Define cyclical and irregular variation in time series analysis.

• A. Cyclical: rise and fall of frequency at intervals longer than 1 year; irregular: random variation.
• B. Cyclical: monthly fluctuations; irregular: year-to-year changes.
• C. Cyclical: constant frequency; irregular: deterministic.
• D. Cyclical: sudden spikes; irregular: persistent trend.

Answer: (A)

In time series analysis, cyclical variation refers to fluctuations that rise and fall over time spans longer than a year, with periods and amplitudes that are not fixed. These long-term up-and-down movements are often tied to broader forces like economic or business cycles, and their timing can vary from one cycle to the next. Irregular variation is the random, unpredictable part of the series—noise that cannot be explained by trend, seasonality, or cycles. It represents random shocks or measurement error and is typically treated as white noise with no systematic pattern. So the best description is that cyclical changes occur at intervals longer than one year, while irregular changes are random variation.