Case study 3: SEASONAL ARIMA MODEL

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Case study 3
SEASONAL ARIMA MODEL

• Average monthly temperatures in Dubuque, Iowa,
  January 1964 December 1975
• Reference Cryer 1986, pg. 268.

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Example 1 Average monthly temperatures in
Dubuque, Iowa (January 1964 December 1975)
Cryer 1986, pg. 268
Low temperature
Medium temperature
High temperature
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Example 1 IDENTIFICATION step stationary,
ACF and PACF
PACF
ACF
Nonstationer (seasonal) time series
Dies down slowly
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Example 1 IDENTIFICATION step Seasonal
Difference Zt Yt Yt-12
Zt ? MA(1)12 or Yt ? IMA(1,1)12
Stationary time series
ACF
PACF
Cuts off after lag 12
Dies down at seasonal lag
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Example 1 ESTIMATION and DIAGNOSTIC CHECK step

Yt Yt-12 at 0.8633 at-12
Estimation and Testing parameter
Diagnostic Check (white noise residual)
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Example 1 DIAGNOSTIC CHECK step Normality
test of residuals
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Example 1 FORECASTING step
MINITAB output
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Example 1 Comparison Actual v.s. Forecast
Forecast data
Upper
Actual data
Lower