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Correlogram - ACF

Correlogram - ACF. Modeling for Forecast. The Base Model. Linear Trend. Data. Forecast. Logistic Growth. Others Models. Look for a best approximation of the truth. Forecasting Skill. Tools for Identifying a Best Model Review. Scatterplot and Correlation Coefficient - Review. Y.

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Correlogram - ACF

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  1. Correlogram - ACF

  2. Modeling for Forecast The Base Model Linear Trend Data Forecast Logistic Growth Others Models Look for a best approximation of the truth Forecasting Skill

  3. Tools for Identifying a Best ModelReview

  4. Scatterplot and Correlation Coefficient - Review Y X

  5. Correlogram as Model Identifier Timeplot Models That Work Correlogram

  6. Autocorrelation Coefficient • Definition: The correlation coefficient between Yt and Y(t-k) is called the autocorrelation coefficient at lag k and is denoted as rk . By definition, r0 = 1. • Autocorrelation of a Random Series: If the series is random, rk = 0 for k = 1,...

  7. Process Correlogram rk 1 0 Lag, k -1

  8. Sample Autocorrelation Coefficient Sample Autocorrelation at lag k.

  9. Standard Error of the Sample Autocorrelation Coefficient • Standard Error of the sample autocorrelation if the Series is Random.

  10. Z- Test of H0: rk = 0 Reject H0 if Z < -1.96 or Z > 1.96

  11. Test of Randomness Correlogram

  12. Box-Ljung Q Statistic • Definition

  13. Sampling Distribution of QBL(m) | H0 • H0 : r1=r2=…rk = 0 • QBL(m) | H0 follows a c2 (DF=m) distribution Reject H0 if QBL > c2(95%tile)

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