Multiple Time Series: Seeing the Whole Picture, Not Just One Line

Think of a single time series like tracking the height of one plant in your garden every day. You get a single line going up or down. That tells you something, but it doesn't tell you why the plant grew. Did it rain? Did the temperature rise? Did you add fertiliser?

Now imagine you track the plant's height and the daily rainfall and the average temperature and the amount of fertiliser you added — all for the same days. You now have multiple time series. You can see how one thing moves with another. That is the core idea.

The Precise Meaning

A multiple time series is a set of two or more time series recorded over the same time period. Each series is a sequence of observations of a different variable, taken at regular intervals (daily, monthly, yearly). The key is that they share a common time index — you can line them up side by side.

For example, for the years 2000–2024, you might have:

• India's GDP (in ₹ crore)
• India's total exports (in ₹ crore)
• India's total imports (in ₹ crore)

Each of these is a single time series. Together, they form a multiple time series.

Why It Matters in Economics

A single time series tells you what happened. Multiple time series help you understand relationships between economic variables. This is the foundation of almost all empirical economics.

Consider the relationship between consumption and income. You could plot India's National Disposable Income (NDI) and Private Final Consumption Expenditure (PFCE) year after year. You would see that when NDI rises, PFCE generally rises too — but not by the same amount. That difference is the marginal propensity to consume (MPC), a core concept in macroeconomics.

The Formula That Connects Them (National Income Identity)

In macroeconomics, the most famous multiple time series relationship is the expenditure method of calculating GDP. It is not a statistical formula for the series themselves, but an accounting identity that must hold for every time period.

Where:

• $GDP$ = Gross Domestic Product at market prices (one time series)
• $C$ = Private Final Consumption Expenditure (another time series)
• $I$ = Gross Fixed Capital Formation + Change in Stocks (another series)
• $G$ = Government Final Consumption Expenditure (another series)
• $X - M$ = Net Exports = Exports minus Imports (two more series)

For every year, this identity must be true. If you have the time series for $C$, $I$, $G$, $X$, and $M$, you can compute the $GDP$ series. More importantly, you can see which component contributed most to a change in GDP in a particular year. Was it a jump in investment ($I$) or a fall in net exports ($X-M$)? …