Stats II 6

15 flashcards · Other · by Daniel F.

  1. decomposition of time series data

  2. times series trend component

    Long-term increase or decrease over time (overall upward or downward movement) can be linear or nonlinear

  3. time series seasonal component

    Short-term, observed within a year Regular, wave-like patterns Often monthly or quarterly

  4. time series Cyclical component

    Long-term, length is usually more than one year Regular, wave-like patterns, may vary in length Often measured peak to peak

  5. time series irregular component

    Unpredictable, random, „residual" fluctuations Due to random variations of nature, accidents or unusual events „Noise" in the time-series It represents the residuals or remainder of the time series after the other components have been removed

  6. Moving averages

    The technique is used to get an overall impression of the pattern of movement over time Smooths out the irregular component A series of arithmetic means over time Periods can be odd or even length

  7. Seasonal Index Method

    estimate seasonal impact Assumption: stable seasonal pattern over time For any season the effect of seasonality increases or decreases the series by the same unit (additive model) the same percentage (multiplicative model) The seasonal index method uses the multiplicative model Steps Calculate 100 ⋅ Xt / X*t for each time period Find the median of all of the same-season values Adjust, so that the average over all seasons is 100 (* 100/mean)

  8. Exponential smoothing

    for smoothing and short term forecasting smooths unwanted cyclical and irregular components Weighted moving average Weights decline exponentially Most recent observation is weighted most The weight (smoothing coefficient) is Denoted by alpha Subjectively chosen between 0 and 1 Low value (closer to 0 ) — more smoothing Higher value (closer to 1) — less smoothing

  9. Autocorrelation

    Correlation of a signal with a delayed copy of itself, measuring the similarity between the original signal and its time-shifted version

  10. The Durbin-Watson test

  11. AR(p) processes

  12. Autoregressive Model

    Statistical model that explains the relationship between a dependent variable and its own lagged values

  13. Statistical model that explains the relationship between a dependent variable and its own lagged values

    Autoregressive model with p lags of the original variable

  14. White noise process

    In a white noise process each observation is uncorrelated with all other values in a sequence

  15. Testing for overall AR model significance

    Ljanh-Box Q H0: ρ1 = ρ2 = ... = ρp = 0 (no autocorrelation remaining lags) residuals exhibit white noise process H1: at least one ρi ≠ 0, i=1, ..., p (autocorrelation remaining lags)