“We are not makers of history. We are made by history.” – Martin Luther King, Jr.

Like this quote, Time Series analyses place emphasis on history, or in our case, emphasis on data. For better time series analyses, a full practical history of the data needs to be accounted for with a strong understanding of the context of those data.

There are a few notes about time series analysis one should be aware of.

1. Not all time series are made the same.
2. Do not use a subset of data to make predictions too far out.
3. Time series should constantly be updated with new data.

## Types of Time Series Analysis

There are three main groups of Time Series Analysis Minitab Statistical Software can help analyze. It is best for the analyst to identify these key features.

1. A trend is a general direction of the data. The trend can be linear or quadratic.
2. A season is a repeating cycle of the data.
3. A random time series has no noticeable pattern whatsoever.

Above, an increasing trend is detectable, but there is no seasonal, or systematic pattern, in the series. Trends can be either linear, quadratic, exponential growth, or S-curve. This trend seems to be linear. It is always best to try to keep the simpler model when fitting models.

The series above has both a trend and a seasonal pattern. The seasonal pattern seems to be increasing in effect over time. Notice the widening between the observations. This widening could be a multiplicative pattern. If the seasonal pattern was constant, then an additive model might be better.

Now, this series above does not seem to have any noticeable trend or seasonal pattern. With random data it is very difficult to assume anything systematic to use for prediction, this is when we will depend on the history of the series to make predictions.

There are specific tools in Minitab that can help users forecast these types of series:

• Trend only: Trend Analysis and Double Exponential Smoothing
• Trend and Seasonal: Decomposition and Winter’s Method
• Random: Single Exponential Smoothing and Moving Average

To evaluate the fit of the model, one would need to investigate the accuracy measures: mean accuracy percentage of error (MAPE), the mean absolute deviation (MAD) and the mean squared deviation (MSD). The better the model fits, the lower these values will be. These numbers are not useful alone but in relation to other models.

Below is an example of Trend Analysis with a quadratic and exponential growth model to predict the number of cells growing over time for a pharmaceutical trial to regrow tissue for implants.

Looking at the accuracy measurements, the exponential growth model is better, which leads us to think the fits are more accurate to make better forecasts. Using the better fit the analysts can predict when the full implant will have enough cells for completion.

## Making Realistic Forecasts

The goal of any time series analysis is to make sure we can make realistic forecasts for business decisions. And, if people try to make predictions too far out in time the forecasts could have more errors. In the example below, the first 14 observations were used to forecast the last 14.

The model selected seems to have a good fit, notice the fits are very close to the actual data. But, since we only used 14 data points to predict the last 14, there is more error overtime. Try to avoid forecasting too far out in time. Time Series are very dynamic and should be updated with new data points.

## Time Series Analyses are not Static

To increase the prediction power of the model is to continue to update the model with data. Using the graph above as reference, we added the next 7 data points (Day 15 – 21) to update our forecasts in the below graph. The above graph had much more error for Day 26 compared to the updated data below, here our forecasts are much closer.

## Wrapping Up

Modeling time series analysis requires different methods and comparisons of models. Always check accuracy measurements to see which model is minimizing the errors. It is also good practice to predict forecasts on data you currently have collected to confirm the best fitting model before you make forecasts on unobserved data.