I am trying to detect whether there is a significant change in plankton size over time. As I understand, this is referred to as stationarity testing in time series analysis. Unfortunately, my time series only consists of 11 independent observations, seperated by a two week interval. Small smaple size is obviously never an advantage, but I am unsure whether this small size invalidates my approach. See the following code:
size <- c(0.573, 0.679, 0.577, 0.617, 0.520, 0.454, 0.442, 0.505, 0.443, 0.463, 0.383) time <- c(1:11) ts <- data.frame(time, size)
Plotting the data gives the impression that there is a significant negative trend:
library(ggplot2) ggplot(ts, aes(x=time, y=size)) + geom_point(size=3) + geom_line(group = 1,size=1) + geom_smooth(method="lm",se=F) + labs(x="Time",y="Size") + theme(axis.title=element_text(size=16, face="bold"))
The following tests also seem to support the assumption of non-stationarity:
library(tseries) adf.test(ts$size) Augmented Dickey-Fuller Test data: ts$size Dickey-Fuller = -2.0884, Lag order = 2, p-value = 0.5387 alternative hypothesis: stationary kpss.test(ts$size) KPSS Test for Level Stationarity data: ts$size KPSS Level = 0.43085, Truncation lag parameter = 2, p-value = 0.06386 Box.test(ts$size, lag=10, type="Ljung-Box") Box-Ljung test data: ts$size X-squared = 25.178, df = 10, p-value = 0.005018
A simple acf-plot, however, does not indicate non-stationarity:
Am I using the right approach, or may more conventional regression/correlation methods appropriate?