Time series data with fabricatr

Below, we begin a series of examples discussing the creation of time series style data in fabricatr. This document assumes you are familiar with the basics of building and importing data with fabricatr.

Single unit fixed time trend data

The simplest possible example involves a single unit with specified, time-dependent data, with a linear trend. In this example we generate a geographic location that has a fixed linear time trend in GDP growth.

panel_unit <- fabricate(
  N = 20,
  ts_year = 0:19,
  gdp_measure = 20 + 0.3 * ts_year + rnorm(N, sd=0.3)
)

First, we begin by creating tracking progress on the time trend, here ts_year, which begins at 0 and increases by one across observations. Next, we create a variable that depends on the current value of ts_year; here the GDP measure for our unit begins at 20 (log units) and increases by one third of a log unit each year. We also specify a stochastic error term.

Multiple units with time trends

A more complex example might involve several geographic units, each of which has a separate growth value. Here we can use fabricatr’s support for multi-level, hierarchical data to elaborate:

panel_units <- fabricate(
  countries = add_level(
    N = 5,
    base_gdp = runif(N, 15, 22),
    growth_units = runif(N, 0.2, 0.8),
    growth_error = runif(N, 0.1, 0.5)
  ),
  years = add_level(
    N = 5,
    ts_year = 0:4,
    gdp_measure = base_gdp + (ts_year * growth_units) + rnorm(N, sd=growth_error)
  )
)

Here, each country-year inherits the parameters of the country: a base GDP, an annual growth rate (which is constant in this model), and an error parameter. The resulting data is 25 rows; 5 years for each of 5 countries.

Multiple units with fixed global time trends

Note that it would also be possible to include a fixed global trend in this example by including it as part of the variable specification:

global_trend <- 0.1

global_trend_example <- fabricate(
  countries = add_level(
    N = 5,
    base_gdp = runif(N, 15, 22),
    growth_units = runif(N, 0.2, 0.8),
    growth_error = runif(N, 0.1, 0.5)
  ),
  years = add_level(
    N = 5,
    ts_year = 0:4,
    gdp_measure = base_gdp +
      (ts_year * global_trend) + (ts_year * growth_units) +
      rnorm(N, sd=growth_error)
  )
)

Multiple units with global yearly shocks

Even more complex designs may include non-trend global level shocks (for example, financial crises or booms that affect all countries). The traditional hierarchical data design may not fit here, because we want common country-level data and common year-level data, both combined to form country-year observations. This is a good example of data that can best be described as multiple non-nested levels. Users interested in implementing this should review our manual on cross-classified and panel data. The below example will use cross_levels and non-nested level data.

panel_global_data <- fabricate(
  years = add_level(
    N = 5,
    ts_year = 0:4,
    year_shock = rnorm(N, 0, 0.3)
  ),
  countries = add_level(
    N = 5,
    base_gdp = runif(N, 15, 22),
    growth_units = runif(N, 0.2, 0.5),
    growth_error = runif(N, 0.1, 0.5),
    nest = FALSE
  ),
  country_years = cross_levels(
    by = join_using(years, countries),
    gdp_measure = base_gdp + year_shock + (ts_year * growth_units) +
      rnorm(N, sd=growth_error)
  )
)

Notice that each variable is specified in the appropriate level; time series year indicators and yearly shocks are specified at the year level; country-specific time trend information and base GDP are specified at the country level; and the actual GDP measure, which is country-year, is specified at the country-year level.

Seasonal or ARIMA Time Series

Although fabricatr does not have formal functionality for the creation of ARIMA time series, we recommend that interested users see our guide to using other data creation packages with fabricatr, which includes an example of using the forecast package to generate ARIMA data.

What’s next?