Econometrics II
Stochastic time series analysis – SARIMA models
Based on G ́abor Ruzsa’s slides
2022.04.21.
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Administrative issues
The deadline of the second individual homework is the 27th of April 11:55 pm (extended)
The third individual homework will be available on the 11th week (5th of May)
Group homework: discuss the problems/questions in connection with the data, deadline for the written analysis: 18th of May 11:55 pm (13th week), presentation on the 19th of May
2nd test on the 19th of May (13th week)
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Deterministic time series analysis Additive model
Multiplicative model Different types of trends Filtering/screening methods
Centered MA Not centered MA Exponential MA HP filter
Econometrics II – SARIMA
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Revision II
Stochastic time series analysis White Noise
Stationarity
AR(p), MA(q) and their stability ARMA(p,q) and ARIMA(p,d,q) Box-Jenkins methodology
Econometrics II – SARIMA
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Box-Jenkins methodology
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Dealing with stock prices: stock splits and other events
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Measuring the goodness of forecasts
Root Mean Square Error (RMSE):
∑ Tt = 1 ( y t − y ˆ t ) 2
Mean Absolute Percentage Error (MAPE): 1 T ∣y −yˆ∣
tt T t=1 yt
Econometrics II – SARIMA
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Measuring the goodness of forecasts: train vs test data
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SARMA models
We can include an AR and MA expression with the same lags as the frequency of the data to handle the seasonality
This leads to the SARMA(p,q)(P,Q)m models
p–simple AR order q–simple MA order P–seasonal AR order Q–seasonal MA order m–the frequency
Econometrics II – SARIMA
2022.04.21.
SARIMA models
We can use simple and seasonal differencing as well
We take the differences according to the seasonality (frequency) of the data
This leads to the SARIMA(p,d,q)(P,D,Q)m models
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Task for bonus points
You can choose one from two tasks and get 1 bonus point for it Details in the Moodle at Week 9
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Conclusion
Revision of the first half of the semester Box-Jenkins methodology
Forecasting and measuring the accuracy of forecasts SARMA and SARIMA models
Econometrics II – SARIMA
2022.04.21.
Thank You for Your attention!
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