Correlation of two series, at lags

Correlates two series period by period: Pearson's r with Fisher's interval and the t-test p-value of stats::cor.test(), and the cross-correlations at lags \(-K..K\) as stats::ccf() estimates them (lag k is the correlation of x[t + k] with y[t]; the default K is ccf()'s, floor(10 log10(n / 2))). Two named series are matched by name (the periods both have, in the order of x), so counts from two sources for the same years line up whatever years each covers. With dif the changes from one period to the next are correlated instead of the levels: two series that both trend correlate in level whether or not they move together. Every correlation lies in \([-1, 1]\) (Cauchy-Schwarz, proof("xcser")).

Usage

xcser(x, y, lagmax = NULL, dif = FALSE, level = 0.95)

Arguments

x, y: The series: finite numbers, of one length, or both named by period.
lagmax: NULL or the largest lag: one whole number from 0, below the number of periods.
dif: TRUE to correlate the period-to-period changes.
level: The confidence level: one number strictly between 0 and 1.

Value

An object of class xcser, a list: cor (r, lo, hi, p, n); ccf (lag, r); common, the periods matched by name (NULL without names); and level.

Examples

a <- c("2019" = 120, "2020" = 98, "2021" = 105, "2022" = 130, "2023" = 141)
b <- c("2018" = 50, "2019" = 61, "2020" = 44, "2021" = 52, "2022" = 66,
       "2023" = 70)
xcser(a, b)
#> xcser: 5 periods; r 0.9840288 (95% 0.7719537 to 0.9989935), p 0.002417117
#>  lag          r
#>   -3 -0.3061542
#>   -2 -0.4281115
#>   -1  0.1949278
#>    0  0.9840288
#>    1  0.3245041
#>    2 -0.4603044
#>    3 -0.3987087
xcser(a, b, dif = TRUE)$cor
#>           r        lo        hi          p n
#> 1 0.9734683 0.1922192 0.9994666 0.02653166 4