A moving average is a smoothing technique. It is often used to estimate secular trend in a series. It may be used to roughly make forecasts. However its limitations may include subjectivity of interpretation if used to extrapolate the series.

ARIMA, MCMC and GAMs are stochastic models and their application is not subjective in interpretation. Forecasts based on them are more precise than with moving average.

It is worth noting that the moving average technique, which is the subject of this discussion, is different from the moving average (MA) model which is a special case of an ARIMA model.

Thanks Ette for your clarification. Yes, I’m actually referring to the moving average technique as smoothimg technique.

Moving averages will give you a clearer trend of the data you're showing, but may not represent trends in the population if your index is not well correlated wtih overall abundance. Commercial fisheries data (and a vanishingly small number of recreational/artisinal case studies) are often analyzed with formal assessment models, such as Virtual Population Analyses, Statistical Catch at Age, Delay Difference models, etc. What type(s) of data do you have? You may be able to incorporate multiple data types to get a clearer picture of what's going on and provide a sense of your uncertainty using confidence or credible limits.

Thanks for your answer Brett,

At the moment I have juvenile salmonid densities per 100 square meters at different river locations. The data was obtained by electrofishing the same parts of the river over a period of 20 years. For the same river I have approximately 8 sampling locations per year.

My variables are:

Location Density Year of Sampling

(Sampling site) (density estimate for 100 square meters)

River managers are looking at average density values per river/per site to identify trends over the study period.... but I run a GAM and I just can see no obvious trends.The observed variability in densities per sampling location is so large and I am wondering whether running average can be used as good estimators of the population status in the river.

What would you do in this case?

One possible alternative might be to use Kalman filter techniques for smoothing the data see: Article Simple representation of the dynamics of biomass error propa...

Hey Diego,

Electrofishing is notoriously unreliable for these types of purposes. Usually fisheries data can only really be examined by using some sort of modelling approach (usually GAMM or GLM, mostly log-transformed) to correct for things like region, time, fishing vessel, method, effort, etc...

If one of those methods doesn't help, then you have to find a way to reduce variation, or change the focus of your model (it is possible that you just have too much noise to say anything with any certainty).

For your case, I would use a log-transformation to reduce the observed variation. Worst case you can average-smooth (as you suggest) to reduce noise, but then you're losing data, and I would be very hesitant to make anything of catch trends that were not corrected for abundance. Over 20 years you presumably have different fishermen involved, which can have huge effects on their catch efficiency and effort.

Have you tried looking at the river as a whole just to see if you can identify yearly patterns? If there are none on a whole, you can make the assumption that yearly patterns are not having a large effect, then you can pool your data over the 20 years. At least that way you can potentially identify sites of interest because that will significantly reduce your standard error.

Another alternative is to use site as a continuous variable rather than a factor: consider looking at distance from feature X and use distance rather than site, use that as the primary determinant rather than year.

I'll second Vincent's suggestions (modeling, transformations & pooling). Pooling your data by river may help with the noise and allow you to identify temporal patterns. Keep in mind, of course, that there may not be a 'year' effect!

Have you tried the CMSY method suggested by Froese et al. 2016 in Fish and Fisheries?

Estimating fisheries reference points from catch and resilience.

Rainer Froese, Nazli Demirel, Gianpaolo Coro, Kristin M Kleisner & Henning Winker

Hi Diego,

Are you separating your catches by size? If not, this may also contribute to the variation you're seeing in overall abundance (some years you get a few age-2, others none, etc.)

It's a bit more complicated, but you seem to have a good sampling design; if I were analyzing the data I would think if using a Bayesian hierarchical model, with capture probability at each site/year as a random variable. This method helps sites with poor estimates of capture probability benefit from sites with good capture probability. Capture probability could also grouped by site. You can then estimate annual trends in total abundance across all your sites (which is probably more defensible than extrapolating to the entire river).

Send me an email if you'd like and I'll try and cook up some code for you.

Moving average is fairly good but LOWESS-0.8 is better.