Time Series Regression – Difference Between Time Series Regression and Forecasting

forecastingtime series

I often see the concepts Time Series Regression and Time Series Forecasting refering to something similar but I don't see clearly what's the difference among these two concepts. By now, the idea I have for each concpet is the next one:

  • Time Series Forecasting: The action of predicting future values using previously observed values.

  • Time Series Regression: This is more a method to infer a model to use it later for predicting values.

But so many times, I see people use the second concept to refer to the first one. I don't know if this is correct or if I am missing something. If anyone can help me make myself clear I would appreciate it

Best Answer

In principle what you have said captures the difference. But may be people refer TS Forecasting as TS Regression because technically, TS forecasting involves TS regression.

Another point (concerning your second bullet point) is that every TS regression is not necessarily used for predicting. It may simply be for understanding the relationship between two variables.

Consider a very naive example:

$$C_t = \beta_0+\beta_1Y_t + \epsilon_t$$ where $C_t$ is consumption, $Y_t$ is income.

In the above example, an economist may simply be interested in estimating, $\beta_1$ which is the marginal propensity to consume. In theory, the same model can be used for predicting $C_{t+h}$ given $Y_{t+h}$. But it is the practice (rather than theory) that is more interesting and complicated. Let me mention just 2 differences between TS regression and forecasting that one experiences in practice:

  1. Take above equation. At a given time, you are likely to have published figures for $Y_{t+h}$ but not $C_{t+h}$. This is where first practical different in TS Regression: Choice of Variables. Forecasting requires leading indicators, i.e. those explanatory variables that are available before the the response variable value is known. Here there is less interest discovering whether the given explanatory variable explains the response variable. Interest is more in how well it can predict the response variable. For example, for forecasting $C_t$ you may want to use volume of credit card transactions. We know that it is obviously going to explain $C_t$ (so not of interest to an economist) but very helpful in forecasting if the data is available in advance.

  2. Diagnostics: In TS regression the diagnostics of regression output usually involves checking for significance of explanatory variables - to ensure how well it explains changes in response variables. In forecasting it may not be so important (Rob Hyndman has given some example somewhere in his blog, I don't remember, however, exact topic). Another example is $R^2$ - important in forecasting, but not as much in general regression. There are many more (frankly, I have been thinking of posting this question for a list of separate diagnostic list for regression and forecasting).

I am sure others here can give some more interesting inputs.

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