Finding Hidden Patterns in Datasets: Flowchart

The following flowchart suggests a strategy for analyzing a data set, using the tools presented in this dissertation. Section 3.4 contains examples illustrating the application of the procedure presented here.

Data Set $$\{(t_i,y_i)\}_{i=1}^N$$

$\boldsymbol\downarrow$

(Possible Pre-Processing of Data)

Locate repeated time values; arrange time values in increasing order; check for uniform time list, Section 1.2

Remove NaN's, Section 3.4

Noise removal; use smoothing filters, Chapter 3

Interpolation, to achieve a uniform time list, Section 2.5

$\boldsymbol\downarrow$

Is data a sum of relatively prime cycles? Section 1.3

$\boldsymbol\downarrow$

Is it likely that the data was randomly generated? Section 2.1

$\boldsymbol\downarrow \text{YES}$

$\boldsymbol\downarrow \text{NO}$

Search for deterministic components may be fruitless. See if Section 2.1, Economics Application, applies.

Are there specific conjecture components?

(If NO, go to bottom of page.)

YES
$\boldsymbol\swarrow$

YES
$\boldsymbol\downarrow$

Linear least-squares approximation, Section 2.2

Large condition numbers? Section 2.3

Nonlinear least-squares, Section 2.4

Gradient methods, a Genetic Algorithm

Sinusoidal components? Filters, Chapter 3

Unknown periodic content; the Periodogram, Section 2.6

Efficient implementation via the Discrete Fourier Transform, Section 2.7