Time Series study2

Time series decomposition

□ Moving averages

  - Trend-Cycle을 추정하는데 사용

  - MA의 차수는 smoothness를 결정함( m↑ → smoother)

  - MA of MA : 가운데 자료에 가중치를 더 준다.(smoother)

□ Classical decomposition

  - assumption : the seasonal component is constant from year to year.

    * seasonal indices : 계절지수

  - 더 나은 방법들이 있기에 잘 쓰이진 않음.

    1) trend-cycle : 양 끝으로 사라지는 값이 존재 + over-smooth rapid rises and falls in the data

    2) seasonal component가 매년 반복될 것을 가정 but 그렇지 않은 경우가 많음. → 긴 시간 변화에 따른 seasonal change를 포착하지 못함.

    3) not robust to unusual values

□ X11 decomposition

  - quarterly and monthly data

  - based on classical decomposition

  - 양 끝 값에 대한 추정이 가능 + seasonal component : vary slowly over time.

  - has some sophisticated methods for handling trading day variation, holiday effects and the effects of known predictors. 

  - is entirely automatic and tends to be highly robust to outliers and level shifts

□ SEATS decomposition

  : Seasonal Extraction in ARIMA Time Series

  - works only with quarterly and monthly data.

□ STL decomposition

    * versatile : 다재다능한

  - will handle any type of seasonality, not only monthly and quarterly data.

  - be controlled by the user(change over time, the rate of change, the smoothness of the trend-cycle)

  - It can be robust to outliers 

  - unusual obs가 trend-cycle, seasonal components의 추정에 영향을 미치지 않지만,

    remainder component에는 영향을 미친다.

  - does not handle trading day or calendar variation automatically

  ★ parameters

      1) trend-cycle window(t.window) : is the number of consecutive observations to be used 

                                                           when estimating the trend-cycle

      2) seasonal window(s.window) : is the number of consecutive years to be used in 

                                                         estimating each value in the seasonal component. / 디폴트X

      → control how rapidly the trend-cycle and seasonal components can change.(smaller → rapid changes)

           should be odd numbers!

< Exponential smoothing >

  - 예측은 과거 값들의 가중평균이며, 순서가 멀어질수록 가중치가 낮아진다.

□ Simple exponential smoothing

  - is suitable for forecasting data with no clear trend or seasonal pattern.

  - 과거의 데이터보다 현재와 가까울수록 가중치를 둔다.

  - smoothing parameter : alpha in [0,1]

□ Trend methods

  - Holt's linear trend method