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Detect Turning Points and Unwanted Ripples in a Time Series

Source: R/turningpoints.R
turning_points.Rd

Identifies turning points (upturns and downturns) and unwanted short-term ripples in a time series object using local extremum criteria.

Usage

turning_points(x, start = NULL, end = NULL, digits = 6, k = 3, m = 1)

upturn(x, start = NULL, end = NULL, digits = 6, k = 3, m = 1)

downturn(x, start = NULL, end = NULL, digits = 6, k = 3, m = 1)

unwanted_ripples(x, start = NULL, end = NULL, digits = 6, k = 3, m = 1)

Arguments

x

An input time series (object of class "ts").

start, end

Numeric vectors specifying the start and end of the time interval (e.g., c(2020, 1)) in which to search for turning points.

digits

Integer specifying the number of decimal digits used when comparing values to determine turning points. Defaults to NULL (no rounding).

k, m

Integers specifying the required number of preceding (\(k\)) and succeeding (\(m\)) observations to define a local extremum. See details.

Value

  • turning_points() returns a named list with two components: "upturn" and "downturn", each containing a vector of dates (or empty vectors if none found).

  • upturn() and downturn() return a vector of dates corresponding to the detected upturns or downturns, respectively.

  • unwanted_ripples() returns an integer representing the number of unwanted ripples detected in the series.

Details

Turning points are identified following the operational definition adapted from Zellner, Hong, and Min (1991), typically with \(k = 3\) and \(m = 1\):

  • An upturn occurs at time \(t\) if: $$y_{t-k} \ge \dots \ge y_{t-1} < y_t \le y_{t+1} \le \dots \le y_{t+m}$$

  • A downturn occurs at time \(t\) if: $$y_{t-k} \le \dots \le y_{t-1} > y_t \ge y_{t+1} \ge \dots \ge y_{t+m}$$

An unwanted ripple is defined as any occurrence where two turning points of the same type (two upturns or two downturns) occur within a 10-month window (i.e., short cycles lasting less than 11 months).

References

Zellner, A., Hong, C., & Min, C. (1991). Forecasting Turning Points in International Growth Rates using Bayesian Exponential Smoothing Methods. Journal of Econometrics, 49(1–2), 275–304. doi:10.1016/0304-4076(91)90016-7

Examples

if (FALSE) { # rjd3jars::check_java_version(silent = TRUE)
tc <- henderson_smoothing(french_ipi[, "manufacturing"])
turning_points(tc)
unwanted_ripples(tc)
}