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Questions and Answers
What type of data does a Seasonal ARIMA model (SARIMA) primarily handle?
What type of data does a Seasonal ARIMA model (SARIMA) primarily handle?
In a SARIMA model represented as SARIMA(k, d, q)(K, D, Q)p, what does the parameter D represent?
In a SARIMA model represented as SARIMA(k, d, q)(K, D, Q)p, what does the parameter D represent?
Which of the following is a special case of SARIMA?
Which of the following is a special case of SARIMA?
What does the notation (1 - B) represent in the context of the SARIMA model?
What does the notation (1 - B) represent in the context of the SARIMA model?
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If a SARIMA model is specified as SARIMA(2, 1, 1)(1, 0, 1)p, which of the following indicates the order of the seasonal moving average component?
If a SARIMA model is specified as SARIMA(2, 1, 1)(1, 0, 1)p, which of the following indicates the order of the seasonal moving average component?
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In the equation for a seasonal ARIMA model, what role does the term εt play?
In the equation for a seasonal ARIMA model, what role does the term εt play?
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What is the primary benefit of using SARIMA models over standard ARIMA models?
What is the primary benefit of using SARIMA models over standard ARIMA models?
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Which test can be used to check for trends in time series data?
Which test can be used to check for trends in time series data?
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Which part of the SARIMA model is represented by the parameter p?
Which part of the SARIMA model is represented by the parameter p?
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In the context of seasonal unit root tests, what does HEGY stand for?
In the context of seasonal unit root tests, what does HEGY stand for?
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What is the rule of thumb for determining the order of seasonal differencing in SARIMA models?
What is the rule of thumb for determining the order of seasonal differencing in SARIMA models?
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Which models can be estimated using the ACF and PACF plots?
Which models can be estimated using the ACF and PACF plots?
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What does the SARIMA model notation SARIMA(p, d, q)(P, D, Q)m signify?
What does the SARIMA model notation SARIMA(p, d, q)(P, D, Q)m signify?
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What is typically used to identify SAR or SMA parameters in a SARIMA model?
What is typically used to identify SAR or SMA parameters in a SARIMA model?
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What does ndiffs() function do in R when applied to a time series object?
What does ndiffs() function do in R when applied to a time series object?
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What type of predictions does a SARIMA model provide?
What type of predictions does a SARIMA model provide?
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Study Notes
Forecasting - Seasonal ARIMA
- Course: DAT320
- Instructor: Kristian Hovde Liland
- Semester: Autumn 2024
- Institution: Norwegian University of Life Sciences
Extensions of ARIMA
- ARIMA models are extended to handle seasonal data and long-term dependencies
- SARIMA (Seasonal ARIMA)
- FARIMA (Fractional ARIMA)
- ARIMAX (ARIMA with exogenous inputs)
- VARIMA (Vector ARIMA)
Seasonal ARIMA (SARIMA) Model
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SARIMA(p,d,q)(P,D,Q)m models combine non-seasonal and seasonal components
- p: non-seasonal autoregressive order
- d: non-seasonal integration order
- q: non-seasonal moving average order
- P: seasonal autoregressive order
- D: seasonal integration order
- Q: seasonal moving average order
- m: seasonal period
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Special cases include SAR(P) and SMA(Q) for seasonal AR and MA components, respectively.
Multiplicative Combination of Terms in SARIMA(p,d,q)(P,D,Q)m
- The model's terms are multiplicatively combined
- AR(p) and SAR(P) terms
- Differencing terms (d and D)
- MA(q) and SMA(Q) terms
SARIMA Model (Graphical Representation)
- The model's structure is illustrated in a diagram depicting connections between time series observations, highlighting the lagged dependencies.
Seasonal Unit Root Test
- Used to identify the presence of trends and seasonality to determine the number of seasonal differences.
- Hylleberg-Engle-Granger-Yoo (HEGY) test is commonly used
Hyperparameter Selection Rule of Thumb for SARIMA
- Determine the appropriate differencing orders (d and D) using KPSS and HEGY tests.
- Visualize the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify AR and MA parameters.
- Use patterns of seasonal spikes in ACF and PACF to estimate SAR and SMA parameters.
FARIMA Model
- FARIMA (fractionally integrated ARIMA):
- Handles long-term dependencies
- Uses fractional difference order (d) (typically between -0.5 and 0.5)
- Fractional calculus is required to calculate these models.
ARCH & GARCH Model
- ARCH (Autoregressive Conditional Heteroscedasticity) models the error variance as an autoregressive process.
- GARCH (Generalized ARCH) models the error variance as an autoregressive moving average (ARMA) process.
- These models address volatility clustering.
R Code Examples
- Provides specific code snippets for implementing various models/tests/steps in R programming language using existing packages
- Includes functions like library(datasets), library(forecast), library(fGarch) and others.
- Examples are used for models such as ARIMA, SARIMA, FARIMA, ARCH, and GARCH applied to the "AirPassengers" and "EuStockMarkets" datasets.
Stationarity
- Key indicators of violations of stationarity include trends, seasonality, and non-constant variance (heteroscedasticity).
- Different stationarity tests like KPSS, HEGY, Brown-Forsythe, Levene and Bartlett are used to determine whether data are stationary.
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Description
This quiz covers the fundamentals of Seasonal ARIMA (SARIMA) models, including extensions like FARIMA and ARIMAX. Learn about the combination of non-seasonal and seasonal components in ARIMA models, and understand the terms and parameters used in SARIMA modeling. Perfect for students in the DAT320 course at the Norwegian University of Life Sciences.
