Chapter 2 (Time series graphics) Flashcards
Index Variable
Indexes the time series, different points in time (eg. Monthly, quarterly, yearly)
Key variables
Determines the different unique time series
Measured variables
Values we might wish to model, also y-values
Trend
A long-term increase or decrease in data
Seasonal
A series is influenced by seasonal factors
Always of a fixed and known period
Cyclic
Data exhibit rises and falls that are NOT of a fixed frequency (duration at least 2 years)
Difference between seasonal and cyclic patterns
Seasonal pattern constant length; cyclic pattern variable length
Average length of cycle longer than length of seasonal pattern
Magnitude of cycle more variable than magnitude of seasonal pattern
Seasonal plot
Data is plotted against the individual “seasons”
Seasonal subseries plot
Data for each season is collected together in separate mini time plots
Scatterplot
Visualise the relationship between the variables
Correlation Coefficients
measures the strength of the linear relationship between two variables
‘r’ lies between -1 to 1
Lag plots
Enables us to look at how different values of the time series relate to lagged values in the same series
Autocorrelation
measures the linear relationship between lagged values of a time series
Trend and seasonality in ACF plots
Trend: autocorrelations for small lags tend to be large and positive and slowly decrease as lags increase
Seasonal: autocorrelations will be larger for the seasonal lags than for other lags (scalloped shape)
White noise
Time series that show no autocorrelation (no impact on lagged values)
ACF plot: if spikes exceed blue dashed line, reject hypothesis of white noise. Autocorrelation is present.
