---
title: "Getting started with RSDC"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Getting started with RSDC}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 6, fig.height = 3.4,
                      message = FALSE, warning = FALSE)
options(digits = 4)
```

```{r setup}
library(RSDC)
```

This vignette walks through the package API: estimating the three model
variants, using the standard S3 methods on a fitted object, comparing models with
`AIC`/`BIC`, forecasting, and simulating. To keep the build fast we use a small
simulated data set and a reduced optimizer budget via `control`; in real use, keep
the defaults.

## A fitted object is an `"rsdc_fit"`

```{r data}
set.seed(1)
n  <- 300L
X  <- cbind(intercept = 1, z = as.numeric(scale(seq_len(n))))   # include an intercept
beta <- rbind(c(1.5, -0.6),     # regime 1 (logistic stay-prob coefficients)
              c(1.0,  0.2))     # regime 2
rho  <- rbind(0.2, 0.8)         # K = 2 -> one correlation per regime
Sig  <- array(c(matrix(c(1, 0.2, 0.2, 1), 2),
                matrix(c(1, 0.8, 0.8, 1), 2)), dim = c(2, 2, 2))
sim  <- rsdc_simulate(n = n, X = X, beta = beta, mu = matrix(0, 2, 2),
                      sigma = Sig, N = 2, seed = 42)
y <- scale(sim$observations)    # treated as unit-variance standardized residuals

ctrl <- list(itermax = 30, NP = 40, seed = 1)   # small budget for the vignette
fit <- rsdc_estimate("tvtp", residuals = y, N = 2, X = X, control = ctrl)
class(fit)
fit
```

## Standard methods

`AIC()` / `BIC()` work directly because `logLik()` carries `df` and `nobs`:

```{r methods}
logLik(fit)
c(AIC = AIC(fit), BIC = BIC(fit), nobs = nobs(fit))
coef(fit)
```

`summary()` reports a coefficient table with standard errors (from the observed
information at the MLE), and `confint()` gives Wald intervals:

```{r summary}
summary(fit)
head(confint(fit))
```

## Model comparison

```{r compare}
fit_const <- rsdc_estimate("const", residuals = y, control = ctrl)
fit_noX   <- rsdc_estimate("noX",   residuals = y, N = 2, control = ctrl)
data.frame(
  model = c("const", "noX(N=2)", "tvtp(N=2)"),
  AIC   = c(AIC(fit_const), AIC(fit_noX), AIC(fit)),
  BIC   = c(BIC(fit_const), BIC(fit_noX), BIC(fit))
)
```

## Forecasting and simulation

`predict()` wraps `rsdc_forecast()`; supply the conditional volatilities:

```{r predict}
sigma_mat <- matrix(1, n, 2, dimnames = list(NULL, c("a", "b")))   # unit vols here
fc <- predict(fit, residuals = y, sigma_matrix = sigma_mat,
              value_cols = c("a", "b"), X = X)
str(fc$predicted_correlations)
```

`simulate()` draws a new path from the fitted model (here, TVTP given `X`):

```{r simulate}
sim2 <- simulate(fit, X = X, seed = 7)
table(sim2$states)
```

## Genuine out-of-sample forecasts

For a look-ahead-free forecast, set `out_of_sample = TRUE`: the filter is run on the
first 70% of the sample, its terminal state initializes the held-out run, and the
out-of-sample correlations are weighted by **filtered** (not smoothed) probabilities
so no future information leaks in.

```{r oos}
fc_oos <- predict(fit, residuals = y, sigma_matrix = sigma_mat,
                  value_cols = c("a", "b"), X = X, out_of_sample = TRUE)
nrow(fc_oos$predicted_correlations)   # length of the 30% hold-out
fc_oos$BIC                            # out-of-sample predictive score
```

## Uncertainty, decoding, multi-step forecasts, and tidy output

The following tools were added in version 1.5-0.

**Multi-start estimation.** `control$n_starts` repeats the global + local search
from several seeds and keeps the highest-likelihood fit, storing each start's
log-likelihood. Because `DEoptim` is a *stochastic* global search whose result
depends on the seed, this is primarily a stability/reproducibility diagnostic
(do the seeds agree?) rather than a replacement for the global search:

```{r multistart}
fit_ms <- rsdc_estimate("tvtp", residuals = y, N = 2, X = X,
                        control = c(ctrl, list(n_starts = 3)))
fit_ms$start_logliks            # one log-likelihood per start
```

**Uncertainty bands on the predicted correlation.** `rsdc_corr_bands()` draws
parameter vectors from the fitted sampling distribution, re-runs the filter for
each, and returns pointwise quantile bands (one matrix per asset pair, with
columns `fit`, `lower`, `upper`):

```{r bands}
bands <- rsdc_corr_bands(fit, B = 100, seed = 1)
head(bands[[1]])
```

**Most likely regime path (Viterbi).** `rsdc_viterbi()` returns the single most
likely *joint* regime sequence, complementing the marginal smoothed
probabilities:

```{r viterbi}
table(rsdc_viterbi(fit))
```

**Multi-step-ahead forecasts.** `rsdc_forecast_ahead()` propagates the terminal
filtered state through the Markov chain to forecast the regime distribution and
the implied correlations `h` steps ahead (pass `X_future` for the time-varying
case; here the last covariate row is held constant):

```{r ahead}
fa <- rsdc_forecast_ahead(fit, horizon = 5)
fa$predicted_correlations
```

**Tidy output and plotting.** `rsdc_fit` objects work with the \pkg{broom}
generics `tidy()` / `glance()` / `augment()` and a \pkg{ggplot2} `autoplot()`
method:

```{r broom}
generics::tidy(fit)
generics::glance(fit)
```

```{r autoplot, eval = requireNamespace("ggplot2", quietly = TRUE), fig.alt = "Stacked smoothed regime probabilities over time"}
ggplot2::autoplot(fit)          # stacked smoothed regime probabilities
```

## More than three regimes

`N >= 4` is supported for `"noX"` and `"tvtp"`:

```{r bign}
fit4 <- rsdc_estimate("noX", residuals = y, N = 4,
                      control = list(itermax = 20, NP = 60, seed = 1))
dim(fit4$transition_matrix)
```

## Validation: parameter recovery

Because the data above were simulated with known regime correlations
(`rho = c(0.2, 0.8)`), we can check that the estimator recovers them — the fitted
`tvtp(N = 2)` correlations should be close to the truth:

```{r recovery}
rbind(true = c(0.2, 0.8),
      estimated = sort(as.numeric(fit$correlations)))
```

A full Monte-Carlo study (five model variants, $M = 100$ replications,
$T \in \{500, 1000, 2000\}$, $K \in \{2, 3, 4\}$, reporting bias/RMSE/MCSE) ships with
the package in `inst/simulation/monte_carlo_study.R` and can be run from the package
root with `source(system.file("simulation", "monte_carlo_study.R", package = "RSDC"))`.