Time Series, Trends and Rates of Change
What Is a Time Series?
A time series is data recorded at successive time points — monthly sales figures, quarterly unemployment rates, annual birth rates. Plotting these values against time produces a time series graph (sometimes called a line chart) that lets you see patterns that would be invisible in a table of numbers.
Trends
The trend is the overall direction a time series is heading in the long run, ignoring short-term ups and downs. A trend might be rising (e.g. average house prices in the UK over decades), falling (e.g. infant mortality rates over the last century), or roughly constant. Identifying the trend is the first step in interpreting a time series.
It is important to distinguish the trend from short-term variation. A shop’s weekly sales might spike before Christmas and dip in January, but the underlying trend over several years might be consistently rising. The trend is what you would see if you smoothed out the seasonal bumps.
A trend is the long-term overall direction. A seasonal pattern is a regular, repeating short-term fluctuation at the same time each year (or each cycle). Both can be present in the same time series.
Seasonal and Cyclic Trends
A seasonal trend is a regular, repeating pattern tied to the time of year. Ice cream sales peak in summer and fall in winter every year; gas and electricity consumption peaks in winter every year; retail sales peak before Christmas every year. These patterns are predictable and expected.
A cyclic trend is similar but not tied to a fixed calendar period — it represents a pattern that rises and falls over a longer, less regular time scale (such as economic business cycles that might last several years). The specification uses the term “cyclic” as well as “seasonal” and you should be able to interpret both.
When a question asks you to use a seasonal or cyclic trend to make a prediction, always say: “Based on the seasonal pattern in the data, I would expect [variable] to [rise/fall] in [period] because [reason from the pattern].” Predictions based on time series should acknowledge that the pattern may not continue indefinitely.
Rates of Change
A rate of change expresses how quickly something changes over time. Rather than just showing the raw count, a rate puts change in proportion — allowing meaningful comparison between populations of different sizes or time periods of different lengths.
The specification covers several specific rate measures used in real UK contexts. These include the birth rate (number of live births per 1,000 people per year), the death rate (number of deaths per 1,000 people per year), house price change, and unemployment rates. All rate-of-change formulae will be given in the question — you will not be asked to recall them from memory. What matters is reading the formula carefully and applying it correctly to the data given.
A larger country has more births per year than a smaller one, simply because it has more people. Comparing raw birth counts tells you little. The birth rate (births per 1,000 population) corrects for population size, allowing a fair comparison between countries or regions of different sizes.
Similarly, a rise in the number of deaths does not necessarily mean mortality is worsening — the population may have grown or aged. The death rate puts this in proportion. Always use rates when comparing populations of different sizes.
Index Numbers
Index numbers express a value relative to a chosen base period (usually set to 100). Instead of quoting actual prices or quantities, an index shows how much a value has changed from the base. If the base year has an index of 100 and a later year has an index of 115, then the value has risen by 15% from the base.
UK economists and statisticians use three important index numbers that you should know by name:
- RPI (Retail Price Index): Measures changes in the average price of a basket of goods and services purchased by households. Published monthly by the ONS, it is a legacy measure used for long-term indexation, including index-linked gilts and bonds.
- CPI (Consumer Price Index): Similar to RPI but uses a different methodology and basket of goods. The Bank of England uses CPI as its target measure for inflation.
- GDP (Gross Domestic Product): Measures the total economic output of a country. GDP index tracks growth or contraction of the economy over time.
RPI and CPI both measure price inflation, with RPI and CPI differing in methodology. GDP measures total economic output. All three are published by UK government bodies and used in policy decisions. All rate-of-change formulae are given in the exam — focus on reading and applying them, not memorising them.
Calculating Rates of Change
At Foundation and Higher tier, you may be asked to calculate rates of change from tables using a formula that is given in the question. Typical examples include: calculating a birth rate from a table of births and population figures, or calculating a percentage change in house price from year-to-year data.
The key skill is identifying the right values to substitute into the formula. Read the column headers carefully to identify which values go where. State your working clearly and give your answer in the correct units (rates are usually expressed per 1,000 or as a percentage).
Weighted Index Numbers (Higher)
A weighted index number assigns different weights to different items based on their importance in a typical household’s spending. For example, if a family spends 40% of its budget on housing and 5% on entertainment, housing gets a much larger weight in the index. A simple (unweighted) average of all price changes would understate the effect of rising housing costs on the household’s total bill.
The CPI and RPI are both weighted indices. The formula for a weighted index will be given in the question. Your task is to apply it correctly: multiply each item’s price relative by its weight, sum these products, and divide by the sum of the weights.
When asked to interpret a time series graph in the exam, work through these steps:
- State the overall trend — is it rising, falling, or steady over the period shown?
- Identify any seasonal pattern — is there a regular peak and trough that repeats each year or cycle?
- Note any unusual features — a sudden spike or dip that breaks the trend; is there a plausible real-world explanation?
- Quantify where possible — “the value rose from approximately 40 to 65 between 2010 and 2020” is better than “it went up.”