Data considerations for Partial Autocorrelation

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

Record data in chronological order

Time series data are collected at regular intervals and are recorded in time order. You should record the data in the worksheet in the same order that you collect it. If the data are not in chronological order, you cannot assess time-related patterns in the data. However, you can still use Scatterplot to investigate the relationship between a pair of continuous variables.

Collect enough data to assess trends or patterns

Collect enough data so that you can fully assess trends or patterns in the data. Minitab displays correlations for only the first n/4 lags. So if you have monthly data, you'll need a large sample size when you want to determine the seasonal model. For example, you need at least 144 observations to see up to lag 36 in the autocorrelation plot.

Collect data at appropriate time intervals

Choose the time interval based on the patterns that you want to detect. For example, to look for month-to-month patterns in a process, collect data at the same time each month. If you collect data each week, then the monthly pattern may be lost in the noise of the weekly data. If you collect data each quarter, the monthly pattern may be lost when it is averaged out in each quarter.

If you are looking only for general trends or shifts in the data over time, and not for patterns associated with a specific time interval, the length of the interval is less important.

The data should be stationary

A stationary time series has a mean, variance, and autocorrelation function that are essentially constant through time. The data is non-stationary when there is a large spike at lag 1 that slowly decreases over several lags. If you see this pattern, you should difference the data before you attempt to identify a model. To difference the data, use Differences. Once you difference the data, obtain another partial autocorrelation plot.

The same pattern may occur at the seasonal lags. That is, a large correlation occurs at the first season lag and decreases over several seasonal lags. If you see this pattern, you should difference the data using a lag equal to the seasonal length before you attempt to identify a model.