For time series the order of the observations carries information: a
synthetic series should reproduce the marginal distribution and
the autocorrelation (and, for several series, the cross-correlation).
fit_synthesizer() has a method for ts objects
with four generators.
Copula-VAR
Each series is transformed to normal scores through its empirical
distribution, a vector autoregression is fitted (order chosen by AIC up
to max_lag), new paths are simulated with innovations
resampled from the fitted residuals, and the paths are mapped back
through the empirical quantile functions.
fit <- fit_synthesizer(ldeaths)
fit
#> <sp_ts_synthesizer>
#> trained on : 72 time points, 1 series (frequency 12)
#> method : copula_var (VAR order 5)
syn <- generate(fit, seed = 1)
plot_ts(ldeaths, syn)
plot_acf(ldeaths, syn, lag_max = 24)
Synthetic series can be of any length and start anywhere:
long <- generate(fit, n = 240, start = c(1980, 1), seed = 2)
tsp(long)
#> [1] 1980.000 1999.917 12.000
Several series
returns <- diff(log(EuStockMarkets))
fit_mv <- fit_synthesizer(returns)
syn_mv <- generate(fit_mv, seed = 1)
round(cor(returns) - cor(syn_mv), 3)
#> DAX SMI CAC FTSE
#> DAX 0.000 0.008 0.000 -0.028
#> SMI 0.008 0.000 -0.007 -0.012
#> CAC 0.000 -0.007 0.000 -0.022
#> FTSE -0.028 -0.012 -0.022 0.000
Bootstraps
Block bootstraps resample stretches of the observed series, so they
keep short-range dependence and the exact values (and non-linear
features within blocks), at the price of repeating observed values:
fit_b <- fit_synthesizer(lh, method = "stationary", block_length = 8)
syn_b <- generate(fit_b, n = 96, seed = 1)
plot_ts(lh, syn_b)
References
Politis, D. N. and Romano, J. P. (1994). The stationary bootstrap.
Journal of the American Statistical Association, 89(428),
1303–1313.