Lecture 4 Modelling Time Series Flashcards
Time Series Components
Trend: very long term, smooth
Seasonal: Pattern which repeat annually, may be a constant or variable. Can be predictable or stochastic. EG Gasoline consumption, employment
Cycle: Business cycle.
Deterministic vs Stochastic seasonality?
Seasonal Adjustment?
If seasonal pattern repeats year after year: deterministic and predictable. (dont use in some cases a constant in regression, eg january to dezember -> multicollinearity can appear.
If seasonal pattern roughly evolves over the years, stochastic and only partially predictable.
Most of the published data is seasonal adjusted.
Why use logs and first differences?
To make it linear –> interprete it as elasticity e.g. rGDP has not so an explosive growth
First differences for removing trend.
How to select break dates?
Judgemental, Visual inspection or formal data-based like least squares break data estimator (estimate regression for many possible breakdates)
Why use differencing?
Can help stabilize the mean of time series by removing changes in the level of a time series, and so eliminating the trend and seasonality.
ACF plot is also useful for identifying non stat. time series.
For stationary ACF will drop to zero quickly, otherwise not.
RW model?
y’t = delta yt = yt - yt-1 widely used for non stationary data. Has typically long periods of apparent trends up or down and sudden and unpredictable changes in direction.eg with a drift c, c>0 yt will trend upwards (average change is an increase in the value of yt)
Second order differencing
y’‘t , population and prices are integrated of order 2, in practice almost never necessary to go beyond second
What are seasonal differencing?
y’t = yt - yt-m +et also called lag m differences as we substract the observation after a lag of m periods.
What is unit root?
A linear stochastic process has a unit root, if 1 is a root of the process charact. equation. Such a process is nonstationary, but doesnt have always a trend.
HP filter?
y = T + C, T is constructed to minimize. The larger lambda, the greater the penalty and smoother the resulting trend (typically 1600 for quarterly data). … HP filtered GDP seems to fit better than linear model (Still not perfect (optimiert die Trendbeschreibung)
Production function has positive and decreasing marginal products for each factor that tend to zero, when the respective factor tends to infinity.
Good to know
Are time series with trend or seasonality stationary?
With cyclical?
No, stationary doesnt depend on time at which the series is observed. Time series with cyclic behavior is stationary.
Stationary process wont have predictable patterns in the long term (time plots will be roughly horizontal with constant variance)
