1. FOURIER-BASED STUDY OF THE OSCILLATORY BEHAVIOR OF THE TELECOMMUNICATIONS INDUSTRY Federico Kuhlmann, Maria Elena Algorri, Christian Norman Holschneider Flores Instituto Tecnológico Autónomo de México Digital Systems Department Mexico

2. Introduction  Eli M. Noam has recently discussed long-term lessons of the recent upturn and downturn in the telecommunications industry.  One of the theories (Austrian theory) was used to explain industry behavior; has its focus on the creation of a large overcapacity.  Various network operators have over-optimistically projected long distance market growth.  Noam speculates that cyclicality will be an inherent part of the telecom sector in the future - investors will very likely seek consolidation and cooperation.

3. Objective  Identify variables in telecom industry, which have oscillatory behavior.  Analyze and characterize these variables.  Use historical “oscillatory” trends to construct near- term future scenarios.

4. Approach  Identify variables with oscillatory behavior.  Use signal processing techniques (DFT) to characterize oscillations, based on historical data.  “Remove” low energy components which are disturbances (deviations from macro-trend). “Keep” high energy components, which are associated with macro-trends.  Reconstruct signal and construct a “harmonic” extrapolation to imagine near-term future.

5. Discrete Fourier Transform (DFT)  The DFT provides a frequency representation of a finite duration time sequence.  Useful to analyze phenomena that display oscillatory behavior.  Allows identification of possible periodicities and measurement of the relative magnitudes of periodic components.

6. Application a) The yearly variation of the indicator (e.g., Telecom Investments) is calculated. b) The DFT is applied to the time series of (a), yielding a frequency representation of the data. c) The frequency components with less energy are eliminated. d) The inverse Fourier transform of the remaining frequency components is calculated. e) Assuming that the macro-trends will not suffer major changes, the future values of the indicator can be now calculated by replicating the sequence in (d).

7. Total Telecom Investment Worldwide Telecom Investments display a “reasonably” steady growth trend 1975-2000. No “noteworthy” harmonic behavoir

8. Total Telecom Investment However, year-to- year incremental values display clear oscillatory behavior.

9. Analysis  The “macro” trends, which could likely appear again in the future, are the highest energy spectral components of the DFT.  The lower energy spectral components originate the generally slight deviations from this general trend.  Most of the lower energy components are in the higher frequency band (samples 10 to 20). The origin of these low energy components are possibly minor short-term (i.e., fast) perturbations, which very likely will not reappear again in the future.  

10. Analysis (contd.)  Increasingly eliminate lowest energy spectral components, until the total energy of the signal is reduced by 30%. (Up to this value the distortion, which was introduced to the original data, was not significant).  Retain high energy components (macro trends) and calculate Inverse Discrete Fourier Transform (IDFT) of remaining components.  The general form of the time series has little variation. The loss of high frequencies eliminates large negative isolated peaks, but leaves the slower varying signal unaltered. Possible future behavior:

11. Results  Recover time series from DFT to “predict” the near term future by replicating the data corresponding to years 1975 through 2002, to imagine incremental investment behavior for years 2003 through 2020.  Based solely on the trends contained in recent historical data, a relatively short recovery period could be expected (the next 2 years), which, in turn, could trigger a new contraction period of approximately 5 years.

12. Discussion  Possible explanation: the last few years have witnessed an accelerated growth in capacity deployment, which, as a consequence, had large network portions remaining “dark” and/or underutilized.  The recent down cycle (already showing signs of recovery) will probably not be completely reversed, until a larger portion of the installed capacity is used, a fact which very likely will happen when there is a significant growth on the demand side (for example, with massive offering of wideband and multimedia services using existing networks).

13. 2. Other Applications (contd) Fixed lines, Telmex (deviation from a logistic MMSE trend)

14. 3. Other Applications (mobile subscribers) Mobile subscribers, deviation from logistic projection

15. 4. Other Applications (DLD, Telmex) Traffic data for Domestic Long Distance: Raw Data and Normalized Yearly Variations Investment and Infrastructure can be misleading indicators of the Telecom Industry development

16. Other Applications (contd) DFT Analysis of Traffic Variations, high frequency removal

17. Other Applications (contd) Smoothed Normalized Variations (after high frequency elimination) and extrapolation of data to the near future Note the presence of 2 cycles, a longer one corresponding to small yearly variations, and a shorter one showing more dramatic yearly changes in traffic data.

18. Conclusion The DFT-based method does not pretend to exactly predict industry behavior for the next few years. It allows, however, to construct scenarios, which could eventually be used to design, and implement actions that allow a faster recovery from down- periods, and expand the durations of growth periods. It must be stressed, that these results should be used with caution, to imagine “macro” trend- based possibilities for the near-term future.