Correlogram - ACF

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

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Process Correlogram
rk
1
0
Lag, k
-1
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Sample Autocorrelation Coefficient

• Sample Autocorrelation at lag k.

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Standard Error of the Sample Autocorrelation
Coefficient

• Standard Error of the sample autocorrelation
• if the Series is Random.

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Z- Test of H0 rk 0
Reject H0 if Z lt -1.96 or Z gt 1.96
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Test of Randomness Correlogram
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Box-Ljung Q Statistic

• Definition

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Sampling Distribution of QBL(m) H0

• H0 r1r2rk 0
• QBL(m) H0 follows a c2 (DFm) distribution
• Reject H0 if QBL gt c2(95tile)