estimate_lag function

Estimate Lag Function

Uses polynomial approximation and derivatives for time series objects to estimate lag between series.

estimate_lag(
  time_series1,
  time_series2,
  possible_lags,
  method = c("cross-correlation", "MSE", "rank"),
  leave_off,
  estimated_change = 0,
  order_of_polynomial_approximation = 7,
  order_of_derivative = 1,
  spline = FALSE,
  ...
)

Arguments

• time_series1: A numeric vector which stores the time series of interest in the log scale.
• time_series2: A numeric vector which stores the trend proxy time series in the log scale. The length of trend_proxy must be the same as that of time_series1.
• possible_lags: A numeric vector specifying all the candidate lags for trend_proxy. The default option is -36:36.
• method: A character vector specifying the method used to obtain the lag estimate. "polynomial" uses polynomial approximation, while "cross-correlation" uses cross-correlation.
• leave_off: A positive integer specifying the number of observations to be left off when estimating the lag.
• estimated_change: A numeric specifying the estimated change in the visitation trend. The default option is 0, implying no change in the trend.
• order_of_polynomial_approximation: A numeric specifying the order of the polynomial approximation of the difference between time series used in estimate_lag. The default option is 7, the seventh-degree polynomial.
• order_of_derivative: A numeric specifying the order of derivative for the approximated difference between time_series1 and lagged time_series2. The default option is 1, the first derivative.
• spline: A Boolean specifying whether or not to use a smoothing spline for the lag estimation.
• ...: Additional arguments to be passed onto the smooth.spline function, if method is "polynomial".

Returns

• cc_lag: A numeric indicating the estimated lag with the cross-correlation criterion.

• mse_criterion: A numeric indicating the estimated lag with the MSE criterion.

• rank_criterion: A numeric indicating the estimate lag with the rank criterion.

Examples

# Generate dataset with known lag and recover this lag --------------#'

lag <- 3
n <- 156
start_year <- 2005
frequency <- 12
trend_function <- function(x) x^2

x <- seq(-3,3, length.out = n)

y1 <- ts(trend_function(x),start = start_year, freq = frequency)
y2 <- stats::lag(y1, k = lag)

# Recover lag
estimate_lag(y1,y2, possible_lags = -36:36,
             method = "rank",leave_off = 0, spline = FALSE)