The `{fHMM}`

R package allows for the detection and
characterization of financial market regimes in time series data by
applying hidden Markov Models (HMMs). The detailed
documentation outlines the functionality and the model formulation.
Below, we provide an initial application to the German stock index DAX.

You can install the released version of `{fHMM}`

from CRAN with:

`install.packages("fHMM")`

And the development version from GitHub with:

```
# install.packages("devtools")
::install_github("loelschlaeger/fHMM") devtools
```

We are open to contributions and would appreciate your input! If you encounter any issues, please submit bug reports as issues. If you have any ideas for new features, please submit them as feature requests. If you would like to add extensions to the package, please fork the “master” branch and submit merge requests. We look forward to your contributions!

We fit a 3-state HMM with state-dependent t-distributions to the DAX log-returns from 2000 to 2022. The states can be interpreted as proxies for bearish (green below) and bullish markets (red) and an “in-between” market state (yellow).

`library("fHMM")`

The package has a build-in function to download financial data from Yahoo Finance:

`<- download_data(symbol = "^GDAXI", file = NULL, verbose = FALSE) dax `

We first need to define the model:

```
<- list(
controls states = 3,
sdds = "t",
data = list(file = dax,
date_column = "Date",
data_column = "Close",
logreturns = TRUE,
from = "2000-01-01",
to = "2022-12-31")
)<- set_controls(controls) controls
```

The function `prepare_data()`

then prepares the data for
estimation:

`<- prepare_data(controls) data `

The `summary()`

method gives an overview:

```
summary(data)
#> Summary of fHMM empirical data
#> * number of observations: 5882
#> * data source: data.frame
#> * date column: Date
#> * log returns: TRUE
```

We fit the model and subsequently decode the hidden states and compute (pseudo-) residuals:

```
<- fit_model(data)
model <- decode_states(model)
model <- compute_residuals(model) model
```

The `summary()`

method gives an overview of the model
fit:

```
summary(model)
#> Summary of fHMM model
#>
#> simulated hierarchy LL AIC BIC
#> 1 FALSE FALSE 17649.52 -35269.03 -35168.84
#>
#> State-dependent distributions:
#> t()
#>
#> Estimates:
#> lb estimate ub
#> Gamma_2.1 1.286e-02 2.007e-02 3.113e-02
#> Gamma_3.1 1.208e-06 1.198e-06 1.180e-06
#> Gamma_1.2 1.557e-02 2.489e-02 3.959e-02
#> Gamma_3.2 1.036e-02 1.877e-02 3.378e-02
#> Gamma_1.3 4.119e-07 4.080e-07 4.019e-07
#> Gamma_2.3 2.935e-03 5.275e-03 9.422e-03
#> mu_1 9.655e-04 1.271e-03 1.576e-03
#> mu_2 -8.483e-04 -3.102e-04 2.278e-04
#> mu_3 -3.813e-03 -1.760e-03 2.932e-04
#> sigma_1 5.417e-03 5.853e-03 6.324e-03
#> sigma_2 1.278e-02 1.330e-02 1.384e-02
#> sigma_3 2.348e-02 2.579e-02 2.832e-02
#> df_1 3.957e+00 5.198e+00 6.828e+00
#> df_2 3.870e+08 3.870e+08 3.870e+08
#> df_3 5.549e+00 1.078e+01 2.095e+01
#>
#> States:
#> decoded
#> 1 2 3
#> 2278 2900 704
#>
#> Residuals:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -3.519694 -0.658831 0.009613 -0.002206 0.669598 3.905726
```

Having estimated the model, we can visualize the state-dependent distributions and the decoded time series:

```
<- fHMM_events(
events list(dates = c("2001-09-11", "2008-09-15", "2020-01-27"),
labels = c("9/11 terrorist attack", "Bankruptcy Lehman Brothers", "First COVID-19 case Germany"))
)plot(model, plot_type = c("sdds","ts"), events = events)
```

The (pseudo-) residuals help to evaluate the model fit:

`plot(model, plot_type = "pr")`