.
## Trying to compile a simple C file
## Running "C:/PROGRA~1/R/R-46~1.0/bin/x64/Rcmd.exe" SHLIB foo.c
## using C compiler: 'gcc.exe (GCC) 14.2.0'
## gcc  -I"C:/PROGRA~1/R/R-46~1.0/include" -DNDEBUG   -I"C:/Users/omori/AppData/Local/R/win-library/4.6/Rcpp/include/"  -I"C:/Users/omori/AppData/Local/R/win-library/4.6/RcppEigen/include/"  -I"C:/Users/omori/AppData/Local/R/win-library/4.6/RcppEigen/include/unsupported"  -I"C:/Users/omori/AppData/Local/R/win-library/4.6/BH/include" -I"C:/Users/omori/AppData/Local/R/win-library/4.6/StanHeaders/include/src/"  -I"C:/Users/omori/AppData/Local/R/win-library/4.6/StanHeaders/include/"  -I"C:/Users/omori/AppData/Local/R/win-library/4.6/RcppParallel/include/" -DRCPP_PARALLEL_USE_TBB=1 -I"C:/Users/omori/AppData/Local/R/win-library/4.6/rstan/include" -DEIGEN_NO_DEBUG  -DBOOST_DISABLE_ASSERTS  -DBOOST_PENDING_INTEGER_LOG2_HPP  -DSTAN_THREADS  -DUSE_STANC3 -DSTRICT_R_HEADERS  -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION  -D_HAS_AUTO_PTR_ETC=0  -include "C:/Users/omori/AppData/Local/R/win-library/4.6/StanHeaders/include/stan/math/prim/fun/Eigen.hpp"  -std=c++1y    -I"C:/rtools45/x86_64-w64-mingw32.static.posix/include"      -O2 -Wall -std=gnu2x  -mfpmath=sse -msse2 -mstackrealign   -c foo.c -o foo.o
## cc1.exe: warning: command-line option '-std=c++14' is valid for C++/ObjC++ but not for C
## In file included from C:/Users/omori/AppData/Local/R/win-library/4.6/RcppEigen/include/Eigen/Core:19,
##                  from C:/Users/omori/AppData/Local/R/win-library/4.6/RcppEigen/include/Eigen/Dense:1,
##                  from C:/Users/omori/AppData/Local/R/win-library/4.6/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22,
##                  from <command-line>:
## C:/Users/omori/AppData/Local/R/win-library/4.6/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: cmath: No such file or directory
##   679 | #include <cmath>
##       |          ^~~~~~~
## compilation terminated.
## make: *** [C:/PROGRA~1/R/R-46~1.0/etc/x64/Makeconf:297: foo.o] Error 1
## WARNING: Rtools is required to build R packages, but is not currently installed.
## 
## Please download and install the appropriate version of Rtools for 4.6.0 from
## https://cran.r-project.org/bin/windows/Rtools/.
param <-c("omega","alpha","beta", "mu", "gamma")
print(fit, pars = param, digits=3)
## Inference for Stan model: anon_model.
## 4 chains, each with iter=11000; warmup=1000; thin=10; 
## post-warmup draws per chain=1000, total post-warmup draws=4000.
## 
##        mean se_mean    sd   2.5%   25%   50%   75% 97.5% n_eff  Rhat
## omega 0.215   0.001 0.050  0.125 0.180 0.214 0.247 0.315  4066 1.000
## alpha 0.031   0.000 0.022  0.001 0.014 0.027 0.043 0.082  3894 0.999
## beta  0.670   0.001 0.057  0.553 0.631 0.669 0.710 0.777  3951 1.000
## mu    0.045   0.000 0.027 -0.008 0.027 0.044 0.064 0.100  4019 0.999
## gamma 0.244   0.001 0.045  0.162 0.213 0.241 0.273 0.342  3739 1.000
## 
## Samples were drawn using NUTS(diag_e) at Sat May 30 16:08:29 2026.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at 
## convergence, Rhat=1).
stan_dens(fit,  pars = param, nrow = 3, ncol = 2, separate_chains = TRUE)

stan_trace(fit, pars = param, nrow = 3, ncol = 2)

stan_ac(fit, pars = param, nrow = 3, ncol = 2, separate_chains = TRUE)
## Warning in (function (mapping = NULL, data = NULL, stat = "count", position =
## "stack", : Ignoring unknown parameters: `size`

mcmcout <- rstan::extract(fit)
nparam  <- length(param)
cat("AIC=",-2*max(mcmcout$loglik)+2*nparam,"BIC=",-2*max(mcmcout$loglik)+nparam*log(n))
## AIC= 3870.351 BIC= 3896.274

Plot the median of conditional variances

v_med = rep(0, n);
for(t in 1:n){
  v_med[t] = quantile(mcmcout$sigma2[,t], 0.5);
}
variance.df <-data.frame(dates = mydate, med = v_med)  
#
ggplot(variance.df) + geom_line(aes(x=dates, y=v_med)) + 
  xlab("Date") + 
  ylab("Estimated Conditional Variance") +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y")