Forecasting Concepts

In this activity, we’ll get a quick introduction to two methods for exploring future trends in data: null hypothesis testing and time-series analysis.

With data analytics, we can actually tell the future. This is because the past is the key to the future.

If we have the appropriate statistical tools, we can identify current and past trends and assess whether we think they’re likely to continue. Let’s look at two approaches to forecasting:

Null Hypothesis Testing

With null hypothesis testing, we look at the trends present in our data and assess whether we think they’re real. For example., are they strong enough to be real trends that go beyond just the quirks and idiosyncrasies of your data? Or are they just quirks and idiosyncrasies and aren’t likely to continue.

Example 1

A school principal claims that students in her school score an average of 7 out of 10 in exams. The null hypothesis is that the population mean is 7.0.

To test this null hypothesis, we record the marks of 30 students (sample) from the entire student population of the school (300 students) and calculate the mean of that sample.

We can then compare the (calculated) sample mean to the (hypothesised) population mean of 7.0 and attempt to reject the null hypothesis (the null hypothesis here, that the population mean is 7.0, cannot be proven using the sample data; it can only be rejected).

Example 2

Using another example: The annual return of a particular mutual fund is claimed to be 8%. Assume that mutual fund has been in existence for 20 years.

The null hypothesis is that the mean return is 8% for the mutual fund. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.

Comparing Examples 1 and 2:

For the above examples, null hypotheses are:

• Example 1: Students in the school score an average of 7 out of 10 in exams.
• Example 2: Mean annual return of the mutual fund is 8% per annum.

To determine whether to reject the null hypothesis, the null hypothesis to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0).

Then, if the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be explainable by chance alone, being within the range that is determined by chance alone.

Time-Series Analysis

Whether we wish to predict the trend in financial markets or electricity consumption, time is an important factor that must now be considered in our models.

For example, it would be interesting to forecast at what hour during the day is there going to be a peak consumption in electricity, such as to adjust the price or the production of electricity.

This is where we apply a time-series. A time-series is simply a series of data points ordered in time. In a time series, time is often the independent variable and the goal is usually to make a forecast for the future.

However, other aspects come into play when dealing with time series, which we are not going to go into too much detail here because Excel has amazing tools that can help you to perform an effective time-series analysis.