Q.Moving averages are useful in identifying ______.

5-year moving totals $=30,35,35,34,35$; dividing by 5 gives trend values $6, 7, 7, 6.8, 7$ centred on 1976–1980.

Data (production in '000 metric tons):

A 5-yearly moving average is found by summing five consecutive values and dividing by 5, and the result is written against the middle (3rd) year of that group.

5-year moving totals and averages:

• $1974\text{–}1978$: $0+4+9+9+8 = 30 \Rightarrow 30/5 = 6$ (centred 1976)
• $1975\text{–}1979$: $4+9+9+8+5 = 35 \Rightarrow 35/5 = 7$ (centred 1977)
• $1976\text{–}1980$: $9+9+8+5+4 = 35 \Rightarrow 35/5 = 7$ (centred 1978)
• $1977\text{–}1981$: $9+8+5+4+8 = 34 \Rightarrow 34/5 = 6.8$ (centred 1979) …

A moving average averages successive groups of values, cancelling short-term ups and downs and revealing the smooth long-term direction of the series — the trend component.

A time series has four components: trend, seasonal, cyclical and irregular. The method of moving averages computes the average of a fixed number of consecutive observations and slides this window along the series. Averaging tends to cancel the seasonal, cyclical and irregular fluctuations (which oscillate above and below the general level), leaving behind the …