Seasonal ARIMA Models and Forecasting Principles

Flashcards covering key concepts about Seasonal ARIMA models and their application in forecasting.

What does ARIMA stand for?

AutoRegressive Integrated Moving Average.

What does the seasonal component in an ARIMA model represent?

Seasonal patterns in time series data, captured by the seasonal part of the model (represented as (P,D,Q)m).

What is the general form of a seasonal ARIMA model?

ARIMA(p,d,q)(P,D,Q)m where m is the number of periods per season.

What is the form of the ARIMA(1,1,1)(1,1,1)4 model without a constant?

(1 - 1B)(1 - 1B4)(1 + θ1B)(1 + φ1B4)et.

What are the common ARIMA models used by the US Census Bureau?

ARIMA(0,1,1)(0,1,1)m, ARIMA(0,1,2)(0,1,1)m, ARIMA(2,1,0)(0,1,1)m, ARIMA(0,2,2)(0,1,1)m, and ARIMA(2,1,2)(0,1,1)m.

What does ACF stand for in the context of ARIMA models?

Autocorrelation Function.

What does PACF stand for in the context of ARIMA models?

Partial Autocorrelation Function.

What can you determine about ARIMA(0,0,0)(0,0,1)12 from its ACF and PACF?

ACF has a spike at lag 12; PACF shows exponential decay in seasonal lags.

In the context of ARIMA, what does a significant spike in the ACF suggest?

It suggests the presence of a non-seasonal or seasonal MA component.

What does adopting a Box-Cox transformation do in ARIMA modeling?

It stabilizes the variance in the time series data.

How does the AICc criterion assist in model selection?

Lower AICc values suggest a better-fitting model among competing models.

Which ARIMA model can be considered equivalent to Simple Exponential Smoothing?

ARIMA(0,1,1), where parameters are related to the smoothing coefficient.

What is one directive given for Lab Session 8?

Evaluate whether the selected time series data need transformation and assess for stationarity.