Flashcards in Time Series Analysis Deck (16):
Define time series.
A collection of well-defined data items obtained through repeated measurements over time.
Consistently measured at equally spaced time intervals.
Time is 1 variable (x-axis).
Has a natural order.
Define time intervals.
The time intervals at which the same data is collected.
Examples of time intervals.
What are the 3 components in a time series (the 3 component model)?
Underlying trend (predictable)
Regular 'seasonal' component (predicable)
Irregular random fluctuations (unpredictable)
Formula for the observed time series.
OTS = UT + SC + RC
Observed time series = underling trend + seasonal component + random component
Steps in time series analysis.
Identify underlying trend
Predict seasonal effects
Remove seasonal component (seasonal adjustment)
Make a future prediction
Define moving average.
A technique used to obtain an overall idea of the trend.
Represents the 'middle' of a data set.
Uses a small window of data which is 'moved' through the whole time series.
What should the size of a moving average be?
Each 'season' should be represented once in the average.
How to calculate a moving average.
Put a window over the required number of points.
Calculate the average.
Put the average in the middle of the window.
Slide window down one point.
Define seasonal index.
Used to predict the seasonal component.
Measure of the average effect of that season.
Average size of peaks compared to underlying trend.
An indicator of the measure of something.
How to make a prediction.
Smooth data using moving average to uncover trend.
Do a linear regression on trend.
Make a future prediction.
Add or take the appropriate amount to account for the seasonal component.
Purpose of seasonal adjustments.
Allows for future predictions
Accounts for effect of future
Used for future predictions or missing data
Formula for underlying trend/deseasonal adjustment.
DA = OD ÷ SI
Deseasonal adjustment = observed data ÷ seasonal index
Formula for seasonal adjustment.
SA = FP × SI
Seasonal adjustment = future prediction × seasonal index