Can we reliably forecast individual 3G usage data?

1. Cosmo Zheng Can we reliably forecast individual 3G usage data? An analysis using mathematical simulation of time series algorithms

2. Background • Fluctuations in daily demand for bandwidth make ordinary usage pricing inefficient • Solution: Time-dependent pricing to persuade users to defer usage http://scenic.princeton.edu/tube/overview.html

3. Our Problem • Users must be informed of expected future prices, to assess the costs of deferring usage • We need a reliable way to predict future usage based on past data http://scenic.princeton.edu/tube/technology.html

4. The Algorithms • Nonlinear regression – generate a fitted function of the form D + A*sin(2πt/24) + B*sin(2πt/12) + C*sin(2πt/6) • Use fitted function to extrapolate

5. Algorithms (cont.) • Time series decomposition – isolate trend, seasonal, and residual components • Extend trend and seasonal components into the future

6. Algorithms (cont.) • Exponential smoothing – generate {St} based on a weighted average of previous data • Simplest form is S1= X0, St = αXt-1 + (1-α)St-1 for t>1, where α is a smoothing factor

7. The Data • Use simulated datasets, representing usage each hour over 5 days • {Xt} for 1 <= t <= 120 • First 4 days are historical data (training set), 5th day is the test set

8. Algorithm 1: Regression

9. Regression (cont.) R2 = 0.424

10. Algorithm 2: Decomposition

11. Decomposition (cont.) R2 = 0.693

12. Algorithm 3: Smoothing

13. Smoothing (cont.) R2 = 0.516

14. Additional Trials Sum of absolute error R2

15. Conclusions • Time series decomposition provided most accurate prediction of future usage, followed by exponential smoothing, then regression • Possible explanation: usage pattern is strongly cyclic; repeats itself on a daily basis • Suggestion: investigate further into better means of isolating seasonal data; some more sophisticated algorithms exist (ARIMA, stochastic volatility models).