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:

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"))

enter image description here

The following tests also seem to support the assumption of non-stationarity:

	Augmented Dickey-Fuller Test
data:  ts$size
Dickey-Fuller = -2.0884, Lag order = 2, p-value = 0.5387
alternative hypothesis: stationary

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:


enter image description here

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

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

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