What is a time series forecast?

Answer 1

Short Answer: Time series forecasting is a type of statistical modeling in which the data are chronologically ordered and each data point is assumed to depend on the previous data points.

Long Answer: Here's the shortest summary I can give you. Fair warning, some of it will be gross (over)simplification.

In statistics, we have the idea that we can take quantitative independent variables (X₁, X₂, X₃,....) and use a linear sum of them to predict the value of a dependent variable (Y). In equation form, that looks like:

Y = c₁X₁ + c₂X₂ + c₃X₃ + ... + c_nX_n + ε

The c's are constants that express how significant its independent variable is on Y and ε (epsilon) is a kind of fudge factor for variance.

The values of the c's are calculated through a technique called linear regression, by using actual data. For instance, maybe you want to predict house values with characteristics of the neighborhood the house is in (e.g. population density, average income per capita, local tax rates, crime rate, etc.) For many data sets, each data point is assumed to have no effect on any other data point.

And then there's data where there's a very definite impact of each data point on each other - the weather and stock market prices, for example. Each data point depends on the data points that precede it. This is where a time series forecast comes into play. So instead of that first equation, you have something like:

Y_i = c₁X₁ + c₂X₂ + c₃X₃ + ... + c_nX_n + k₁Y_i-1 + ... k_jY_i-j + ε

The ε and the X portions are the same here. But do you notice how the Y on the left is now indexed? And there are Y's on the right that have a negative term in the index? That's simply math for, you have to add in the j terms preceding Y_i to predict the value of Y_i.

And that's what constitutes a very simple time series model.

Cheers!

TMC