Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Time Series Testing data analysis tool which consolidates many of the capabilities described in this part of the website.
To use this tool for the data in Example 1 of Stationary Process (repeated in Figure 1), press Ctr-m and choose the Time Series option. Select the Testing option on the dialog box that appears and click on the OK button. Now, fill in the dialog box that appears as shown in Figure 1.
In Figure 1 we have inserted the time series values in the Input Range field, without column heading or date information. You can optionally request the ACF, ACVF and/or PACF values by placing a positive integer value in the corresponding field. In Figure 1 we have requested the ACF(k) values for lags k = 1, 2, 3, 4, 5. We could have requested any combination of ACF, ACVF or PACF values, or none at all.
Similarly, we can request any combination of the white noise tests (Bartlett’s, Box-Pierce, Ljung-Box) or none at all by inserting a positive integer in the corresponding field. In Figure 1 we have requested only the Ljung-Box test on ACF for lags up to 5.
Finally, we can optionally request the ADF test by inserting a non-negative integer value (including 0) in the # of Lags field or by leaving this field empty and selecting the Schwert option. We can also request to use the Drift or Trend options of the test. In Figure 1, we have requested the test with drift based on the number of lags specified by the Schwert criterion.
Figure 1 – Time Series Testing data analysis dialog box
The Schwert criteria calculates the lag based on the Excel formula
=ROUND(12 * (n / 100) ^ (1 / 4), 0)
which in this case is ROUND(12*(22/100)^(1/4),0) = 8. The AIC criteria is then used with lags = 8.
The output for this analysis is shown in Figure 2 (only the first 12 of the 22 data elements are shown in columns D and E).
Figure 2 – Time Series data analysis
The first 5 ACF values are shown in column H. The Ljung-Box test gives a significant result (cell M6), which means that at least one of the first 5 autocorrelations is significantly difference from zero. The Augmented Dickey-Fuller test shows that the time series is not stationary (cell P13).
Example 2: Repeat Example 1 on the first differences of the data in Example 1.
We fill in the dialog box shown in Figure 1 with two changes, namely we change the # of Diff field from the default value of zero to 1 and used the ADF test without drift. The result is shown in Figure 3 (only the first 12 of 21 data values is shown in columns D and E).
Figure 3 – Time Series data analysis after differencing
This time we see that the first five ACF values are not statistically different from zero (cell M6) and that the data is stationary (cell P13).
