Many time series change in cycles, with increases and decreases that cannot be explained by a smooth trend line.
Seasonal patterns
Some cycles are seasonal. Seasonal patterns are distinguished by a period that repeats exactly — for example, monthly data has a period of exactly 12 months.
Seasonal patterns are not usually referred to as 'cyclical'.
Cyclical patterns
Other cycles repeat much less regularly. Sun-spot activity has cycles of approximately 11 years, and the 'business cycle' can be anywhere between 3 and 10 years. In both cases, different cycles are not exactly the same length.
The AR(1) method can be used to obtain forecasts for cyclical data with irregular cycle lengths.
We will not distinguish cyclical patterns from other forms of autocorrelation here.