TD_CUMUL_PERIODOGRAM is a cumulative periodogram statistics test, also known as Bartlett's test. It determines if any periodicities (seasonal cycles) exist in the residual series being tested. This function is typically used, but not limited to, testing the residuals that remain after an ARIMA validation exercise.
The cumulative periodogram statistical test involves calculating the cumulative periodogram, which is the sum of the periodogram values over a range of frequencies. The test does not require assumptions about the distribution of the data. It does require that the time series is stationary and has a finite second moment. The test compares a theoretical reference distribution derived from the null hypothesis that the time series is purely random. If the cumulative periodogram exceeds a certain critical value, the null hypothesis is rejected, and the time series exhibits some form of periodicity.
The functionality of TD_CUMUL_PERIODOGRAM is similar to the TD_SIGNIF_PERIODICITIES function, with the exception that the TD_CUMUL_PERIODOGRAM function tests periodicities at the same time instead of sequentially.
TD_CUMUL_PERIODOGRAM is used in signal processing, econometrics, and finance. It is useful for detecting seasonal patterns in time series data, such as sales data, stock prices, or weather data.
- Use TD_ARIMAESTIMATE to estimate the coefficients for an ARIMA model. Set FIT_PERCENTAGE to some value less than 100% to reserve some of the dataset for model validation.
- Use TD_ARIMAVALIDATE to validate the ARIMA estimate model created in the previous step. Set RESIDUALS to 1 to force the generation of an ARTFITRESIDUALS layer.
- Use an ART_SPEC to directly pass the TD_ARIMAVALIDATE ART to TD_CUMUL_PERIODOGRAM for the testing of the residuals in the ARTFITRESIDUALS layer.
- Select the results from TD_CUMUL_PERIODOGRAM to see the null hypothesis result. ACCEPT means no significant periodicities were found. REJECT means that apparent significant periodicities were found.
- [Optional] Use TD_PLOT to plot the contents in the ARTCPDATA layer.