9.1. Time Series Flashcards
Time series…
A sequence of observations on a variable measured at successive points in time.
The pattern of data is important in understanding how the time series has behaved in the past.
If such behaviour can be expected to continue in the future, we can use the past pattern to guide us in selecting an appropriate forecasting method.
Horizontal patterns…
Data fluctuates around a constant mean.
Stationary time series have statistical properties that are independent of time:
- The data has a constant mean.
- The variability of the time series is constant over time.
Stationary time series always exhibit a horizontal pattern; but a horizontal pattern doesn’t imply a stationary time series.
Trend patterns…
Movements to relatively higher or lower values over a period of time.
A trend is usually the result of long-term factors.
For example, the stock price of Mastercard Incorporated that has gradually increased over time.
Seasonal patterns…
Repeating patterns over successive periods of time.
For example, unemployment levels that follow similar patterns throughout the year, across many years.
Cyclical patterns…
Alternating sequences of points above and below the trend line, lasting more than one year.
Can be difficult to analyse.
Often combined with the trend-cycle effect.
Trend, seasonal and cyclical patterns are considered systematic components.
Random components…
Cannot be predicted.
These are the components after trend, seasonal and cyclical patterns have been considered.
Decomposing the time series…
Multiplicative method: Xt=TCS*R.
- Isolate the trend (smoothing).
- Isolate seasonal factors.
- Seasonal adjustments.
Isolate the trend (smoothing)…
Averages out short-term fluctuations in the dataset by creating averages of successive observations.
How much should be averaged?:
- Depends on the desired degree of smoothing of the data and the nature of the fluctuation.
- The longer the period of the moving average, the greater the smoothing.
- The longer the period of the moving average, the less the cycle is captured.
- If data is relatively consistent between time periods (like it is above), then a moving average is more appropriate.
We can also create a 12-month moving average (a trend), averaging figures for the entire year.
Isolating seasonal factors…
Take the multiplicative method and remove the cyclical component.
Xt=TSR (/T),
Xt/T=S*R.
This allows us to calculate a ratio, representing seasonal irregular values (=seasonal+random component).
The random components approximately cancel out, leaving just the seasonal component.
The seasonal factor is obtained by averaging the ratios from each respective month.
Seasonal adjustments…
Seasonal adjustments can be made.
Xt/S=TCR
Linear trend projection…
Yi=a+bXi (linear regression model).
We can model a linear trend:
Tt=a+bt .
(Where Tt refers to the trend value of a time series in period t).
Time series (no question)…
Please do examples on 9.1. Time Series.
