lecture 8 - time series data

Question 1

what is time series data?

Answer 1

x(t)

anything attached to a time stamp e.g. months, years, seconds

Question 2

when studying time series data we are interested in?

Answer 2

• any changes in a specific variable over time
• obvious oscillations
• obvious trends

Question 3

data and patterns can be considered as:

Answer 3

• random
• clustered
• cyclic
• chaotic

Question 4

what are the different components of a time series?

Answer 4

• trend component
• periodic component
• random noise component

Question 5

what is interpolation?

Answer 5

the estimation of an unknown quantity between two known quantities

Question 6

types of interpoaltion

Answer 6

• linear
• nearest neighbour
• cubic

Question 7

steps of linear interpolation

Answer 7

1 - identify the gap
2 - subtract the difference between the values before and after the gap
3 - divide this by the number of missing values +1
4 - either add the answer to the data point (if ascending)
OR subtract (if descending)

Question 8

what is signal processing?

Answer 8

the alteration of a time series to extract specific components to reduce noise

Question 9

define noise

Answer 9

the amount of unexplained variation in a sample

Question 10

reducing noise is also known as?

Answer 10

smoothing

Question 11

methods of smoothing

Answer 11

• moving average

- Savitzky-Golay filtering

Question 12

root-mean-square

Answer 12

removes negatives

used to determine strength of a signal

Question 13

define frequency

Answer 13

number of cycles or data points within a period of time (generally 1 second)

Question 14

what is a wavelength?

Answer 14

time and distance between 2 identical points e.g. peak to peak

Question 15

what is amplitude?

Answer 15

height of the wave (from zero)

also known as power or force

Question 16

what is phase?

Answer 16

refers to the difference between troughs and peaks in amplitude

Question 17

what does “in phase mean”?

Answer 17

2 datasets are identical - matching peaks and troughs

Question 18

what does anti-phase mean?

Answer 18

the peak in one signal is directly above the trough in another

Question 19

Savitzky-Golay filtering is better than moving average for:

Answer 19

• preserving the periodic component

- where there is a lot of high frequency noise on low frequency signals

Question 20

Savitzky-Golay filetring uses?

Answer 20

polynomial least squares

Question 21

what does polynomial mean?

Answer 21

equation with multiple terms

Question 22

polynomial least squares performs

Answer 22

a curved fit - not linear

Question 23

time series regression

Answer 23

y = a + bx + u
*x = the timestamp

Question 24

how do you assess normality?

Answer 24

use a Q-Q plot (Quantile-Quantile plot)

compares the quantiles of a variable against theoretical quantiles of one with a normal distribution

Question 25

what is a quantile?

Answer 25

subdivision of a dataset whereby an expected number of values would be expected

Question 26

sample autocorrelation:

Answer 26

detects oscillations
assumes that the periodic component is stable
correlates the series against itself and an identical dataset which is shifted by a range of lags

Question 27

cross-correlation determines?

Answer 27

links between offset data

Question 28

the aim is to remove the noise component to reveal?

Answer 28

• trend component

- periodic component

Question 29

why do we smooth data?

Answer 29

• to reduce noise
• to find the trend component
• to find the periodic component