Time Series

Question 1

Preprocessing time series

Answer 1

Techniques assume independence between time points
Hence need to verify correlation between data
Because proba characteristic should not change overtime: weak stationarity

Data will have trends, seasonality, … such non stationarity characteristics need to be removed

x=trend+season+stationary remainder

Question 2

Trend

Answer 2

the general tendency of the data to increase or decrease during a long period of time. A trend is a smooth, general, long-term, average tendency. It is not always necessary that the increase or decrease is in the same direction throughout the given period of time.

Question 3

Seasonality

Answer 3

cycles that repeat regularly over time; a repeating pattern

Question 4

stationary time series

Answer 4

A time series is stationary if its statistical properties are all constant over time. More specifically a stationary timeseries has the following properties:

no trend
variations around its mean have a constant amplitude
it wiggles in a consistent fashion (i.e., its short-term random time patterns always look the same)

Question 5

unit root

Answer 5

proof that it has a trend
If a time series has a unit root, it shows a systematic pattern that is unpredictable.
If the time series follow the line then it has trend hence it is not stationary (thus even if time series go away from line at times, it would always go back to it).

Question 6

correlogram

Answer 6

check that a time point does not help predict the next one. Once that the correlation is 0
if doesn’t help then it is stationary
having a point outside the red region is evidence against randomness

Question 7

Difference Partial Autocorrelation and Correlogram ?

Answer 7

Correlogram just looks at correlation between a time point and the next one to see if can predict. However, the time point could itself be correlated with the previous one and thus contain information from it. Partial does the same principle of looking at a time point and its relation to the next one but make sure to remove the dependence that can be found with other points.