T1. Time Series Data Flashcards
What are time series data?
A sequence of data points recorded in chronological order.
When are observations made?
At equally-spaced intervals in time (e.g. annually, monthly, weekly)
Key difference between time series data and cross-sectional data
Cross section data are (can be?) independent, time series are not.
5 phenomena of time series data
Trends, breaks, seasonality, cycles, noise
What is meant by trends in time series data?
The gerenal direction in which time series data develops
How can linearise trends in data?
Applying approriate transformation (e.g. taking logs).
What is meant by breaks in time series data?
Variations that occur due to sudden causes and are usually ex ante unpredictable (but usually rationalisable with hindsight).
What is meant by seasonality in time series data?
A predictable periodic pattern that recurs or repeats over regular intervals.
What is meant by cycles in time series data?
Cycles occur when a series follows an up and down pattern that is not seasonal.
4 phases of cycles
Peak, recession, trough, expansion
How are cycles different from seasonality?
The periodicity of cycles is variable and the durations of each phases in the cycle also varies.
What is meant by noise in time series data?
Some time series are highly unpredictable. Pure as-if-random noise for example is often an irreducible component of time series.
Time series data notation
Xt denotes a variable observed at time t.
where t = 1, 2, 3, … is the sequence
Notation for 1st, 2nd, and h’s lag
The first lag of the variable is the value in the periods before: Xt-1
The second lag of the variable is the value two periods before: Xt-2
h’s lag: Xt-h
Notation for h’s lead
h’s lead is Xt+h
Equation for autocorrelation
Correlogram for strong autocorrelation with past values
Correlogram for strong seasonal correlation
Correlogram for no correlation with past values
