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4307 - Forecasting Analytics - Coggle Diagram

- - - - Tidy (prep)
      - Plot (visualize)
      - Define model (specify)
      - train model (estimate)
      - check performance (evaluate)
      - Forecast
      - &. Visualize forecast
    - - naive: forecast = last value
      - seasonal naive = last value fr same season
      - drift method = seasonal, but take trend into consideration
    - - residuals = diff actual n forecast, yt based on y(t-1)
        
        gg_tsresiduals()
        function
      - y(t-1) = fitted value
      - good characteristics
        
        o corelation between them
        
        0 mean, or else biased
      - data training = use majority of past data as training, rest as test data to evaluate model
      - measure of accuracy (page 33)
        
        accuracy
      - Prediction interval
        
        hilo() converts into distribution
  - - - calendar
      - population
      - infliation
      - math
        
        box cox transformation
        
        tranform value using an equation, then forcast, then reverse the transformation (ex slide 17)
        
        a math transformation
    - - seasonal, trend, cycle
    - - simple moving method
        
        smooth data to reduce variation
        
        for example average of 5 years in a row
      - Additive decomposition/nultiplicative decomposition
      - Modern decomposition STL
        
        "Seasonal and Trend decomposition using Loess"
- - - - a controls level
        
        =0 -> never update (mean), =1 -> updates constantly (naive)
      - b controls flexibility
        
        0-> linear, 1-> changes every observation
      - y controls seasonality
        
        0 -> seasonality never update, 1 -> update completely
  - - - weights most recent obs = a and most recent forecast 1-a
      - 𝐹𝑡+1 = α𝑌𝑡 + 1 − α 𝐹𝑡
    - - extended single smoothing, model with trend
      - slide 25 w4
- - - - BASICALLY MESURES THE CHANGES
  - - - roughly horizontal
      - constant variance
      - no pattern
  - - - yt - y(t-1) = c+et
        
        might need 2nd diff
      - c is average changes
      - instead of -1 can -m to account for seasonal diff
        
        can apply both, no matter order
    - - Unit root tests
      - in this course, use KPSS
      - google_2018 %>% features(Close, unitroot_kpss)
      - backshift notation
        
        describe process of differecing, aka how many period go back
        
        A dth-order difference can be written (1-B)^d*yt
        
        first difference
    - - google_2018 %>% features(Close, unitroot_ndiffs)
      - ndiff=1 -> need 1 difference
  - - - multiple regression past errors as predictor, as opposed to using past values
      - diff than m.a.smoothing: smoothing is for detrend
  - - - use both past values and past errors
    - - p = order of autoregressive
      - d = degree of first differencing
      - q = order of moving average
      - could be represent as like (1,0,0)
    - - example: slide 41 w8, steps on slide 38
        
        Afircan, has trend, no chnaging variance
        
        Take first differencing
        
        look at pacf, choose the first line that crosses the blueline
  - - - its a technique
    - - manual way:L page 42 week 8 L the pacf leg of 4, so choose 4
      - automated: ARIMA()
    - - used to evaluate model accuracy, lower better
  - - - p,d,q = non seasonal
      - P,D,Q = seasonal, with m = period
        
        Q > 0 if q >0, also same for p
        
        Find P,D, Q by looking at the last significant spike IN SEASON (12, 24), as opposed to p,d,q in which look for small time frame