funtimes (version 8.0)

ccf_boot: Cross-Correlation Function of Time Series with Sieve Bootstrap p-values

Description

Account for possible autocorrelation of time series when assessing statistical significance of their cross-correlation. A sieve bootstrap approach is used to generate multiple copies of the time series with the same autoregressive dependence, under the null hypothesis of the two time series under investigation being uncorrelated. Significance of cross-correlation coefficients is assessed based on the distribution of their bootstrapped counterparts. Both Pearson and Spearman types of coefficients are obtained, but plot is provided for only one type, with significant correlations shown using filled circles.

Usage

ccf_boot(
  x,
  y,
  lag.max = NULL,
  plot = c("Pearson", "Spearman", "none"),
  level = 0.95,
  B = 1000,
  ...
)

Arguments

x, y

univariate numeric time series objects or numeric vectors for which to compute cross-correlation. Different time attributes in ts objects are acknowledged, see Example 2 below.

lag.max

maximum lag at which to calculate the cross-correlation. Will be automatically limited as in ccf.

plot

choose whether to plot results for Pearson correlation (default, or use plot = "Pearson"), Spearman correlation (use plot = "Spearman"), or suppress plotting (use plot = "none"). Both Pearson and Spearman results are given in the output, irregardless of the plot setting.

level

confidence level, from 0 to 1. Default is 0.95, that is, 95% confidence.

B

number of bootstrap simulations to obtain empirical critical values. Default is 1000.

...

other parameters passed to the function ARest to control how autoregressive dependencies are estimated. The same set of parameters is used separately on x and y.

Value

A data frame with the following columns:

Lag

lags for which the following values were obtained.

rP

observed Pearson correlations.

pP

bootstrap p-value for Pearson correlations.

lowerP, upperP

lower and upper quantiles (for the confidence level set by level) of the bootstrapped Pearson correlations.

rS

observed Spearman correlations.

pS

bootstrap p-value for Spearman correlations.

lowerS, upperS

lower and upper quantiles (for the confidence level set by level) of the bootstrapped Spearman correlations.

See Also

ARest, ar, ccf, HVK

Examples

# NOT RUN {
# Fix seed for reproducible simulations:
set.seed(1)

# Example 1
# Simulate independent normal time series of same lengths
x <- rnorm(100)
y <- rnorm(100)
ccf(x, y) # default CCF with parametric confidence band
tmp <- ccf_boot(x, y) # CCF with bootstrap
tmp$rP; tmp$rS # can always extract results for both Pearson and Spearman correlations

# Example 2
# Simulated ts objects of different lengths and starts (incomplete overlap)
x <- arima.sim(list(order = c(1, 0, 0), ar = 0.5), n = 30)
x <- ts(x, start = 2001)
y <- arima.sim(list(order = c(2, 0, 0), ar = c(0.5, 0.2)), n = 40)
y <- ts(y, start = 2020)
ts.plot(x, y, col = 1:2, lty = 1:2) # show how x and y are aligned
ccf(x, y)
ccf_boot(x, y, plot = "Spearman") # CCF with bootstrap
# Notice that only +-7 lags can be calculated in both cases because of the small 
# overlap of the time series. If save these time series as plain vectors, the time
# information would be lost, and time series will be misaligned. 
ccf(as.numeric(x), as.numeric(y))

# Example 3
# Box & Jenkins time series of sales and a leading indicator, see ?BJsales
plot.ts(cbind(BJsales.lead, BJsales))
# Each of the BJ time series looks as having a stochastic linear trend, so apply differences:
plot.ts(cbind(diff(BJsales.lead), diff(BJsales)))
# Get cross-correlation of the differenced series:
ccf_boot(diff(BJsales.lead), diff(BJsales), plot = "Spearman")
# The leading indicator "stands out" with significant correlations at negative lags, 
# showing it can be used to predict the sales 2-3 time steps ahead (that is,
# diff(BJsales.lead) at times t-2 and t-3 is strongly correlated with diff(BJsales) at 
# current time t).
# }
# NOT RUN {
# }