# PERIODOGRAM - Periodogram Power Spectral Density (PSD) Estimate

Calculates the periodogram power spectral density estimate value of a time series.

## Syntax

Periodogram(X, Order, Option, $\alpha$)

X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

Order is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).

Order Description
1 ascending (the first data point corresponds to the earliest date) (default)
0 descending (the first data point corresponds to the latest date)

Option are the pre-processing flag for the input time series (1 = none (default), 2 = detrend-only, 3 = difference only, 4 = auto processing).

Method Description
1 None (default)
2 Detrend (Remove deterministic trend)
3 Difference (1-L)
4 Automatic (detrend/difference)

$\alpha$ is the statistical significance level (i.e. alpha) - Needed for the auto-processing procedure. If missing or omitted, an alpha value of 5% is assumed.

## Remarks

1. The time series is homogeneous or equally spaced.
2. The time series may include missing values (e.g. #N/A) at either end.
3. In the auto-processing option, the periodogram function uses ADF test to examine stationarity and differentiate between a deterministic trend and a stochastic drift.
4. The step (k) must be less than or equal to the time series size, or else an error value (#VALUE!) is returned.
5. The PERIODOGRAM function is available starting with version 1.64 TURRET.

## References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
• Chan, K. H., Hayya, J. C., & Ord, J. K. (1977). A note on trend removal methods: The case of polynomial regression versus variate differencing. Econometrica, 45, 737–744.
• Ayat, L., & Burridge, P. (2000). Unit root tests in the presence of uncertainty about the non-stochastic trend. Journal of Econometrics, 95, 71–96.
• Dickey, D. A. (1984). Power of unit root tests. Proceedings of Business and Economic Statistics Section of ASA, pp. 489–493.
• Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.
• Diebold, F. X., & Kilian, L. (2000). Unit root tests are useful for selecting forecasting model. Journal of Business and Economic Statistics, 18, 265–273.