be23-AUdata.qmd

---
title: "Australian Data Forecasting with Package BVAR"
author: 
  - name: "Type your name"
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    theme: cosmo
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---

> **Task:** Adjust this **Quarto** template to perform your Bayesian VAR model estimation and forecasting. Search for the variables of interest using function `readrba::browse_rba_series()`, download the chosen 4 variables using function `readrba::read_rba()`, and create a data matrix. Subsequently employ the model estimation and forecasting workflow using package **BVAR** and report the basic outputs of your analysis.

# Download the data

```{r interest data}
#| echo: true
#| message: false
#| warning: false

# download daily interest rates
icr_dwnld   = readrba::read_rba(series_id = "FIRMMCRTD")   # Cash Rate Target
icr_tmp     = xts::xts(icr_dwnld$value, icr_dwnld$date)

by1m_dwnld = readrba::read_rba(series_id = "FIRMMBAB30D")
by1m_tmp   = xts::xts(by1m_dwnld$value, by1m_dwnld$date)

short       = na.omit(merge(icr_tmp, by1m_tmp))
forecast_day          = "/2023-09-06"

# daily data
variables             = short
colnames(variables)   = c("cash rate", "1m")
variables             = variables[forecast_day]

# monthly data
monthly               = xts::to.monthly(variables, OHLC = FALSE)
plot(monthly)
```

# Prior Setup

```{r priors}
set.seed(42)
library(BVAR)

# priors
mn      = bv_minnesota(
  lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5),
  alpha = bv_alpha(mode = 2), 
  psi <- bv_psi(scale = 0.004, shape = 0.004, mode = "auto", min = "auto", max = "auto"),
  var = 1e07
)

soc     = bv_soc(mode = 1, sd = 1, min = 1e-04, max = 50)
sur     = bv_sur(mode = 1, sd = 1, min = 1e-04, max = 50)

priors  = bv_priors(hyper = "auto", mn = mn, soc = soc, sur = sur)

# MH setup
mh      = bv_metropolis(
  scale_hess = c(0.05, 0.0001, 0.0001),
  adjust_acc = TRUE, 
  acc_lower = 0.25, 
  acc_upper = 0.45
)
```

# Estimation

## Estimate the model

```{r estimation}
#| echo: true
#| message: false
#| warning: false
#| error: false

# estimation
p     = 1
run   = bvar(
  monthly, 
  lags = p, 
  n_draw = 3e4,
  n_burn = 1e4,
  n_thin = 1,
  priors = priors, 
  mh = mh, 
  verbose = FALSE # without progress bar
)
```

## Report MCMC convergence

```{r mcmc}
plot.ts(run$hyper, main = "", col = "#FF00FF", xlab = "s")
```

## Report the Posterior Moments

```{r means}
mean_A  = t(apply(run$beta, 2:3, mean))
rownames(mean_A) = colnames(monthly)
knitr::kable(mean_A, caption = "Posterior estimates for autoregressive parameters", digits = 3)
```

# Forecasting

```{r forecasting}
# forecasting 
predict(run) <- predict(
  run, 
  horizon = 20, 
  conf_bands = seq(from = 0.05, to = 0.4, by = 0.01)
)
plot(
  predict(run), 
  area = TRUE, 
  t_back = 32
)
```

# Conclusion!

Thank you!