# Get estimates of time-dependent properties of models. `get_stats` estimates time-dependent properties of models (e.g., variance) from ensemble time series. ```r get_stats( x, center_trend = "grand_mean", center_kernel = c("gaussian", "uniform"), center_bandwidth = NULL, stat_trend = c("local_constant", "local_linear"), stat_kernel = c("uniform", "gaussian"), stat_bandwidth = NULL, lag = 1, backward_only = FALSE ) ``` ## Arguments - `x`: A univariate or multivariate numeric time series object or a numeric vector or matrix. - `center_trend`: Character string giving method of calculating the trend to subtract. Allowed values are '"assume_zero"', '"grand_mean"', '"ensemble_means"', '"local_constant"', and '"local_linear"'. Will be partially matched. - `center_kernel`: Character string giving the kernel for any local detrending. Allowed values are '"gaussian"' and '"uniform"'. - `center_bandwidth`: Bandwidth of kernel for any local detrending done. A numeric value >= 1. - `stat_trend`: Character string giving method of smoothing estimates. Allowed values are '"local_constant"', and '"local_linear"'. Will be partially matched. - `stat_kernel`: Character string giving the kernel for local smoothing of estimates. Allowed values are '"gaussian"' and '"uniform"'. - `stat_bandwidth`: Bandwidth of kernel for local smoothing of estimates. A numeric value >= 1. - `lag`: Integer lag at which to calculate the acf. This lag is in terms of the index of `x` and does not account for the frequency of `x` if `x` is a time series. It should be non-negative. - `backward_only`: Logical value (defaulting to 'FALSE') that determines whether any uniform smoothing kernels are restricted to using data before the index of the smoothed estimate. ## Returns A list with elements '"stats"', '"taus"', '"centered"', '"stat_trend"', '"stat_kernel"', '"stat_bandwidth"', and '"lag"'. "stats" is a list containing vectors of the estimates. '"taus"' is a list containing Kendall's correlation coefficient of each element of '"stats"' with time. '"centered"' is a list of the detrended time series, the trend subtracted, and the bandwidth used in the detrending. The other elements record the parameters provided to this function for future reference. ## Details Any missing values in 'x' will cause an error. Bandwidths affect weights in local smoothers as follows. To get the local estimate corresponding to index i, the distance to each other index j is calculated as (i - j) / h, where h is the bandwidth. Then that distance is plugged into the kernel function to obtain a weight. The weights are normalized to sum to one for each index. The gaussian kernel is equivalent to a standard Gaussian density function. The uniform kernel is an indicator function of whether the distance is less than 1. Thus selecting a uniform kernel with a bandwidth of 2 is equivalent to a sliding window of length 3 that is centered on the focal index. In general, if n is the greatest integer that is less than the value of the bandwidth h, the window includes the n nearest values on each side of the focal index. '"local_constant"' smoothers are local means computed with the kernel weights. '"local_linear"' smoothers are the fitted values of local linear regressions with the kernel weights. The linear smoothers avoid biases that the one-sided kernels at the ends of the time series can create for the local constant smoothers. See the vignette "Getting Started with spaero" for the formulas used for each estimate. ## Examples ```r # A highly autocorrelated time series x <- 1:10 get_stats(x, stat_bandwidth = 3)$stats # Plot log of acf plot(log(get_stats(x, stat_bandwidth = 3)$stats$autocor)) # Check estimates with AR1 simulations with lag-1 core 0.1 w <- rnorm(1000) xnext <- function(xlast, w) 0.1 * xlast + w x <- Reduce(xnext, x = w, init = 0, accumulate = TRUE) acf(x, lag.max = 1, plot = FALSE) head(get_stats(x, stat_bandwidth = length(x))$stats$autocor) # Check detrending ability x2 <- x + seq(1, 10, len = length(x)) ans <- get_stats(x2, center_trend = "local_linear", center_bandwidth = length(x), stat_bandwidth = length(x))$stats head(ans$autocor) # The simple acf estimate is inflated by the trend acf(x2, lag.max = 1, plot = FALSE) # Check ability to estimate time-dependent autocorrelation xnext <- function(xlast, w) 0.8 * xlast + w xhi <- Reduce(xnext, x = w, init = 0, accumulate = TRUE) acf(xhi, lag.max = 1, plot = FALSE) wt <- seq(0, 1, len = length(x)) xdynamic <- wt * xhi + (1 - wt) * x get_stats(xdynamic, stat_bandwidth = 100)$stats$autocor ``` ## See Also `acf`, `var`, `kurtosis`, and `skewness` for estimation of properties that are not time-dependent. See `generic_ews` for another approach to estimation of time-dependent properties.

get_stats function