spaero (version 0.1.0)

get_stats: Get estimates of time-dependent statistics.

Description

get_stats estimates time-dependent statistics from ensemble time series.

Usage

get_stats(x, center_trend = "grand_mean", center_kernel = "gaussian",
  center_bandwidth = NULL, stat_trend = "local_constant",
  stat_kernel = "uniform", stat_bandwidth = NULL, lag = 1)

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

Bandwith of kernel for any local detrending done. A numeric value >= 1.

stat_trend

Character string giving method of smoothing statistics estimated. Allowed values are '"local_constant"', and '"local_linear"'. Will be partially matched.

stat_kernel

Character string giving the kernel for local smoothing of estimated statistics. Allowed values are '"gaussian"' and '"uniform"'.

stat_bandwidth

Bandwith of kernel for local smoothing of statistics. 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 positive.

Value

• A list with elements '"stats"', '"centered"', '"stat_trend"', '"stat_kernel"', '"stat_bandwidth"', and '"lag"'. "stats" is a list containg vectors of the estimated statistics. '"centered"' is a list of the detrend 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.

'"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 to calculate each statistic.

See Also

acf, var, kurtosis, and skewness for estimation of statistics that are not time-dependent.

Examples

# 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