R: Fourier Features for Modeling Seasonality

step_fourier {timetk} | R Documentation

## Fourier Features for Modeling Seasonality

### Description

`step_fourier` creates a a specification of a recipe step that will convert a Date or Date-time column into a Fourier series

### Usage

    step_fourier(
      recipe,
      ...,
      period,
      K,
      role = "predictor",
      trained = FALSE,
      columns = NULL,
      scale_factor = NULL,
      skip = FALSE,
      id = rand_id("fourier")
    )

    ## S3 method for class 'step_fourier'
    tidy(x, ...)

### Arguments

`recipe` | A recipe object. The step will be added to the sequence of operations for this recipe.
`...` | A single column with class `Date` or `POSIXct`. See `recipes::selections()` for more details. For the `tidy` method, these are not currently used.
`period` | The numeric period for the oscillation frequency. See details for examples of `period` specification.
`K` | The number of orders to include for each sine/cosine fourier series. More orders increase the number of fourier terms and therefore the variance of the fitted model at the expense of bias. See details for examples of `K` specification.
`role` | For model terms created by this step, what analysis role should they be assigned?. By default, the function assumes that the new variable columns created by the original variables will be used as predictors in a model.
`trained` | A logical to indicate if the quantities for preprocessing have been estimated.
`columns` | A character string of variables that will be used as inputs. This field is a placeholder and will be populated once `recipes::prep()` is used.
`scale_factor` | A factor for scaling the numeric index extracted from the date or date-time feature. This is a placeholder and will be populated once `recipes::prep()` is used.
`skip` | A logical. Should the step be skipped when the recipe is baked by bake.recipe()? While all operations are baked when prep.recipe() is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using skip = TRUE as it may affect the computations for subsequent operations.
`id` | A character string that is unique to this step to identify it.
`x` | A `step_fourier` object.

### Details

Date Variable

Unlike other steps, `step_fourier` does not remove the original date variables. `recipes::step_rm()` can be used for this purpose.

Period Specification

The `period` argument is used to generate the distance between peaks in the fourier sequence. The key is to line up the peaks with unique seasonalities in the data.

For Daily Data, typical period specifications are:

- Yearly frequency is 365

- Quarterly frequency is 365 / 4 = 91.25

- Monthly frequency is 365 / 12 = 30.42

K Specification

The `K` argument specifies the maximum number of orders of Fourier terms. Examples:

- Specifying `period = 365` and `K = 1` will return a `cos365_K1` and `sin365_K1` fourier series

- Specifying `period = 365` and `K = 2` will return a `cos365_K1`, `cos365_K2`, `sin365_K1` and `sin365_K2` sequence, which tends to increase the models ability to fit vs the `K = 1` specification (at the expense of possibly overfitting).

Multiple values of `period` and `K`

It's possible to specify multiple values of `period` in a single step such as `step_fourier(period = c(91.25, 365), K = 2`. This returns 8 Fouriers series:

- `cos91.25_K1`, `sin91.25_K1`, `cos91.25_K2`, `sin91.25_K2`

- `cos365_K1`, `sin365_K1`, `cos365_K2`, `sin365_K2`

### Value

For `step_fourier`, an updated version of recipe with the new step added to the sequence of existing steps (if any). For the `tidy` method, a tibble with columns `terms` (the selectors or variables selected), `value` (the feature names).

### See Also

Time Series Analysis:

- Engineered Features: `step_timeseries_signature()`, `step_holiday_signature()`, `step_fourier()`

- Diffs & Lags `step_diff()`, `recipes::step_lag()`

- Smoothing: `step_slidify()`, `step_smooth()`

- Variance Reduction: `step_box_cox()`

- Imputation: `step_ts_impute()`, `step_ts_clean()`

- Padding: `step_ts_pad()`

Main Recipe Functions:

- `recipes::recipe()`

- `recipes::prep()`

- `recipes::bake()`

### Examples

    library(recipes)
    library(tidyverse)
    library(tidyquant)
    library(timetk)

    FB_tbl <- FANG %>%
        filter(symbol == "FB") %>%
        select(symbol, date, adjusted)

    # Create a recipe object with a timeseries signature step
    # - 252 Trade days per year
    # - period = c(252/4, 252): Adds quarterly and yearly fourier series
    # - K = 2: Adds 1st and 2nd fourier orders

    rec_obj <- recipe(adjusted ~ ., data = FB_tbl) %>%
        step_fourier(date, period = c(252/4, 252), K = 2)

    # View the recipe object
    rec_obj

    # Prepare the recipe object
    prep(rec_obj)

    # Bake the recipe object - Adds the Fourier Series
    bake(prep(rec_obj), FB_tbl)

    # Tidy shows which features have been added during the 1st step
    #  in this case, step 1 is the step_timeseries_signature step
    tidy(prep(rec_obj))
    tidy(prep(rec_obj), number = 1)

[Package timetk version 2.4.0 Index]