# Detecting significant trend / non-stationarity in small sample time series

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:

 acf(ts\$size)


Am I using the right approach, or may more conventional regression/correlation methods appropriate?

• You are on the good way. Gathering more data is still recommended, though – David Jun 18 at 14:36