Correlogram - ACF. Modeling for Forecast Forecast Data The Base Model Linear Trend Logistic Growth Others Models Look for a best approximation of the.

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Presentation transcript:

Correlogram - ACF

Modeling for Forecast Forecast Data The Base Model Linear Trend 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 X

Correlogram as Model Identifier Timeplot Correlogram Models That Work

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

Process Correlogram Lag, k kk 1 

Sample Autocorrelation Coefficient Sample Autocorrelation at lag k.

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

Z- Test of H 0 :  k = 0 Reject H 0 if Z 1.96

Test of Randomness Correlogram

Box-Ljung Q Statistic Definition

Sampling Distribution of Q BL (m) | H 0 H 0 :  1 =  2 =…  k = 0 Q BL (m) | H 0 follows a  2 (DF=m) distribution Reject H 0 if Q BL >  2 (95%tile)