A time series is a collection of values over time. You can analyze time series data using two approaches:
- Time-domain approach: Data occurs discretely at equally-spaced time intervals.
- Frequency-domain approach: Data is continuous - this uses sine and cosine somehow.
Some non-standard features of time-series data are:
- Unequally spaced data (missing values)
- Continuous-time series
- Aggregation
(!) When you aggregate data, it does not behave in the same way as the original data set!
Time series may be considered to be composed of unobserved components. Statisticians try to decompose time series into their constituent parts through the unobserved components method (UC method).
Time-series data comprises four components:
- Trend, y(T): Slow variation over the period of years caused by structural factors
- Cyclical, y(C): Quasi-periodic fluctuation characterized by alternating periods of expansion and contraction
- Seasonal, y(S): Effect of climactic and institutional events that repeat more or less regularly each year
- Irregular, y(I): Unforseeable movements related to various events. These can be well-behaved or be extreme values (outliers).
Trend, cyclical and seasonal effects are signals, while irregular effects are noise. Sometimes, trend and cyclical effects cannot be separated, so they are considered one component, y(TC).
Seaonality may be caused by:
- Calendar effects: Dates of national holidays
- Institutional factors: Tax periods, bonuses, dividends
- Weather or climate
- Expectations
Seasonal adjustment: The isolation of seasonal fluctuations
This is done in a 3-step process:
- Identification: Test for the presence of seasonality
- Estimation: Measure the magnitude of seasonal effects
- Removal: Extraction of seasonal variations from the series
The result is a seasonally adjusted, or deseasonalized series.
The reasons for seasonal adjustment are:
- To facilitate the interpretation of data without significant loss of information
- To use seasonally adjusted series in models.
“Seasonal adjustment is done to simplify data so that they may be more easily interpreted by statistically unsophisticated users without a significant loss of information.” (Bell and Hellmer, 1992)
NB: For non-seasonally adjusted data that exhibit seasonality, rates of growth should be compared year-on-year.