Controls

The fHMM package allows for multiple hidden Markov model specifications, including different data transformations, state-dependent distributions, and a hierarchical model structure. This vignette¹ outlines what and how specifications are possible.

We first load the package via the familiar library() call:

library("fHMM")

The `set_controls` function

The fHMM philosophy is to start the modeling process by setting all data, model, and estimation specifications. This is done by defining a named list of controls and passing it to the set_controls() function. The function checks the specifications and returns an fHMM_controls object which stores all specifications and thereby provides required information for other fHMM functionalities.

Example specifications

For demonstration, we list example specifications using data from the Deutscher Aktienindex DAX² (Janßen and Rudolph 1992):

dax <- download_data(symbol = "^GDAXI")
head(dax)
#>         Date    Open    High     Low   Close Adj.Close Volume
#> 1 1987-12-30 1005.19 1005.19 1005.19 1005.19   1005.19      0
#> 2 1987-12-31      NA      NA      NA      NA        NA     NA
#> 3 1988-01-01      NA      NA      NA      NA        NA     NA
#> 4 1988-01-04  956.49  956.49  956.49  956.49    956.49      0
#> 5 1988-01-05  996.10  996.10  996.10  996.10    996.10      0
#> 6 1988-01-06 1006.01 1006.01 1006.01 1006.01   1006.01      0

HMMs for empirical data

The following lines of code specify a 3-state HMM with state-dependent t-distributions on the data in the file dax.csv. The dates are provided in the column called Date and the data in the column called Close. The logreturns = TRUE line transforms the index data to log-returns. The runs = 50 line sets the number of numerical optimization runs to 50.

controls <- list(
  states = 3,
  sdds   = "t",
  data   = list(file        = dax,
                date_column = "Date",
                data_column = "Close",
                logreturns  = TRUE),
  fit    = list(runs        = 50)
)
set_controls(controls)
#> fHMM controls:
#> * hierarchy: FALSE 
#> * data type: empirical 
#> * number of states: 3 
#> * sdds: t() 
#> * number of runs: 50

Simulated HMM data

The following specifies a 2-state HMM with state-dependent Gamma distributions, where the expectation values for state 1 and 2 are fixed to 0.5 and 2, respectively. The model will be fitted to 500 data points (horizon = 500), that are going to be simulated from this model specification.

controls <- list(
  states  = 2,
  sdds    = "gamma(mu = 0.5|2)",
  horizon = 500
)
set_controls(controls)
#> fHMM controls:
#> * hierarchy: FALSE 
#> * data type: simulated 
#> * number of states: 2 
#> * sdds: gamma(mu = 0.5|2) 
#> * number of runs: 10

Hierarchical HMMs

Specifying hierarchical HMMs is analogously, except that new parameters can be specified (for example period, see below) and some parameters now can be specified for both hierarchies.

controls <- list(
  hierarchy = TRUE,
  horizon   = c(100, 10),
  sdds      = c("t(df = 1)", "t(df = Inf)"),
  period    = "m"
)
set_controls(controls)
#> fHMM controls:
#> * hierarchy: TRUE 
#> * data type: simulated 
#> * number of states: 2 2 
#> * sdds: t(df = 1) t(df = Inf) 
#> * number of runs: 10

The help page of the set_controls() function provides an overview of all possible specifications, it can be accessed via help("set_controls", package = "fHMM").

References