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

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

## Files Examples

## 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.

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