HMMs for Finance

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.

Installation

You can install the released version of {fHMM} from CRAN with:

install.packages("fHMM")

And the development version from GitHub with:

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

Contributing

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!

Example: Fitting an HMM to the DAX

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:

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

We first need to define the model:

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

The function prepare_data() then prepares the data for estimation:

data <- prepare_data(controls)

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:

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

events <- fHMM_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")