6.1: Descriptions
- Page ID
- 121977
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- Stochastic - random elements that incorporate uncertainty of measurement to functional form
- Deterministic - something for which written functional form can be produced
- Periodic - repeats the trend/behavior at some frequency
- Recall simple periodics have single frequency \[ x(t) = A\cos(\omega t) \]
- Complex periodic functions have multiple combination of characteristics that can be summed together: \[ y(t) = A_{0} + \sum_{i} C_{i}\cos(2\pi f_{i} t + \phi_{i}) \]
- Subscript \(i\) indicates a unique combination of amplitude, frequency, and phase shift
- Time \(t\) is the continuous variable
- Adding more combinations \(i \rightarrow \infty\) gets closer to representing observations
- Observed results can be combination of all three features
- Isolation of terms within deterministic functions already covered in weighted-least-square regression
- Periodic representation can be determined from Fourier coefficients of \(C_{i}\) (section 6.2)
- Stochastic features can be removed through statistical or filtering mechanisms (section 6.3)