I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?
Okay so the first thing you need to understand is that when you're analysing a time series plot, there are two main features:
(a) Trend - increasing (upward) or decreasing downward
(b) Variation - seasonal (pattern), cyclical (pattern) or random.
Seasonal variation can easily be identified by looking at a period of one year or less and observing evidently regular fluctuations (i.e. troughs and peaks occur at consistent time intervals over the time frame under analysis.
Now its one thing to identify seasonal variation, and another to determine trend. I had a TIME SERIES SAC today and my time series plot showed a decreasing (downward) trend with seasonal variation. Just note that in order to calculate seasonal indices, you MUST have a seasonal component (i.e. seasonal variation). Just a tip if you're stuck with what type of variation you've got.
Trend can be identified two ways. Firstly, sometimes its extremely easy to see a visible trend simply by looking at the graph, usually if you have a fair few plotted points (i.e. 8 points +). However, sometimes you have insufficient points to see any visible trend, and a tip would be to simply use your calculator to find the regression line of your time series plot; if the gradient/slope is (+), you're looking at an increasing trend, and (-) slope/gradient corresponds to a decreasing downward trend. Sometimes, there is no trend. It is possible to have seasonal variation with NO trend (i.e. over many years, you're having consistency in the seasonal component and the DV does not decrease/increase over the timeframe).
If there is a trend, you can use your rule to see a visible trend simply by looking at the overall trend of the graph, or as mentioned, using your calculator. But if no trend is visible, you practically see that there is no increase/decrease in DV over the timeframe. You can also look at the raw data; if the values of the data decrease over the quarters/months/terms, etc, there is probably going to be a decreasing (downward) trend.
Hope this helped, and best of luck!