# 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

Janßen, B., and B. Rudolph. 1992. “Der Deutsche Aktienindex DAX.” Knapp Verlag.

1. This vignette was build using R 4.4.0 with the `{fHMM}` 1.3.1 package.↩︎

2. The `download_data()` function is explained in the vignette on data management.↩︎